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Avijeet is a Senior Research Analyst at Simplilearn. Passionate about Data Analytics, Machine Learning, and Deep Learning, Avijeet is also interested in politics, cricket, and football.
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What is hypothesis testing.
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
Attrition refers to participants leaving a study. It always happens to some extent—for example, in randomized controlled trials for medical research.
Differential attrition occurs when attrition or dropout rates differ systematically between the intervention and the control group . As a result, the characteristics of the participants who drop out differ from the characteristics of those who stay in the study. Because of this, study results may be biased .
Action research is conducted in order to solve a particular issue immediately, while case studies are often conducted over a longer period of time and focus more on observing and analyzing a particular ongoing phenomenon.
Action research is focused on solving a problem or informing individual and community-based knowledge in a way that impacts teaching, learning, and other related processes. It is less focused on contributing theoretical input, instead producing actionable input.
Action research is particularly popular with educators as a form of systematic inquiry because it prioritizes reflection and bridges the gap between theory and practice. Educators are able to simultaneously investigate an issue as they solve it, and the method is very iterative and flexible.
A cycle of inquiry is another name for action research . It is usually visualized in a spiral shape following a series of steps, such as “planning → acting → observing → reflecting.”
To make quantitative observations , you need to use instruments that are capable of measuring the quantity you want to observe. For example, you might use a ruler to measure the length of an object or a thermometer to measure its temperature.
Criterion validity and construct validity are both types of measurement validity . In other words, they both show you how accurately a method measures something.
While construct validity is the degree to which a test or other measurement method measures what it claims to measure, criterion validity is the degree to which a test can predictively (in the future) or concurrently (in the present) measure something.
Construct validity is often considered the overarching type of measurement validity . You need to have face validity , content validity , and criterion validity in order to achieve construct validity.
Convergent validity and discriminant validity are both subtypes of construct validity . Together, they help you evaluate whether a test measures the concept it was designed to measure.
You need to assess both in order to demonstrate construct validity. Neither one alone is sufficient for establishing construct validity.
Content validity shows you how accurately a test or other measurement method taps into the various aspects of the specific construct you are researching.
In other words, it helps you answer the question: “does the test measure all aspects of the construct I want to measure?” If it does, then the test has high content validity.
The higher the content validity, the more accurate the measurement of the construct.
If the test fails to include parts of the construct, or irrelevant parts are included, the validity of the instrument is threatened, which brings your results into question.
Face validity and content validity are similar in that they both evaluate how suitable the content of a test is. The difference is that face validity is subjective, and assesses content at surface level.
When a test has strong face validity, anyone would agree that the test’s questions appear to measure what they are intended to measure.
For example, looking at a 4th grade math test consisting of problems in which students have to add and multiply, most people would agree that it has strong face validity (i.e., it looks like a math test).
On the other hand, content validity evaluates how well a test represents all the aspects of a topic. Assessing content validity is more systematic and relies on expert evaluation. of each question, analyzing whether each one covers the aspects that the test was designed to cover.
A 4th grade math test would have high content validity if it covered all the skills taught in that grade. Experts(in this case, math teachers), would have to evaluate the content validity by comparing the test to the learning objectives.
Snowball sampling is a non-probability sampling method . Unlike probability sampling (which involves some form of random selection ), the initial individuals selected to be studied are the ones who recruit new participants.
Because not every member of the target population has an equal chance of being recruited into the sample, selection in snowball sampling is non-random.
Snowball sampling is a non-probability sampling method , where there is not an equal chance for every member of the population to be included in the sample .
This means that you cannot use inferential statistics and make generalizations —often the goal of quantitative research . As such, a snowball sample is not representative of the target population and is usually a better fit for qualitative research .
Snowball sampling relies on the use of referrals. Here, the researcher recruits one or more initial participants, who then recruit the next ones.
Participants share similar characteristics and/or know each other. Because of this, not every member of the population has an equal chance of being included in the sample, giving rise to sampling bias .
Snowball sampling is best used in the following cases:
The reproducibility and replicability of a study can be ensured by writing a transparent, detailed method section and using clear, unambiguous language.
Reproducibility and replicability are related terms.
Stratified sampling and quota sampling both involve dividing the population into subgroups and selecting units from each subgroup. The purpose in both cases is to select a representative sample and/or to allow comparisons between subgroups.
The main difference is that in stratified sampling, you draw a random sample from each subgroup ( probability sampling ). In quota sampling you select a predetermined number or proportion of units, in a non-random manner ( non-probability sampling ).
Purposive and convenience sampling are both sampling methods that are typically used in qualitative data collection.
A convenience sample is drawn from a source that is conveniently accessible to the researcher. Convenience sampling does not distinguish characteristics among the participants. On the other hand, purposive sampling focuses on selecting participants possessing characteristics associated with the research study.
The findings of studies based on either convenience or purposive sampling can only be generalized to the (sub)population from which the sample is drawn, and not to the entire population.
Random sampling or probability sampling is based on random selection. This means that each unit has an equal chance (i.e., equal probability) of being included in the sample.
On the other hand, convenience sampling involves stopping people at random, which means that not everyone has an equal chance of being selected depending on the place, time, or day you are collecting your data.
Convenience sampling and quota sampling are both non-probability sampling methods. They both use non-random criteria like availability, geographical proximity, or expert knowledge to recruit study participants.
However, in convenience sampling, you continue to sample units or cases until you reach the required sample size.
In quota sampling, you first need to divide your population of interest into subgroups (strata) and estimate their proportions (quota) in the population. Then you can start your data collection, using convenience sampling to recruit participants, until the proportions in each subgroup coincide with the estimated proportions in the population.
A sampling frame is a list of every member in the entire population . It is important that the sampling frame is as complete as possible, so that your sample accurately reflects your population.
Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous , so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous , as units share characteristics.
Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population .
A systematic review is secondary research because it uses existing research. You don’t collect new data yourself.
The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .
An observational study is a great choice for you if your research question is based purely on observations. If there are ethical, logistical, or practical concerns that prevent you from conducting a traditional experiment , an observational study may be a good choice. In an observational study, there is no interference or manipulation of the research subjects, as well as no control or treatment groups .
It’s often best to ask a variety of people to review your measurements. You can ask experts, such as other researchers, or laypeople, such as potential participants, to judge the face validity of tests.
While experts have a deep understanding of research methods , the people you’re studying can provide you with valuable insights you may have missed otherwise.
Face validity is important because it’s a simple first step to measuring the overall validity of a test or technique. It’s a relatively intuitive, quick, and easy way to start checking whether a new measure seems useful at first glance.
Good face validity means that anyone who reviews your measure says that it seems to be measuring what it’s supposed to. With poor face validity, someone reviewing your measure may be left confused about what you’re measuring and why you’re using this method.
Face validity is about whether a test appears to measure what it’s supposed to measure. This type of validity is concerned with whether a measure seems relevant and appropriate for what it’s assessing only on the surface.
Statistical analyses are often applied to test validity with data from your measures. You test convergent validity and discriminant validity with correlations to see if results from your test are positively or negatively related to those of other established tests.
You can also use regression analyses to assess whether your measure is actually predictive of outcomes that you expect it to predict theoretically. A regression analysis that supports your expectations strengthens your claim of construct validity .
When designing or evaluating a measure, construct validity helps you ensure you’re actually measuring the construct you’re interested in. If you don’t have construct validity, you may inadvertently measure unrelated or distinct constructs and lose precision in your research.
Construct validity is often considered the overarching type of measurement validity , because it covers all of the other types. You need to have face validity , content validity , and criterion validity to achieve construct validity.
Construct validity is about how well a test measures the concept it was designed to evaluate. It’s one of four types of measurement validity , which includes construct validity, face validity , and criterion validity.
There are two subtypes of construct validity.
Naturalistic observation is a valuable tool because of its flexibility, external validity , and suitability for topics that can’t be studied in a lab setting.
The downsides of naturalistic observation include its lack of scientific control , ethical considerations , and potential for bias from observers and subjects.
Naturalistic observation is a qualitative research method where you record the behaviors of your research subjects in real world settings. You avoid interfering or influencing anything in a naturalistic observation.
You can think of naturalistic observation as “people watching” with a purpose.
A dependent variable is what changes as a result of the independent variable manipulation in experiments . It’s what you’re interested in measuring, and it “depends” on your independent variable.
In statistics, dependent variables are also called:
An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.
Independent variables are also called:
As a rule of thumb, questions related to thoughts, beliefs, and feelings work well in focus groups. Take your time formulating strong questions, paying special attention to phrasing. Be careful to avoid leading questions , which can bias your responses.
Overall, your focus group questions should be:
A structured interview is a data collection method that relies on asking questions in a set order to collect data on a topic. They are often quantitative in nature. Structured interviews are best used when:
More flexible interview options include semi-structured interviews , unstructured interviews , and focus groups .
Social desirability bias is the tendency for interview participants to give responses that will be viewed favorably by the interviewer or other participants. It occurs in all types of interviews and surveys , but is most common in semi-structured interviews , unstructured interviews , and focus groups .
Social desirability bias can be mitigated by ensuring participants feel at ease and comfortable sharing their views. Make sure to pay attention to your own body language and any physical or verbal cues, such as nodding or widening your eyes.
This type of bias can also occur in observations if the participants know they’re being observed. They might alter their behavior accordingly.
The interviewer effect is a type of bias that emerges when a characteristic of an interviewer (race, age, gender identity, etc.) influences the responses given by the interviewee.
There is a risk of an interviewer effect in all types of interviews , but it can be mitigated by writing really high-quality interview questions.
A semi-structured interview is a blend of structured and unstructured types of interviews. Semi-structured interviews are best used when:
An unstructured interview is the most flexible type of interview, but it is not always the best fit for your research topic.
Unstructured interviews are best used when:
The four most common types of interviews are:
Deductive reasoning is commonly used in scientific research, and it’s especially associated with quantitative research .
In research, you might have come across something called the hypothetico-deductive method . It’s the scientific method of testing hypotheses to check whether your predictions are substantiated by real-world data.
Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.
Deductive reasoning is also called deductive logic.
There are many different types of inductive reasoning that people use formally or informally.
Here are a few common types:
Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.
Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.
In inductive research , you start by making observations or gathering data. Then, you take a broad scan of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.
Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.
Inductive reasoning is also called inductive logic or bottom-up reasoning.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.
A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Triangulation can help:
But triangulation can also pose problems:
There are four main types of triangulation :
Many academic fields use peer review , largely to determine whether a manuscript is suitable for publication. Peer review enhances the credibility of the published manuscript.
However, peer review is also common in non-academic settings. The United Nations, the European Union, and many individual nations use peer review to evaluate grant applications. It is also widely used in medical and health-related fields as a teaching or quality-of-care measure.
Peer assessment is often used in the classroom as a pedagogical tool. Both receiving feedback and providing it are thought to enhance the learning process, helping students think critically and collaboratively.
Peer review can stop obviously problematic, falsified, or otherwise untrustworthy research from being published. It also represents an excellent opportunity to get feedback from renowned experts in your field. It acts as a first defense, helping you ensure your argument is clear and that there are no gaps, vague terms, or unanswered questions for readers who weren’t involved in the research process.
Peer-reviewed articles are considered a highly credible source due to this stringent process they go through before publication.
In general, the peer review process follows the following steps:
Exploratory research is often used when the issue you’re studying is new or when the data collection process is challenging for some reason.
You can use exploratory research if you have a general idea or a specific question that you want to study but there is no preexisting knowledge or paradigm with which to study it.
Exploratory research is a methodology approach that explores research questions that have not previously been studied in depth. It is often used when the issue you’re studying is new, or the data collection process is challenging in some way.
Explanatory research is used to investigate how or why a phenomenon occurs. Therefore, this type of research is often one of the first stages in the research process , serving as a jumping-off point for future research.
Exploratory research aims to explore the main aspects of an under-researched problem, while explanatory research aims to explain the causes and consequences of a well-defined problem.
Explanatory research is a research method used to investigate how or why something occurs when only a small amount of information is available pertaining to that topic. It can help you increase your understanding of a given topic.
Clean data are valid, accurate, complete, consistent, unique, and uniform. Dirty data include inconsistencies and errors.
Dirty data can come from any part of the research process, including poor research design , inappropriate measurement materials, or flawed data entry.
Data cleaning takes place between data collection and data analyses. But you can use some methods even before collecting data.
For clean data, you should start by designing measures that collect valid data. Data validation at the time of data entry or collection helps you minimize the amount of data cleaning you’ll need to do.
After data collection, you can use data standardization and data transformation to clean your data. You’ll also deal with any missing values, outliers, and duplicate values.
Every dataset requires different techniques to clean dirty data , but you need to address these issues in a systematic way. You focus on finding and resolving data points that don’t agree or fit with the rest of your dataset.
These data might be missing values, outliers, duplicate values, incorrectly formatted, or irrelevant. You’ll start with screening and diagnosing your data. Then, you’ll often standardize and accept or remove data to make your dataset consistent and valid.
Data cleaning is necessary for valid and appropriate analyses. Dirty data contain inconsistencies or errors , but cleaning your data helps you minimize or resolve these.
Without data cleaning, you could end up with a Type I or II error in your conclusion. These types of erroneous conclusions can be practically significant with important consequences, because they lead to misplaced investments or missed opportunities.
Data cleaning involves spotting and resolving potential data inconsistencies or errors to improve your data quality. An error is any value (e.g., recorded weight) that doesn’t reflect the true value (e.g., actual weight) of something that’s being measured.
In this process, you review, analyze, detect, modify, or remove “dirty” data to make your dataset “clean.” Data cleaning is also called data cleansing or data scrubbing.
Research misconduct means making up or falsifying data, manipulating data analyses, or misrepresenting results in research reports. It’s a form of academic fraud.
These actions are committed intentionally and can have serious consequences; research misconduct is not a simple mistake or a point of disagreement but a serious ethical failure.
Anonymity means you don’t know who the participants are, while confidentiality means you know who they are but remove identifying information from your research report. Both are important ethical considerations .
You can only guarantee anonymity by not collecting any personally identifying information—for example, names, phone numbers, email addresses, IP addresses, physical characteristics, photos, or videos.
You can keep data confidential by using aggregate information in your research report, so that you only refer to groups of participants rather than individuals.
Research ethics matter for scientific integrity, human rights and dignity, and collaboration between science and society. These principles make sure that participation in studies is voluntary, informed, and safe.
Ethical considerations in research are a set of principles that guide your research designs and practices. These principles include voluntary participation, informed consent, anonymity, confidentiality, potential for harm, and results communication.
Scientists and researchers must always adhere to a certain code of conduct when collecting data from others .
These considerations protect the rights of research participants, enhance research validity , and maintain scientific integrity.
In multistage sampling , you can use probability or non-probability sampling methods .
For a probability sample, you have to conduct probability sampling at every stage.
You can mix it up by using simple random sampling , systematic sampling , or stratified sampling to select units at different stages, depending on what is applicable and relevant to your study.
Multistage sampling can simplify data collection when you have large, geographically spread samples, and you can obtain a probability sample without a complete sampling frame.
But multistage sampling may not lead to a representative sample, and larger samples are needed for multistage samples to achieve the statistical properties of simple random samples .
These are four of the most common mixed methods designs :
Triangulation in research means using multiple datasets, methods, theories and/or investigators to address a research question. It’s a research strategy that can help you enhance the validity and credibility of your findings.
Triangulation is mainly used in qualitative research , but it’s also commonly applied in quantitative research . Mixed methods research always uses triangulation.
In multistage sampling , or multistage cluster sampling, you draw a sample from a population using smaller and smaller groups at each stage.
This method is often used to collect data from a large, geographically spread group of people in national surveys, for example. You take advantage of hierarchical groupings (e.g., from state to city to neighborhood) to create a sample that’s less expensive and time-consuming to collect data from.
No, the steepness or slope of the line isn’t related to the correlation coefficient value. The correlation coefficient only tells you how closely your data fit on a line, so two datasets with the same correlation coefficient can have very different slopes.
To find the slope of the line, you’ll need to perform a regression analysis .
Correlation coefficients always range between -1 and 1.
The sign of the coefficient tells you the direction of the relationship: a positive value means the variables change together in the same direction, while a negative value means they change together in opposite directions.
The absolute value of a number is equal to the number without its sign. The absolute value of a correlation coefficient tells you the magnitude of the correlation: the greater the absolute value, the stronger the correlation.
These are the assumptions your data must meet if you want to use Pearson’s r :
Quantitative research designs can be divided into two main categories:
Qualitative research designs tend to be more flexible. Common types of qualitative design include case study , ethnography , and grounded theory designs.
A well-planned research design helps ensure that your methods match your research aims, that you collect high-quality data, and that you use the right kind of analysis to answer your questions, utilizing credible sources . This allows you to draw valid , trustworthy conclusions.
The priorities of a research design can vary depending on the field, but you usually have to specify:
A research design is a strategy for answering your research question . It defines your overall approach and determines how you will collect and analyze data.
Questionnaires can be self-administered or researcher-administered.
Self-administered questionnaires can be delivered online or in paper-and-pen formats, in person or through mail. All questions are standardized so that all respondents receive the same questions with identical wording.
Researcher-administered questionnaires are interviews that take place by phone, in-person, or online between researchers and respondents. You can gain deeper insights by clarifying questions for respondents or asking follow-up questions.
You can organize the questions logically, with a clear progression from simple to complex, or randomly between respondents. A logical flow helps respondents process the questionnaire easier and quicker, but it may lead to bias. Randomization can minimize the bias from order effects.
Closed-ended, or restricted-choice, questions offer respondents a fixed set of choices to select from. These questions are easier to answer quickly.
Open-ended or long-form questions allow respondents to answer in their own words. Because there are no restrictions on their choices, respondents can answer in ways that researchers may not have otherwise considered.
A questionnaire is a data collection tool or instrument, while a survey is an overarching research method that involves collecting and analyzing data from people using questionnaires.
The third variable and directionality problems are two main reasons why correlation isn’t causation .
The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not.
The directionality problem is when two variables correlate and might actually have a causal relationship, but it’s impossible to conclude which variable causes changes in the other.
Correlation describes an association between variables : when one variable changes, so does the other. A correlation is a statistical indicator of the relationship between variables.
Causation means that changes in one variable brings about changes in the other (i.e., there is a cause-and-effect relationship between variables). The two variables are correlated with each other, and there’s also a causal link between them.
While causation and correlation can exist simultaneously, correlation does not imply causation. In other words, correlation is simply a relationship where A relates to B—but A doesn’t necessarily cause B to happen (or vice versa). Mistaking correlation for causation is a common error and can lead to false cause fallacy .
Controlled experiments establish causality, whereas correlational studies only show associations between variables.
In general, correlational research is high in external validity while experimental research is high in internal validity .
A correlation is usually tested for two variables at a time, but you can test correlations between three or more variables.
A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.
Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions . The Pearson product-moment correlation coefficient (Pearson’s r ) is commonly used to assess a linear relationship between two quantitative variables.
A correlational research design investigates relationships between two variables (or more) without the researcher controlling or manipulating any of them. It’s a non-experimental type of quantitative research .
A correlation reflects the strength and/or direction of the association between two or more variables.
Random error is almost always present in scientific studies, even in highly controlled settings. While you can’t eradicate it completely, you can reduce random error by taking repeated measurements, using a large sample, and controlling extraneous variables .
You can avoid systematic error through careful design of your sampling , data collection , and analysis procedures. For example, use triangulation to measure your variables using multiple methods; regularly calibrate instruments or procedures; use random sampling and random assignment ; and apply masking (blinding) where possible.
Systematic error is generally a bigger problem in research.
With random error, multiple measurements will tend to cluster around the true value. When you’re collecting data from a large sample , the errors in different directions will cancel each other out.
Systematic errors are much more problematic because they can skew your data away from the true value. This can lead you to false conclusions ( Type I and II errors ) about the relationship between the variables you’re studying.
Random and systematic error are two types of measurement error.
Random error is a chance difference between the observed and true values of something (e.g., a researcher misreading a weighing scale records an incorrect measurement).
Systematic error is a consistent or proportional difference between the observed and true values of something (e.g., a miscalibrated scale consistently records weights as higher than they actually are).
On graphs, the explanatory variable is conventionally placed on the x-axis, while the response variable is placed on the y-axis.
The term “ explanatory variable ” is sometimes preferred over “ independent variable ” because, in real world contexts, independent variables are often influenced by other variables. This means they aren’t totally independent.
Multiple independent variables may also be correlated with each other, so “explanatory variables” is a more appropriate term.
The difference between explanatory and response variables is simple:
In a controlled experiment , all extraneous variables are held constant so that they can’t influence the results. Controlled experiments require:
Depending on your study topic, there are various other methods of controlling variables .
There are 4 main types of extraneous variables :
An extraneous variable is any variable that you’re not investigating that can potentially affect the dependent variable of your research study.
A confounding variable is a type of extraneous variable that not only affects the dependent variable, but is also related to the independent variable.
In a factorial design, multiple independent variables are tested.
If you test two variables, each level of one independent variable is combined with each level of the other independent variable to create different conditions.
Within-subjects designs have many potential threats to internal validity , but they are also very statistically powerful .
Advantages:
Disadvantages:
While a between-subjects design has fewer threats to internal validity , it also requires more participants for high statistical power than a within-subjects design .
Yes. Between-subjects and within-subjects designs can be combined in a single study when you have two or more independent variables (a factorial design). In a mixed factorial design, one variable is altered between subjects and another is altered within subjects.
In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.
In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.
The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.
Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.
In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.
To implement random assignment , assign a unique number to every member of your study’s sample .
Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a dice to randomly assign participants to groups.
Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.
In contrast, random assignment is a way of sorting the sample into control and experimental groups.
Random sampling enhances the external validity or generalizability of your results, while random assignment improves the internal validity of your study.
In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.
“Controlling for a variable” means measuring extraneous variables and accounting for them statistically to remove their effects on other variables.
Researchers often model control variable data along with independent and dependent variable data in regression analyses and ANCOVAs . That way, you can isolate the control variable’s effects from the relationship between the variables of interest.
Control variables help you establish a correlational or causal relationship between variables by enhancing internal validity .
If you don’t control relevant extraneous variables , they may influence the outcomes of your study, and you may not be able to demonstrate that your results are really an effect of your independent variable .
A control variable is any variable that’s held constant in a research study. It’s not a variable of interest in the study, but it’s controlled because it could influence the outcomes.
Including mediators and moderators in your research helps you go beyond studying a simple relationship between two variables for a fuller picture of the real world. They are important to consider when studying complex correlational or causal relationships.
Mediators are part of the causal pathway of an effect, and they tell you how or why an effect takes place. Moderators usually help you judge the external validity of your study by identifying the limitations of when the relationship between variables holds.
If something is a mediating variable :
A confounder is a third variable that affects variables of interest and makes them seem related when they are not. In contrast, a mediator is the mechanism of a relationship between two variables: it explains the process by which they are related.
A mediator variable explains the process through which two variables are related, while a moderator variable affects the strength and direction of that relationship.
There are three key steps in systematic sampling :
Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval – for example, by selecting every 15th person on a list of the population. If the population is in a random order, this can imitate the benefits of simple random sampling .
Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.
For example, if you were stratifying by location with three subgroups (urban, rural, or suburban) and marital status with five subgroups (single, divorced, widowed, married, or partnered), you would have 3 x 5 = 15 subgroups.
You should use stratified sampling when your sample can be divided into mutually exclusive and exhaustive subgroups that you believe will take on different mean values for the variable that you’re studying.
Using stratified sampling will allow you to obtain more precise (with lower variance ) statistical estimates of whatever you are trying to measure.
For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race. Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.
In stratified sampling , researchers divide subjects into subgroups called strata based on characteristics that they share (e.g., race, gender, educational attainment).
Once divided, each subgroup is randomly sampled using another probability sampling method.
Cluster sampling is more time- and cost-efficient than other probability sampling methods , particularly when it comes to large samples spread across a wide geographical area.
However, it provides less statistical certainty than other methods, such as simple random sampling , because it is difficult to ensure that your clusters properly represent the population as a whole.
There are three types of cluster sampling : single-stage, double-stage and multi-stage clustering. In all three types, you first divide the population into clusters, then randomly select clusters for use in your sample.
Cluster sampling is a probability sampling method in which you divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as your sample.
The clusters should ideally each be mini-representations of the population as a whole.
If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity . However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,
If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.
The American Community Survey is an example of simple random sampling . In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.
Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population . Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset.
Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment .
Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity as they can use real-world interventions instead of artificial laboratory settings.
A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference with a true experiment is that the groups are not randomly assigned.
Blinding is important to reduce research bias (e.g., observer bias , demand characteristics ) and ensure a study’s internal validity .
If participants know whether they are in a control or treatment group , they may adjust their behavior in ways that affect the outcome that researchers are trying to measure. If the people administering the treatment are aware of group assignment, they may treat participants differently and thus directly or indirectly influence the final results.
Blinding means hiding who is assigned to the treatment group and who is assigned to the control group in an experiment .
A true experiment (a.k.a. a controlled experiment) always includes at least one control group that doesn’t receive the experimental treatment.
However, some experiments use a within-subjects design to test treatments without a control group. In these designs, you usually compare one group’s outcomes before and after a treatment (instead of comparing outcomes between different groups).
For strong internal validity , it’s usually best to include a control group if possible. Without a control group, it’s harder to be certain that the outcome was caused by the experimental treatment and not by other variables.
An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.
Individual Likert-type questions are generally considered ordinal data , because the items have clear rank order, but don’t have an even distribution.
Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.
The type of data determines what statistical tests you should use to analyze your data.
A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviors. It is made up of 4 or more questions that measure a single attitude or trait when response scores are combined.
To use a Likert scale in a survey , you present participants with Likert-type questions or statements, and a continuum of items, usually with 5 or 7 possible responses, to capture their degree of agreement.
In scientific research, concepts are the abstract ideas or phenomena that are being studied (e.g., educational achievement). Variables are properties or characteristics of the concept (e.g., performance at school), while indicators are ways of measuring or quantifying variables (e.g., yearly grade reports).
The process of turning abstract concepts into measurable variables and indicators is called operationalization .
There are various approaches to qualitative data analysis , but they all share five steps in common:
The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis , thematic analysis , and discourse analysis .
There are five common approaches to qualitative research :
Operationalization means turning abstract conceptual ideas into measurable observations.
For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.
Before collecting data , it’s important to consider how you will operationalize the variables that you want to measure.
When conducting research, collecting original data has significant advantages:
However, there are also some drawbacks: data collection can be time-consuming, labor-intensive and expensive. In some cases, it’s more efficient to use secondary data that has already been collected by someone else, but the data might be less reliable.
Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.
There are several methods you can use to decrease the impact of confounding variables on your research: restriction, matching, statistical control and randomization.
In restriction , you restrict your sample by only including certain subjects that have the same values of potential confounding variables.
In matching , you match each of the subjects in your treatment group with a counterpart in the comparison group. The matched subjects have the same values on any potential confounding variables, and only differ in the independent variable .
In statistical control , you include potential confounders as variables in your regression .
In randomization , you randomly assign the treatment (or independent variable) in your study to a sufficiently large number of subjects, which allows you to control for all potential confounding variables.
A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause , while the dependent variable is the supposed effect . A confounding variable is a third variable that influences both the independent and dependent variables.
Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.
To ensure the internal validity of your research, you must consider the impact of confounding variables. If you fail to account for them, you might over- or underestimate the causal relationship between your independent and dependent variables , or even find a causal relationship where none exists.
Yes, but including more than one of either type requires multiple research questions .
For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.
You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable .
To ensure the internal validity of an experiment , you should only change one independent variable at a time.
No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!
You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment .
Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.
In non-probability sampling , the sample is selected based on non-random criteria, and not every member of the population has a chance of being included.
Common non-probability sampling methods include convenience sampling , voluntary response sampling, purposive sampling , snowball sampling, and quota sampling .
Probability sampling means that every member of the target population has a known chance of being included in the sample.
Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling .
Using careful research design and sampling procedures can help you avoid sampling bias . Oversampling can be used to correct undercoverage bias .
Some common types of sampling bias include self-selection bias , nonresponse bias , undercoverage bias , survivorship bias , pre-screening or advertising bias, and healthy user bias.
Sampling bias is a threat to external validity – it limits the generalizability of your findings to a broader group of people.
A sampling error is the difference between a population parameter and a sample statistic .
A statistic refers to measures about the sample , while a parameter refers to measures about the population .
Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.
Samples are used to make inferences about populations . Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.
There are seven threats to external validity : selection bias , history, experimenter effect, Hawthorne effect , testing effect, aptitude-treatment and situation effect.
The two types of external validity are population validity (whether you can generalize to other groups of people) and ecological validity (whether you can generalize to other situations and settings).
The external validity of a study is the extent to which you can generalize your findings to different groups of people, situations, and measures.
Cross-sectional studies cannot establish a cause-and-effect relationship or analyze behavior over a period of time. To investigate cause and effect, you need to do a longitudinal study or an experimental study .
Cross-sectional studies are less expensive and time-consuming than many other types of study. They can provide useful insights into a population’s characteristics and identify correlations for further research.
Sometimes only cross-sectional data is available for analysis; other times your research question may only require a cross-sectional study to answer it.
Longitudinal studies can last anywhere from weeks to decades, although they tend to be at least a year long.
The 1970 British Cohort Study , which has collected data on the lives of 17,000 Brits since their births in 1970, is one well-known example of a longitudinal study .
Longitudinal studies are better to establish the correct sequence of events, identify changes over time, and provide insight into cause-and-effect relationships, but they also tend to be more expensive and time-consuming than other types of studies.
Longitudinal studies and cross-sectional studies are two different types of research design . In a cross-sectional study you collect data from a population at a specific point in time; in a longitudinal study you repeatedly collect data from the same sample over an extended period of time.
Longitudinal study | Cross-sectional study |
---|---|
observations | Observations at a in time |
Observes the multiple times | Observes (a “cross-section”) in the population |
Follows in participants over time | Provides of society at a given point |
There are eight threats to internal validity : history, maturation, instrumentation, testing, selection bias , regression to the mean, social interaction and attrition .
Internal validity is the extent to which you can be confident that a cause-and-effect relationship established in a study cannot be explained by other factors.
In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .
The research methods you use depend on the type of data you need to answer your research question .
A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.
A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.
In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.
Discrete and continuous variables are two types of quantitative variables :
Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).
Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).
You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .
You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect .
In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:
Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design .
Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:
When designing the experiment, you decide:
Experimental design is essential to the internal and external validity of your experiment.
I nternal validity is the degree of confidence that the causal relationship you are testing is not influenced by other factors or variables .
External validity is the extent to which your results can be generalized to other contexts.
The validity of your experiment depends on your experimental design .
Reliability and validity are both about how well a method measures something:
If you are doing experimental research, you also have to consider the internal and external validity of your experiment.
A sample is a subset of individuals from a larger population . Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.
In statistics, sampling allows you to test a hypothesis about the characteristics of a population.
Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.
Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.
Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.
Methods are the specific tools and procedures you use to collect and analyze data (for example, experiments, surveys , and statistical tests ).
In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .
In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.
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A hypothesis test is a procedure used in statistics to assess whether a particular viewpoint is likely to be true. They follow a strict protocol, and they generate a ‘ p- value’, on the basis of which a decision is made about the truth of the hypothesis under investigation. All of the routine statistical ‘tests’ used in research— t- tests, χ 2 tests, Mann–Whitney tests, etc.—are all hypothesis tests, and in spite of their differences they are all used in essentially the same way. But why do we use them at all?
Comparing the heights of two individuals is easy: we can measure their height in a standardised way and compare them. When we want to compare the heights of two small well-defined groups (for example two groups of children), we need to use a summary statistic that we can calculate for each group. Such summaries (means, medians, etc.) form the basis of descriptive statistics, and are well described elsewhere. 1 However, a problem arises when we try to compare very large groups or populations: it may be impractical or even impossible to take a measurement from everyone in the population, and by the time you do so, the population itself will have changed. A similar problem arises when we try to describe the effects of drugs—for example by how much on average does a particular vasopressor increase MAP?
To solve this problem, we use random samples to estimate values for populations. By convention, the values we calculate from samples are referred to as statistics and denoted by Latin letters ( x ¯ for sample mean; SD for sample standard deviation) while the unknown population values are called parameters , and denoted by Greek letters (μ for population mean, σ for population standard deviation).
Inferential statistics describes the methods we use to estimate population parameters from random samples; how we can quantify the level of inaccuracy in a sample statistic; and how we can go on to use these estimates to compare populations.
There are many reasons why a sample may give an inaccurate picture of the population it represents: it may be biased, it may not be big enough, and it may not be truly random. However, even if we have been careful to avoid these pitfalls, there is an inherent difference between the sample and the population at large. To illustrate this, let us imagine that the actual average height of males in London is 174 cm. If I were to sample 100 male Londoners and take a mean of their heights, I would be very unlikely to get exactly 174 cm. Furthermore, if somebody else were to perform the same exercise, it would be unlikely that they would get the same answer as I did. The sample mean is different each time it is taken, and the way it differs from the actual mean of the population is described by the standard error of the mean (standard error, or SEM ). The standard error is larger if there is a lot of variation in the population, and becomes smaller as the sample size increases. It is calculated thus:
where SD is the sample standard deviation, and n is the sample size.
As errors are normally distributed, we can use this to estimate a 95% confidence interval on our sample mean as follows:
We can interpret this as meaning ‘We are 95% confident that the actual mean is within this range.’
Some confusion arises at this point between the SD and the standard error. The SD is a measure of variation in the sample. The range x ¯ ± ( 1.96 × SD ) will normally contain 95% of all your data. It can be used to illustrate the spread of the data and shows what values are likely. In contrast, standard error tells you about the precision of the mean and is used to calculate confidence intervals.
One straightforward way to compare two samples is to use confidence intervals. If we calculate the mean height of two groups and find that the 95% confidence intervals do not overlap, this can be taken as evidence of a difference between the two means. This method of statistical inference is reasonably intuitive and can be used in many situations. 2 Many journals, however, prefer to report inferential statistics using p -values.
In 1925, the British statistician R.A. Fisher described a technique for comparing groups using a null hypothesis , a method which has dominated statistical comparison ever since. The technique itself is rather straightforward, but often gets lost in the mechanics of how it is done. To illustrate, imagine we want to compare the HR of two different groups of people. We take a random sample from each group, which we call our data. Then:
Formally, we can define a p- value as ‘the probability of finding the observed result or a more extreme result, if the null hypothesis were true.’ Standard practice is to set a cut-off at p <0.05 (this cut-off is termed the alpha value). If the null hypothesis were true, a result such as this would only occur 5% of the time or less; this in turn would indicate that the null hypothesis itself is unlikely. Fisher described the process as follows: ‘Set a low standard of significance at the 5 per cent point, and ignore entirely all results which fail to reach this level. A scientific fact should be regarded as experimentally established only if a properly designed experiment rarely fails to give this level of significance.’ 3 This probably remains the most succinct description of the procedure.
A question which often arises at this point is ‘Why do we use a null hypothesis?’ The simple answer is that it is easy: we can readily describe what we would expect of our data under a null hypothesis, we know how data would behave, and we can readily work out the probability of getting the result that we did. It therefore makes a very simple starting point for our probability assessment. All probabilities require a set of starting conditions, in much the same way that measuring the distance to London needs a starting point. The null hypothesis can be thought of as an easy place to put the start of your ruler.
If a null hypothesis is rejected, an alternate hypothesis must be adopted in its place. The null and alternate hypotheses must be mutually exclusive, but must also between them describe all situations. If a null hypothesis is ‘no difference exists’ then the alternate should be simply ‘a difference exists’.
The components of a hypothesis test can be readily described using the acronym GOST: identify the Groups you wish to compare; define the Outcome to be measured; collect and Summarise the data; then evaluate the likelihood of the null hypothesis, using a Test statistic .
When considering groups, think first about how many. Is there just one group being compared against an audit standard, or are you comparing one group with another? Some studies may wish to compare more than two groups. Another situation may involve a single group measured at different points in time, for example before or after a particular treatment. In this situation each participant is compared with themselves, and this is often referred to as a ‘paired’ or a ‘repeated measures’ design. It is possible to combine these types of groups—for example a researcher may measure arterial BP on a number of different occasions in five different groups of patients. Such studies can be difficult, both to analyse and interpret.
In other studies we may want to see how a continuous variable (such as age or height) affects the outcomes. These techniques involve regression analysis, and are beyond the scope of this article.
The outcome measures are the data being collected. This may be a continuous measure, such as temperature or BMI, or it may be a categorical measure, such as ASA status or surgical specialty. Often, inexperienced researchers will strive to collect lots of outcome measures in an attempt to find something that differs between the groups of interest; if this is done, a ‘primary outcome measure’ should be identified before the research begins. In addition, the results of any hypothesis tests will need to be corrected for multiple measures.
The summary and the test statistic will be defined by the type of data that have been collected. The test statistic is calculated then transformed into a p- value using tables or software. It is worth looking at two common tests in a little more detail: the χ 2 test, and the t -test.
The χ 2 test of independence is a test for comparing categorical outcomes in two or more groups. For example, a number of trials have compared surgical site infections in patients who have been given different concentrations of oxygen perioperatively. In the PROXI trial, 4 685 patients received oxygen 80%, and 701 patients received oxygen 30%. In the 80% group there were 131 infections, while in the 30% group there were 141 infections. In this study, the groups were oxygen 80% and oxygen 30%, and the outcome measure was the presence of a surgical site infection.
The summary is a table ( Table 1 ), and the hypothesis test compares this table (the ‘observed’ table) with the table that would be expected if the proportion of infections in each group was the same (the ‘expected’ table). The test statistic is χ 2 , from which a p- value is calculated. In this instance the p -value is 0.64, which means that results like this would occur 64% of the time if the null hypothesis were true. We thus have no evidence to reject the null hypothesis; the observed difference probably results from sampling variation rather than from an inherent difference between the two groups.
Summary of the results of the PROXI trial. Figures are numbers of patients.
Group | |||
---|---|---|---|
Oxygen 80% | Oxygen 30% | ||
Outcome | Infection | 131 | 141 |
No infection | 554 | 560 | |
Total | 685 | 701 |
The t- test is a statistical method for comparing means, and is one of the most widely used hypothesis tests. Imagine a study where we try to see if there is a difference in the onset time of a new neuromuscular blocking agent compared with suxamethonium. We could enlist 100 volunteers, give them a general anaesthetic, and randomise 50 of them to receive the new drug and 50 of them to receive suxamethonium. We then time how long it takes (in seconds) to have ideal intubation conditions, as measured by a quantitative nerve stimulator. Our data are therefore a list of times. In this case, the groups are ‘new drug’ and suxamethonium, and the outcome is time, measured in seconds. This can be summarised by using means; the hypothesis test will compare the means of the two groups, using a p- value calculated from a ‘ t statistic’. Hopefully it is becoming obvious at this point that the test statistic is usually identified by a letter, and this letter is often cited in the name of the test.
The t -test comes in a number of guises, depending on the comparison being made. A single sample can be compared with a standard (Is the BMI of school leavers in this town different from the national average?); two samples can be compared with each other, as in the example above; or the same study subjects can be measured at two different times. The latter case is referred to as a paired t- test, because each participant provides a pair of measurements—such as in a pre- or postintervention study.
A large number of methods for testing hypotheses exist; the commonest ones and their uses are described in Table 2 . In each case, the test can be described by detailing the groups being compared ( Table 2 , columns) the outcome measures (rows), the summary, and the test statistic. The decision to use a particular test or method should be made during the planning stages of a trial or experiment. At this stage, an estimate needs to be made of how many test subjects will be needed. Such calculations are described in detail elsewhere. 5
The principle types of hypothesis test. Tests comparing more than two samples can indicate that one group differs from the others, but will not identify which. Subsequent ‘post hoc’ testing is required if a difference is found.
Type of data | Number of groups | ||||
---|---|---|---|---|---|
1 (comparison with a standard) | 1 (before and after) | 2 | More than 2 | Measured over a continuous range | |
Categorical | Binomial test | McNemar's test | χ test, or Fisher's exact (2×2 tables), or comparison of proportions | χ test | Logistic regression |
Continuous (normal) | One-sample -test | Paired -test | Independent samples -test | Analysis of variance (ANOVA) | Regression analysis, correlation |
Continuous (non-parametric) | Sign test (for median) | Sign test, or Wilcoxon matched-pairs test | Mann–Whitney test | Kruskal–Wallis test | Spearman's rank correlation |
Although hypothesis tests have been the basis of modern science since the middle of the 20th century, they have been plagued by misconceptions from the outset; this has led to what has been described as a crisis in science in the last few years: some journals have gone so far as to ban p -value s outright. 6 This is not because of any flaw in the concept of a p -value, but because of a lack of understanding of what they mean.
Possibly the most pervasive misunderstanding is the belief that the p- value is the chance that the null hypothesis is true, or that the p- value represents the frequency with which you will be wrong if you reject the null hypothesis (i.e. claim to have found a difference). This interpretation has frequently made it into the literature, and is a very easy trap to fall into when discussing hypothesis tests. To avoid this, it is important to remember that the p- value is telling us something about our sample , not about the null hypothesis. Put in simple terms, we would like to know the probability that the null hypothesis is true, given our data. The p- value tells us the probability of getting these data if the null hypothesis were true, which is not the same thing. This fallacy is referred to as ‘flipping the conditional’; the probability of an outcome under certain conditions is not the same as the probability of those conditions given that the outcome has happened.
A useful example is to imagine a magic trick in which you select a card from a normal deck of 52 cards, and the performer reveals your chosen card in a surprising manner. If the performer were relying purely on chance, this would only happen on average once in every 52 attempts. On the basis of this, we conclude that it is unlikely that the magician is simply relying on chance. Although simple, we have just performed an entire hypothesis test. We have declared a null hypothesis (the performer was relying on chance); we have even calculated a p -value (1 in 52, ≈0.02); and on the basis of this low p- value we have rejected our null hypothesis. We would, however, be wrong to suggest that there is a probability of 0.02 that the performer is relying on chance—that is not what our figure of 0.02 is telling us.
To explore this further we can create two populations, and watch what happens when we use simulation to take repeated samples to compare these populations. Computers allow us to do this repeatedly, and to see what p- value s are generated (see Supplementary online material). 7 Fig 1 illustrates the results of 100,000 simulated t -tests, generated in two set of circumstances. In Fig 1 a , we have a situation in which there is a difference between the two populations. The p- value s cluster below the 0.05 cut-off, although there is a small proportion with p >0.05. Interestingly, the proportion of comparisons where p <0.05 is 0.8 or 80%, which is the power of the study (the sample size was specifically calculated to give a power of 80%).
The p- value s generated when 100,000 t -tests are used to compare two samples taken from defined populations. ( a ) The populations have a difference and the p- value s are mostly significant. ( b ) The samples were taken from the same population (i.e. the null hypothesis is true) and the p- value s are distributed uniformly.
Figure 1 b depicts the situation where repeated samples are taken from the same parent population (i.e. the null hypothesis is true). Somewhat surprisingly, all p- value s occur with equal frequency, with p <0.05 occurring exactly 5% of the time. Thus, when the null hypothesis is true, a type I error will occur with a frequency equal to the alpha significance cut-off.
Figure 1 highlights the underlying problem: when presented with a p -value <0.05, is it possible with no further information, to determine whether you are looking at something from Fig 1 a or Fig 1 b ?
Finally, it cannot be stressed enough that although hypothesis testing identifies whether or not a difference is likely, it is up to us as clinicians to decide whether or not a statistically significant difference is also significant clinically.
As mentioned above, some have suggested moving away from p -values, but it is not entirely clear what we should use instead. Some sources have advocated focussing more on effect size; however, without a measure of significance we have merely returned to our original problem: how do we know that our difference is not just a result of sampling variation?
One solution is to use Bayesian statistics. Up until very recently, these techniques have been considered both too difficult and not sufficiently rigorous. However, recent advances in computing have led to the development of Bayesian equivalents of a number of standard hypothesis tests. 8 These generate a ‘Bayes Factor’ (BF), which tells us how more (or less) likely the alternative hypothesis is after our experiment. A BF of 1.0 indicates that the likelihood of the alternate hypothesis has not changed. A BF of 10 indicates that the alternate hypothesis is 10 times more likely than we originally thought. A number of classifications for BF exist; greater than 10 can be considered ‘strong evidence’, while BF greater than 100 can be classed as ‘decisive’.
Figures such as the BF can be quoted in conjunction with the traditional p- value, but it remains to be seen whether they will become mainstream.
The author declares that they have no conflict of interest.
The associated MCQs (to support CME/CPD activity) will be accessible at www.bjaed.org/cme/home by subscribers to BJA Education .
Jason Walker FRCA FRSS BSc (Hons) Math Stat is a consultant anaesthetist at Ysbyty Gwynedd Hospital, Bangor, Wales, and an honorary senior lecturer at Bangor University. He is vice chair of his local research ethics committee, and an examiner for the Primary FRCA.
Matrix codes: 1A03, 2A04, 3J03
Supplementary data to this article can be found online at https://doi.org/10.1016/j.bjae.2019.03.006 .
The following is the Supplementary data to this article:
Harvard Business School Online's Business Insights Blog provides the career insights you need to achieve your goals and gain confidence in your business skills.
Becoming a more data-driven decision-maker can bring several benefits to your organization, enabling you to identify new opportunities to pursue and threats to abate. Rather than allowing subjective thinking to guide your business strategy, backing your decisions with data can empower your company to become more innovative and, ultimately, profitable.
If you’re new to data-driven decision-making, you might be wondering how data translates into business strategy. The answer lies in generating a hypothesis and verifying or rejecting it based on what various forms of data tell you.
Below is a look at hypothesis testing and the role it plays in helping businesses become more data-driven.
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To understand what hypothesis testing is, it’s important first to understand what a hypothesis is.
A hypothesis or hypothesis statement seeks to explain why something has happened, or what might happen, under certain conditions. It can also be used to understand how different variables relate to each other. Hypotheses are often written as if-then statements; for example, “If this happens, then this will happen.”
Hypothesis testing , then, is a statistical means of testing an assumption stated in a hypothesis. While the specific methodology leveraged depends on the nature of the hypothesis and data available, hypothesis testing typically uses sample data to extrapolate insights about a larger population.
When it comes to data-driven decision-making, there’s a certain amount of risk that can mislead a professional. This could be due to flawed thinking or observations, incomplete or inaccurate data , or the presence of unknown variables. The danger in this is that, if major strategic decisions are made based on flawed insights, it can lead to wasted resources, missed opportunities, and catastrophic outcomes.
The real value of hypothesis testing in business is that it allows professionals to test their theories and assumptions before putting them into action. This essentially allows an organization to verify its analysis is correct before committing resources to implement a broader strategy.
As one example, consider a company that wishes to launch a new marketing campaign to revitalize sales during a slow period. Doing so could be an incredibly expensive endeavor, depending on the campaign’s size and complexity. The company, therefore, may wish to test the campaign on a smaller scale to understand how it will perform.
In this example, the hypothesis that’s being tested would fall along the lines of: “If the company launches a new marketing campaign, then it will translate into an increase in sales.” It may even be possible to quantify how much of a lift in sales the company expects to see from the effort. Pending the results of the pilot campaign, the business would then know whether it makes sense to roll it out more broadly.
Related: 9 Fundamental Data Science Skills for Business Professionals
1. alternative hypothesis and null hypothesis.
In hypothesis testing, the hypothesis that’s being tested is known as the alternative hypothesis . Often, it’s expressed as a correlation or statistical relationship between variables. The null hypothesis , on the other hand, is a statement that’s meant to show there’s no statistical relationship between the variables being tested. It’s typically the exact opposite of whatever is stated in the alternative hypothesis.
For example, consider a company’s leadership team that historically and reliably sees $12 million in monthly revenue. They want to understand if reducing the price of their services will attract more customers and, in turn, increase revenue.
In this case, the alternative hypothesis may take the form of a statement such as: “If we reduce the price of our flagship service by five percent, then we’ll see an increase in sales and realize revenues greater than $12 million in the next month.”
The null hypothesis, on the other hand, would indicate that revenues wouldn’t increase from the base of $12 million, or might even decrease.
Check out the video below about the difference between an alternative and a null hypothesis, and subscribe to our YouTube channel for more explainer content.
Statistically speaking, if you were to run the same scenario 100 times, you’d likely receive somewhat different results each time. If you were to plot these results in a distribution plot, you’d see the most likely outcome is at the tallest point in the graph, with less likely outcomes falling to the right and left of that point.
With this in mind, imagine you’ve completed your hypothesis test and have your results, which indicate there may be a correlation between the variables you were testing. To understand your results' significance, you’ll need to identify a p-value for the test, which helps note how confident you are in the test results.
In statistics, the p-value depicts the probability that, assuming the null hypothesis is correct, you might still observe results that are at least as extreme as the results of your hypothesis test. The smaller the p-value, the more likely the alternative hypothesis is correct, and the greater the significance of your results.
When it’s time to test your hypothesis, it’s important to leverage the correct testing method. The two most common hypothesis testing methods are one-sided and two-sided tests , or one-tailed and two-tailed tests, respectively.
Typically, you’d leverage a one-sided test when you have a strong conviction about the direction of change you expect to see due to your hypothesis test. You’d leverage a two-sided test when you’re less confident in the direction of change.
To perform hypothesis testing in the first place, you need to collect a sample of data to be analyzed. Depending on the question you’re seeking to answer or investigate, you might collect samples through surveys, observational studies, or experiments.
A survey involves asking a series of questions to a random population sample and recording self-reported responses.
Observational studies involve a researcher observing a sample population and collecting data as it occurs naturally, without intervention.
Finally, an experiment involves dividing a sample into multiple groups, one of which acts as the control group. For each non-control group, the variable being studied is manipulated to determine how the data collected differs from that of the control group.
Hypothesis testing is a complex process involving different moving pieces that can allow an organization to effectively leverage its data and inform strategic decisions.
If you’re interested in better understanding hypothesis testing and the role it can play within your organization, one option is to complete a course that focuses on the process. Doing so can lay the statistical and analytical foundation you need to succeed.
Do you want to learn more about hypothesis testing? Explore Business Analytics —one of our online business essentials courses —and download our Beginner’s Guide to Data & Analytics .
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Hypothesis testing in statistics refers to analyzing an assumption about a population parameter. It is used to make an educated guess about an assumption using statistics. With the use of sample data, hypothesis testing makes an assumption about how true the assumption is for the entire population from where the sample is being taken.
Any hypothetical statement we make may or may not be valid, and it is then our responsibility to provide evidence for its possibility. To approach any hypothesis, we follow these four simple steps that test its validity.
First, we formulate two hypothetical statements such that only one of them is true. By doing so, we can check the validity of our own hypothesis.
The next step is to formulate the statistical analysis to be followed based upon the data points.
Then we analyze the given data using our methodology.
The final step is to analyze the result and judge whether the null hypothesis will be rejected or is true.
It is observed that the average recovery time for a knee-surgery patient is 8 weeks. A physician believes that after successful knee surgery if the patient goes for physical therapy twice a week rather than thrice a week, the recovery period will be longer. Conduct hypothesis for this statement.
David is a ten-year-old who finishes a 25-yard freestyle in the meantime of 16.43 seconds. David’s father bought goggles for his son, believing that it would help him to reduce his time. He then recorded a total of fifteen 25-yard freestyle for David, and the average time came out to be 16 seconds. Conduct a hypothesis.
A tire company claims their A-segment of tires have a running life of 50,000 miles before they need to be replaced, and previous studies show a standard deviation of 8,000 miles. After surveying a total of 28 tires, the mean run time came to be 46,500 miles with a standard deviation of 9800 miles. Is the claim made by the tire company consistent with the given data? Conduct hypothesis testing.
All of the hypothesis testing examples are from real-life situations, which leads us to believe that hypothesis testing is a very practical topic indeed. It is an integral part of a researcher's study and is used in every research methodology in one way or another.
Inferential statistics majorly deals with hypothesis testing. The research hypothesis states there is a relationship between the independent variable and dependent variable. Whereas the null hypothesis rejects this claim of any relationship between the two, our job as researchers or students is to check whether there is any relation between the two.
Now that we are clear about what hypothesis testing is? Let's look at the use of hypothesis testing in research methodology. Hypothesis testing is at the centre of research projects.
Often after formulating research statements, the validity of those statements need to be verified. Hypothesis testing offers a statistical approach to the researcher about the theoretical assumptions he/she made. It can be understood as quantitative results for a qualitative problem.
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Hypothesis testing provides various techniques to test the hypothesis statement depending upon the variable and the data points. It finds its use in almost every field of research while answering statements such as whether this new medicine will work, a new testing method is appropriate, or if the outcomes of a random experiment are probable or not.
To find the validity of any statement, we have to strictly follow the stepwise procedure of hypothesis testing. After stating the initial hypothesis, we have to re-write them in the form of a null and alternate hypothesis. The alternate hypothesis predicts a relationship between the variables, whereas the null hypothesis predicts no relationship between the variables.
After writing them as H 0 (null hypothesis) and H a (Alternate hypothesis), only one of the statements can be true. For example, taking the hypothesis that, on average, men are taller than women, we write the statements as:
H 0 : On average, men are not taller than women.
H a : On average, men are taller than women.
Our next aim is to collect sample data, what we call sampling, in a way so that we can test our hypothesis. Your data should come from the concerned population for which you want to make a hypothesis.
What is the p value in hypothesis testing? P-value gives us information about the probability of occurrence of results as extreme as observed results.
You will obtain your p-value after choosing the hypothesis testing method, which will be the guiding factor in rejecting the hypothesis. Usually, the p-value cutoff for rejecting the null hypothesis is 0.05. So anything below that, you will reject the null hypothesis.
A low p-value means that the between-group variance is large enough that there is almost no overlapping, and it is unlikely that these came about by chance. A high p-value suggests there is a high within-group variance and low between-group variance, and any difference in the measure is due to chance only.
When forming conclusions through research, two sorts of errors are common: A hypothesis must be set and defined in statistics during a statistical survey or research. A statistical hypothesis is what it is called. It is, in fact, a population parameter assumption. However, it is unmistakable that this idea is always proven correct. Hypothesis testing refers to the predetermined formal procedures used by statisticians to determine whether hypotheses should be accepted or rejected. The process of selecting hypotheses for a given probability distribution based on observable data is known as hypothesis testing. Hypothesis testing is a fundamental and crucial issue in statistics.
The quick answer is that you must as a scientist; it is part of the scientific process. Science employs a variety of methods to test or reject theories, ensuring that any new hypothesis is free of errors. One protection to ensure your research is not incorrect is to include both a null and an alternate hypothesis. The scientific community considers not incorporating the null hypothesis in your research to be poor practice. You are almost certainly setting yourself up for failure if you set out to prove another theory without first examining it. At the very least, your experiment will not be considered seriously.
There are several types of hypothesis testing, and they are used based on the data provided. Depending on the sample size and the data given, we choose among different hypothesis testing methodologies. Here starts the use of hypothesis testing tools in research methodology.
Normality- This type of testing is used for normal distribution in a population sample. If the data points are grouped around the mean, the probability of them being above or below the mean is equally likely. Its shape resembles a bell curve that is equally distributed on either side of the mean.
T-test- This test is used when the sample size in a normally distributed population is comparatively small, and the standard deviation is unknown. Usually, if the sample size drops below 30, we use a T-test to find the confidence intervals of the population.
Chi-Square Test- The Chi-Square test is used to test the population variance against the known or assumed value of the population variance. It is also a better choice to test the goodness of fit of a distribution of data. The two most common Chi-Square tests are the Chi-Square test of independence and the chi-square test of variance.
ANOVA- Analysis of Variance or ANOVA compares the data sets of two different populations or samples. It is similar in its use to the t-test or the Z-test, but it allows us to compare more than two sample means. ANOVA allows us to test the significance between an independent variable and a dependent variable, namely X and Y, respectively.
Z-test- It is a statistical measure to test that the means of two population samples are different when their variance is known. For a Z-test, the population is assumed to be normally distributed. A z-test is better suited in the case of large sample sizes greater than 30. This is due to the central limit theorem that as the sample size increases, the samples are considered to be distributed normally.
1. Mention the types of hypothesis Tests.
There are two types of a hypothesis tests:
Null Hypothesis: It is denoted as H₀.
Alternative Hypothesis: IT is denoted as H₁ or Hₐ.
2. What are the two errors that can be found while performing the null Hypothesis test?
While performing the null hypothesis test there is a possibility of occurring two types of errors,
Type-1: The type-1 error is denoted by (α), it is also known as the significance level. It is the rejection of the true null hypothesis. It is the error of commission.
Type-2: The type-2 error is denoted by (β). (1 - β) is known as the power test. The false null hypothesis is not rejected. It is the error of the omission.
3. What is the p-value in hypothesis testing?
During hypothetical testing in statistics, the p-value indicates the probability of obtaining the result as extreme as observed results. A smaller p-value provides evidence to accept the alternate hypothesis. The p-value is used as a rejection point that provides the smallest level of significance at which the null hypothesis is rejected. Often p-value is calculated using the p-value tables by calculating the deviation between the observed value and the chosen reference value.
It may also be calculated mathematically by performing integrals on all the values that fall under the curve and areas far from the reference value as the observed value relative to the total area of the curve. The p-value determines the evidence to reject the null hypothesis in hypothesis testing.
4. What is a null hypothesis?
The null hypothesis in statistics says that there is no certain difference between the population. It serves as a conjecture proposing no difference, whereas the alternate hypothesis says there is a difference. When we perform hypothesis testing, we have to state the null hypothesis and alternative hypotheses such that only one of them is ever true.
By determining the p-value, we calculate whether the null hypothesis is to be rejected or not. If the difference between groups is low, it is merely by chance, and the null hypothesis, which states that there is no difference among groups, is true. Therefore, we have no evidence to reject the null hypothesis.
Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps.
2. Identify a test statistic that can be used to assess the truth of the null hypothesis .
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Cite this as:.
Weisstein, Eric W. "Hypothesis Testing." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/HypothesisTesting.html
Hypothesis testing involves formulating assumptions about population parameters based on sample statistics and rigorously evaluating these assumptions against empirical evidence. This article sheds light on the significance of hypothesis testing and the critical steps involved in the process.
A hypothesis is an assumption or idea, specifically a statistical claim about an unknown population parameter. For example, a judge assumes a person is innocent and verifies this by reviewing evidence and hearing testimony before reaching a verdict.
Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data.
To test the validity of the claim or assumption about the population parameter:
Example: You say an average height in the class is 30 or a boy is taller than a girl. All of these is an assumption that we are assuming, and we need some statistical way to prove these. We need some mathematical conclusion whatever we are assuming is true.
Hypothesis testing is an important procedure in statistics. Hypothesis testing evaluates two mutually exclusive population statements to determine which statement is most supported by sample data. When we say that the findings are statistically significant, thanks to hypothesis testing.
One tailed test focuses on one direction, either greater than or less than a specified value. We use a one-tailed test when there is a clear directional expectation based on prior knowledge or theory. The critical region is located on only one side of the distribution curve. If the sample falls into this critical region, the null hypothesis is rejected in favor of the alternative hypothesis.
There are two types of one-tailed test:
A two-tailed test considers both directions, greater than and less than a specified value.We use a two-tailed test when there is no specific directional expectation, and want to detect any significant difference.
Example: H 0 : [Tex]\mu = [/Tex] 50 and H 1 : [Tex]\mu \neq 50 [/Tex]
To delve deeper into differences into both types of test: Refer to link
In hypothesis testing, Type I and Type II errors are two possible errors that researchers can make when drawing conclusions about a population based on a sample of data. These errors are associated with the decisions made regarding the null hypothesis and the alternative hypothesis.
Null Hypothesis is True | Null Hypothesis is False | |
---|---|---|
Null Hypothesis is True (Accept) | Correct Decision | Type II Error (False Negative) |
Alternative Hypothesis is True (Reject) | Type I Error (False Positive) | Correct Decision |
Step 1: define null and alternative hypothesis.
State the null hypothesis ( [Tex]H_0 [/Tex] ), representing no effect, and the alternative hypothesis ( [Tex]H_1 [/Tex] ), suggesting an effect or difference.
We first identify the problem about which we want to make an assumption keeping in mind that our assumption should be contradictory to one another, assuming Normally distributed data.
Select a significance level ( [Tex]\alpha [/Tex] ), typically 0.05, to determine the threshold for rejecting the null hypothesis. It provides validity to our hypothesis test, ensuring that we have sufficient data to back up our claims. Usually, we determine our significance level beforehand of the test. The p-value is the criterion used to calculate our significance value.
Gather relevant data through observation or experimentation. Analyze the data using appropriate statistical methods to obtain a test statistic.
The data for the tests are evaluated in this step we look for various scores based on the characteristics of data. The choice of the test statistic depends on the type of hypothesis test being conducted.
There are various hypothesis tests, each appropriate for various goal to calculate our test. This could be a Z-test , Chi-square , T-test , and so on.
We have a smaller dataset, So, T-test is more appropriate to test our hypothesis.
T-statistic is a measure of the difference between the means of two groups relative to the variability within each group. It is calculated as the difference between the sample means divided by the standard error of the difference. It is also known as the t-value or t-score.
In this stage, we decide where we should accept the null hypothesis or reject the null hypothesis. There are two ways to decide where we should accept or reject the null hypothesis.
Comparing the test statistic and tabulated critical value we have,
Note: Critical values are predetermined threshold values that are used to make a decision in hypothesis testing. To determine critical values for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.
We can also come to an conclusion using the p-value,
Note : The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed in the sample, assuming the null hypothesis is true. To determine p-value for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.
At last, we can conclude our experiment using method A or B.
To validate our hypothesis about a population parameter we use statistical functions . We use the z-score, p-value, and level of significance(alpha) to make evidence for our hypothesis for normally distributed data .
When population means and standard deviations are known.
[Tex]z = \frac{\bar{x} – \mu}{\frac{\sigma}{\sqrt{n}}}[/Tex]
T test is used when n<30,
t-statistic calculation is given by:
[Tex]t=\frac{x̄-μ}{s/\sqrt{n}} [/Tex]
Chi-Square Test for Independence categorical Data (Non-normally distributed) using:
[Tex]\chi^2 = \sum \frac{(O_{ij} – E_{ij})^2}{E_{ij}}[/Tex]
Let’s examine hypothesis testing using two real life situations,
Imagine a pharmaceutical company has developed a new drug that they believe can effectively lower blood pressure in patients with hypertension. Before bringing the drug to market, they need to conduct a study to assess its impact on blood pressure.
Let’s consider the Significance level at 0.05, indicating rejection of the null hypothesis.
If the evidence suggests less than a 5% chance of observing the results due to random variation.
Using paired T-test analyze the data to obtain a test statistic and a p-value.
The test statistic (e.g., T-statistic) is calculated based on the differences between blood pressure measurements before and after treatment.
t = m/(s/√n)
then, m= -3.9, s= 1.8 and n= 10
we, calculate the , T-statistic = -9 based on the formula for paired t test
The calculated t-statistic is -9 and degrees of freedom df = 9, you can find the p-value using statistical software or a t-distribution table.
thus, p-value = 8.538051223166285e-06
Step 5: Result
Conclusion: Since the p-value (8.538051223166285e-06) is less than the significance level (0.05), the researchers reject the null hypothesis. There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.
Let’s create hypothesis testing with python, where we are testing whether a new drug affects blood pressure. For this example, we will use a paired T-test. We’ll use the scipy.stats library for the T-test.
Scipy is a mathematical library in Python that is mostly used for mathematical equations and computations.
We will implement our first real life problem via python,
import numpy as np from scipy import stats # Data before_treatment = np . array ([ 120 , 122 , 118 , 130 , 125 , 128 , 115 , 121 , 123 , 119 ]) after_treatment = np . array ([ 115 , 120 , 112 , 128 , 122 , 125 , 110 , 117 , 119 , 114 ]) # Step 1: Null and Alternate Hypotheses # Null Hypothesis: The new drug has no effect on blood pressure. # Alternate Hypothesis: The new drug has an effect on blood pressure. null_hypothesis = "The new drug has no effect on blood pressure." alternate_hypothesis = "The new drug has an effect on blood pressure." # Step 2: Significance Level alpha = 0.05 # Step 3: Paired T-test t_statistic , p_value = stats . ttest_rel ( after_treatment , before_treatment ) # Step 4: Calculate T-statistic manually m = np . mean ( after_treatment - before_treatment ) s = np . std ( after_treatment - before_treatment , ddof = 1 ) # using ddof=1 for sample standard deviation n = len ( before_treatment ) t_statistic_manual = m / ( s / np . sqrt ( n )) # Step 5: Decision if p_value <= alpha : decision = "Reject" else : decision = "Fail to reject" # Conclusion if decision == "Reject" : conclusion = "There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different." else : conclusion = "There is insufficient evidence to claim a significant difference in average blood pressure before and after treatment with the new drug." # Display results print ( "T-statistic (from scipy):" , t_statistic ) print ( "P-value (from scipy):" , p_value ) print ( "T-statistic (calculated manually):" , t_statistic_manual ) print ( f "Decision: { decision } the null hypothesis at alpha= { alpha } ." ) print ( "Conclusion:" , conclusion )
T-statistic (from scipy): -9.0 P-value (from scipy): 8.538051223166285e-06 T-statistic (calculated manually): -9.0 Decision: Reject the null hypothesis at alpha=0.05. Conclusion: There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.
In the above example, given the T-statistic of approximately -9 and an extremely small p-value, the results indicate a strong case to reject the null hypothesis at a significance level of 0.05.
Data: A sample of 25 individuals is taken, and their cholesterol levels are measured.
Cholesterol Levels (mg/dL): 205, 198, 210, 190, 215, 205, 200, 192, 198, 205, 198, 202, 208, 200, 205, 198, 205, 210, 192, 205, 198, 205, 210, 192, 205.
Populations Mean = 200
Population Standard Deviation (σ): 5 mg/dL(given for this problem)
As the direction of deviation is not given , we assume a two-tailed test, and based on a normal distribution table, the critical values for a significance level of 0.05 (two-tailed) can be calculated through the z-table and are approximately -1.96 and 1.96.
The test statistic is calculated by using the z formula Z = [Tex](203.8 – 200) / (5 \div \sqrt{25}) [/Tex] and we get accordingly , Z =2.039999999999992.
Step 4: Result
Since the absolute value of the test statistic (2.04) is greater than the critical value (1.96), we reject the null hypothesis. And conclude that, there is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL
import scipy.stats as stats import math import numpy as np # Given data sample_data = np . array ( [ 205 , 198 , 210 , 190 , 215 , 205 , 200 , 192 , 198 , 205 , 198 , 202 , 208 , 200 , 205 , 198 , 205 , 210 , 192 , 205 , 198 , 205 , 210 , 192 , 205 ]) population_std_dev = 5 population_mean = 200 sample_size = len ( sample_data ) # Step 1: Define the Hypotheses # Null Hypothesis (H0): The average cholesterol level in a population is 200 mg/dL. # Alternate Hypothesis (H1): The average cholesterol level in a population is different from 200 mg/dL. # Step 2: Define the Significance Level alpha = 0.05 # Two-tailed test # Critical values for a significance level of 0.05 (two-tailed) critical_value_left = stats . norm . ppf ( alpha / 2 ) critical_value_right = - critical_value_left # Step 3: Compute the test statistic sample_mean = sample_data . mean () z_score = ( sample_mean - population_mean ) / \ ( population_std_dev / math . sqrt ( sample_size )) # Step 4: Result # Check if the absolute value of the test statistic is greater than the critical values if abs ( z_score ) > max ( abs ( critical_value_left ), abs ( critical_value_right )): print ( "Reject the null hypothesis." ) print ( "There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL." ) else : print ( "Fail to reject the null hypothesis." ) print ( "There is not enough evidence to conclude that the average cholesterol level in the population is different from 200 mg/dL." )
Reject the null hypothesis. There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL.
Hypothesis testing stands as a cornerstone in statistical analysis, enabling data scientists to navigate uncertainties and draw credible inferences from sample data. By systematically defining null and alternative hypotheses, choosing significance levels, and leveraging statistical tests, researchers can assess the validity of their assumptions. The article also elucidates the critical distinction between Type I and Type II errors, providing a comprehensive understanding of the nuanced decision-making process inherent in hypothesis testing. The real-life example of testing a new drug’s effect on blood pressure using a paired T-test showcases the practical application of these principles, underscoring the importance of statistical rigor in data-driven decision-making.
1. what are the 3 types of hypothesis test.
There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed. Right-tailed tests assess if a parameter is greater, left-tailed if lesser. Two-tailed tests check for non-directional differences, greater or lesser.
Null Hypothesis ( [Tex]H_o [/Tex] ): No effect or difference exists. Alternative Hypothesis ( [Tex]H_1 [/Tex] ): An effect or difference exists. Significance Level ( [Tex]\alpha [/Tex] ): Risk of rejecting null hypothesis when it’s true (Type I error). Test Statistic: Numerical value representing observed evidence against null hypothesis.
Statistical method to evaluate the performance and validity of machine learning models. Tests specific hypotheses about model behavior, like whether features influence predictions or if a model generalizes well to unseen data.
Pytest purposes general testing framework for Python code while Hypothesis is a Property-based testing framework for Python, focusing on generating test cases based on specified properties of the code.
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Last updated on Fri Aug 23 2024
Imagine spending months or even years developing a new feature only to find out it doesn’t resonate with your users, argh! This kind of situation could be any worst Product manager’s nightmare.
There's a way to fix this problem called the Value Hypothesis . This idea helps builders to validate whether the ideas they’re working on are worth pursuing and useful to the people they want to sell to.
This guide will teach you what you need to know about Value Hypothesis and a step-by-step process on how to create a strong one. At the end of this post, you’ll learn how to create a product that satisfies your users.
Are you ready? Let’s get to it!
Scrutinizing this hypothesis helps you as a developer to come up with a product that your customers like and love to use.
Product managers use the Value Hypothesis as a north star, ensuring focus on client needs and avoiding wasted resources. For more on this, read about the product management process .
Let's get into the step-by-step process, but first, we need to understand the basics of the Value Hypothesis:
A Value Hypothesis is like a smart guess you can test to see if your product truly solves a problem for your customers. It’s your way of predicting how well your product will address a particular issue for the people you’re trying to help.
You need to know what a Value Hypothesis is, what it covers, and its key parts before you use it. To learn more about finding out what customers need, take a look at our guide on discovering features .
The Value Hypothesis does more than just help with the initial launch, it guides the whole development process. This keeps teams focused on what their users care about helping them choose features that their audience will like.
A strong Value Hypothesis rests on three key components:
Value Proposition: The Value Proposition spells out the main advantage your product gives to customers. It explains the "what" and "why" of your product showing how it eases a particular pain point.
This proposition targets a specific group of consumers. To learn more, check out our guide on roadmapping .
Customer Segmentation: Knowing and grasping your target audience is essential. This involves studying their demographics, needs, behaviors, and problems. By dividing your market, you can shape your value proposition to address the unique needs of each group.
Customer feedback surveys can prove priceless in this process. Find out more about this in our customer feedback surveys guide.
Problem Statement : The Problem Statement defines the exact issue your product aims to fix. It should zero in on a real fixable pain point your target users face. For hands-on applications, see our product launch communication plan .
Here are some key questions to guide you:
What are the primary challenges and obstacles faced by your target users?
What existing solutions are available, and where do they fall short?
What unmet needs or desires does your target audience have?
For a structured approach to prioritizing features based on customer needs, consider using a feature prioritization matrix .
Now that we've covered the basics, let's look at how to build a convincing Value Hypothesis. Here's a two-step method, along with value hypothesis templates, to point you in the right direction:
To start with, you need to carry out market research. By carrying out proper market research, you will have an understanding of existing solutions and identify areas in which customers' needs are yet to be met. This is integral to effective idea tracking .
Next, use customer interviews, surveys, and support data to understand your target audience's problems and what they want. Check out our list of tools for getting customer feedback to help with this.
Once you've completed your research, it's crucial to identify your customers' needs. By merging insights from market research with direct user feedback, you can pinpoint the key requirements of your customers.
Here are some key questions to think about:
What are the most significant challenges that your target users encounter daily?
Which current solutions are available to them, and how do these solutions fail to fully address their needs?
What specific pain points are your target users struggling with that aren't being resolved?
Are there any gaps or shortcomings in the existing products or services that your customers use?
What unfulfilled needs or desires does your target audience express that aren't currently met by the market?
To prioritize features based on customer needs in a structured way, think about using a feature prioritization matrix .
Once you've created your Value Hypothesis with a template, you need to check if it holds up. Here's how you can do this:
Build a minimum viable product (MVP)—a basic version of your product with essential functions. This lets you test your value proposition with actual users and get feedback without spending too much. To achieve the best outcomes, look into the best practices for customer feedback software .
Build mock-ups to show your product idea. Use these mock-ups to get user input on the user experience and overall value offer.
After you've gathered data about your hypothesis, it's time to examine it. Here are some metrics you can use:
User Engagement : Monitor stats like time on the platform, feature use, and return visits to see how much users interact with your MVP or mock-up.
Conversion Rates : Check conversion rates for key actions like sign-ups, buys, or feature adoption. These numbers help you judge if your value offer clicks with users. To learn more, read our article on SaaS growth benchmarks .
The Value Hypothesis framework shines because you can keep making it better. Here's how to fine-tune your hypothesis:
Set up an ongoing system to gather user data as you develop your product.
Look at what users say to spot areas that need work then update your value proposition based on what you learn.
Read about managing product updates to keep your hypotheses current.
The market keeps changing, and your Value Hypothesis should too. Stay up to date on what's happening in your industry and watch how users' habits change. Tweak your value proposition to stay useful and ahead of the competition.
Here are some ways to keep your Value Hypothesis fresh:
Do market research often to keep up with what's happening in your industry and what your competitors are up to.
Keep an eye on what users are saying to spot new problems or things they need but don't have yet.
Try out different value statements and features to see which ones your audience likes best.
To keep your guesses up-to-date, check out our guide on handling product changes .
While the Value Hypothesis approach is powerful, it's key to steer clear of these common traps:
Avoid Confirmation Bias : People tend to focus on data that backs up their initial guesses. But it's key to look at feedback that goes against your ideas and stay open to different views.
Watch out for Shiny Object Syndrome : Don't let the newest fads sway you unless they solve a main customer problem. Your value proposition should fix actual issues for your users.
Don't Cling to Your First Hypothesis : As the market changes, your value proposition should too. Be ready to shift your hypothesis when new evidence and user feedback comes in.
Don't Mix Up Busywork with Real Progress : Getting user feedback is key, but making sense of it brings real value. Look at the data to find useful insights that can shape your product. To learn more about this, check out our guide on handling customer feedback .
To build a product that succeeds, you need to know your target users inside out and understand how you help them. The Value Hypothesis framework gives you a step-by-step way to do this.
If you follow the steps in this guide, you can create a strong value proposition, check if it works, and keep improving it to ensure your product stays useful and important to your customers.
Keep in mind, a good Value Hypothesis changes as your product and market change. When you use data and put customers first, you're on the right track to create a product that works.
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Critical Care volume 28 , Article number: 288 ( 2024 ) Cite this article
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Physical inactivity and subsequent muscle atrophy are highly prevalent in neurocritical care and are recognized as key mechanisms underlying intensive care unit acquired weakness (ICUAW). The lack of quantifiable biomarkers for inactivity complicates the assessment of its relative importance compared to other conditions under the syndromic diagnosis of ICUAW. We hypothesize that active movement, as opposed to passive movement without active patient participation, can serve as a valid proxy for activity and may help predict muscle atrophy. To test this hypothesis, we utilized non-invasive, body-fixed accelerometers to compute measures of active movement and subsequently developed a machine learning model to predict muscle atrophy.
This study was conducted as a single-center, prospective, observational cohort study as part of the MINCE registry (metabolism and nutrition in neurointensive care, DRKS-ID: DRKS00031472). Atrophy of rectus femoris muscle (RFM) relative to baseline (day 0) was evaluated at days 3, 7 and 10 after intensive care unit (ICU) admission and served as the dependent variable in a generalized linear mixed model with Least Absolute Shrinkage and Selection Operator regularization and nested-cross validation.
Out of 407 patients screened, 53 patients (age: 59.2 years (SD 15.9), 31 (58.5%) male) with a total of 91 available accelerometer datasets were enrolled. RFM thickness changed − 19.5% (SD 12.0) by day 10. Out of 12 demographic, clinical, nutritional and accelerometer-derived variables, baseline RFM muscle mass (beta − 5.1, 95% CI − 7.9 to − 3.8) and proportion of active movement (% activity) (beta 1.6, 95% CI 0.1 to 4.9) were selected as significant predictors of muscle atrophy. Including movement features into the prediction model substantially improved performance on an unseen test data set (including movement features: R 2 = 79%; excluding movement features: R 2 = 55%).
Active movement, as measured with thigh-fixed accelerometers, is a key risk factor for muscle atrophy in neurocritical care patients. Quantifiable biomarkers reflecting the level of activity can support more precise phenotyping of ICUAW and may direct tailored interventions to support activity in the ICU. Studies addressing the external validity of these findings beyond the neurointensive care unit are warranted.
DRKS00031472, retrospectively registered on 13.03.2023.
Intensive care unit acquired weakness (ICUAW) describes a neuromuscular dysfunction secondary to critical illness and its treatment with consecutive generalized weakness. Data on prevalence for ICUAW show considerable variation due to diverse patient demographics and heterogenous methodology. However, with a systematic review pinpointing the median prevalence at 43% [ 1 ], its ubiquity in critical care is evident. Moreover, the impact resulting from ICUAW is profound and long-lasting, with patient outcomes significantly compromised for up to five years after discharge [ 2 , 3 , 4 , 5 , 6 ]. Therefore, ICUAW is acknowledged as a key component of post intensive care syndrome (PICS), highlighting its importance in the continuum of long-term recovery following critical care [ 7 , 8 ].
ICUAW needs to be recognized as a clinical syndrome, rather than a specific disease entity. As such, it exhibits great heterogeneity and partially overlapping pathologies, which has diluted research findings and made the identification of treatable targets challenging in the past [ 9 , 10 , 11 , 12 ]. Relevant and common entities include critical illness myopathy (CIM), critical illness polyneuropathy (CIP) as well as critical illness polyneuromyopathy (CIPNM) as an overlap syndrome [ 9 , 11 , 12 ]. Electrophysiological methods including nerve conduction studies (NCS), electromyography and direct muscle stimulation have been successfully used to establish biomarkers for CIM, CIP and CIPMN [ 9 , 13 , 14 ]. Muscle atrophy due to mechanical unloading is also being recognized as a critical component of ICUAW. However, measurable biomarkers to assess the extent of inactivity of muscles are lacking.
In this regard, it is important to note that activity arises from active movement, as opposed to passive movement during mobilization without active patient participation. Hence, we postulate that establishing a proxy for activity can be achieved by applying non-invasive, body-fixed accelerometers to the lower extremities of critically ill patients while prospectively excluding episodes with passive mobilization such as intrahospital transports, physiotherapy and patient positioning. By introducing these biomarkers as continuous measures of active movement and incorporating these variables into a machine learning model, we aimed to predict rectus femoris muscle atrophy, as measured by ultrasound up to day 10 of intensive care unit (ICU) treatment. Based on the hypothesis that neurocritical care patients exhibit a higher prevalence of inactivity due to disorders of consciousness and motor deficits, we specifically included patients with acute brain injury in this trial.
This study was designed as a single-center, prospective, observational cohort study as part of the MINCE registry (metabolism and nutrition in neurointensive care, DRKS-ID: DRKS00031472, retrospectively registered on 13.03.2023) at a tertiary academic center (LMU University Hospital, Munich, Germany). Reporting follows the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) reporting guidelines. This study was approved by the local ethics committee (LMU Munich, project number 22-0173, 11.04.2022). Written consent was obtained from all participants or their next of kin. The study recruited from April 2022 to March 2024 and included patients within 48 h after ICU admission with age ≥ 18 years, neurologic disease as admitting diagnosis, and expected ICU length of stay ≥ 10 days. Patients with pre-existing neuromuscular disease, renal replacement therapy, pregnancy, pre-existing neoplastic disease, recent hospitalization (hospital stays longer than three days in the last three months, ICU treatment within the last three months), pre-existing confinement to bed, and pre-existing frailty (Clinical Frailty Scale > 3) were excluded.
Patients were mobilized at the treating physicians’ discretion. If indicated, patients received physiotherapy for 20–40 min/day on six days of the week and were repositioned and transferred from bed to chair regularly by the nursing staff. Nutritional therapy was conducted according to the European Society of Parenteral and Enteral Nutrition (ESPEN) guidelines, with caloric and protein targets of 25 kcal/kg/day and 1.3 g/kg/day, respectively [ 15 ]. As a reference, body weight as measured with bed scales was used for non-obese patients, and ideal body weight was used for patients with a body mass index (BMI) > 30 kg/m 2 [ 15 ]. During the acute phase of illness (days 1–3), hypocaloric nutrition (70% of energy expenditure (EE)) was aimed for. From day 4 on, isocaloric (100% of EE) nutrition was implemented.
Clinical data prospectively collected on the ICU included age, sex, body mass index (BMI), admission diagnosis, cumulative protein and calorie deficit, duration of mechanical ventilation, ICU length of stay (LOS), daily Sepsis-related Organ Failure Assessment score (SOFA) and SOFA without Glasgow Coma Scale (GCS) score (mSOFA), Acute Physiology and Chronic Health Evaluation (APACHE II) score on ICU admission, Nutrition Risk in Critically ill score (NUTRIC) on admission, premorbid modified Rankin Scale (pmRS) and Glasgow Outcome Scale Extended (GOSE) at ICU discharge.
Ultrasound of the upper thigh (rectus femoris muscle, RFM) and temporalis muscle (TM) was performed bilaterally using a 20 MHz linear probe (MyLabOmega, Esaote, Genoa, Italy) upon admission, and on days 3, 7 and 10. As previously described [ 16 , 17 ], the site of measurement for RFM was marked in the lower third of the connecting line between the anterior superior iliac spine and the upper edge of the patella with a permanent marker to ensure reproducibility between measurements (Supplementary Fig. 1 ). Measurements were conducted according to a local protocol that emphasized minimal compression during RFM sonography and called for individual adjustments of depth and gain to optimally visualize the surface of the femur and to delineate fascial borders, respectively. Measurement of TM followed the protocol as described by Maskos et al. [ 17 ] Three repeated measurements were performed by one of six raters (TP, LG, LR, AM, JB, SI), using the built-in software of the ultrasound machine to measure muscle thickness. The mean value of the repeated measurements was used for further analysis. Reliability of repeated ultrasound measurements is reported in Supplementary Table 1 .
Tri-axial accelerometers (range ± 16 g; sampling rate 12.5 Hz; Axivity Ltd., Newcastle upon Tyne, UK) were attached within 48 h of admission to both upper thighs with transparent adhesive tape. Skin inspections and minor adjustments to the sensor placement were performed every third day to prevent any pressure damage. To exclude any passive movement not contributing to the patient’s activity, episodes with physiotherapy, intrahospital transports, or repositioning by nursing staff were prospectively documented and excluded from the recorded data. The sensor data was extracted and analyzed by an author (MW) not involved in the patients’ clinical management and blinded for the ultrasound measurements.
As a positive control, accelerometers were attached to healthy individuals (n = 3). Static placement of sensors served as a negative control (Supplementary Table 2 ).
OmGUI version 1.0.0.11 software was used to download the raw acceleration data from the devices. MATLAB (Mathworks Inc., Natick, USA, release R2022a, version 9.12.0) was used for data processing. Periods of active movement were identified following a previously established procedure that has been already used for activity recognition in ICU settings [ 18 , 19 ]. Accordingly, recorded time series from each axial component (x, y, z) were first down-sampled to 10 Hz and subsequently high-pass filtered (4th order Butterworth filter, cutoff frequency at 0.2 Hz) to remove baseline offset and low-frequency effects reflecting static postural orientation. Filtered time series were segmented into non-overlapping 5 s windows for subsequent motion feature extraction. Signal magnitude area (SMA) was then computed for every window [ 19 ] to identify activity bouts (AB) using a defined threshold of SMA ≥ 0.135 g [ 18 ]. Across all identified AB, the mean intensity (AB-intensity) and duration (AB-duration) as well as the variability (standard deviation, SD) of these features were calculated. The distribution of motion features across ABs is log-normal, which required estimating mean and SD via a maximum likelihood technique [ 20 ]. The overall movement intensity, the proportion of active movement (%active) and ABs per hour were calculated based on the entire duration of the recording (Fig. 1 ).
Accelerometer-derived features. Body motion was monitored using tri-axial accelerometers bilaterally attached to the upper thigh (1). Raw triaxial accelerometer recordings were first offset eliminated, and the time series were segmented into non-overlapping 5 s windows. The signal magnitude area was computed for every window (2). Bouts of dynamic activity were identified based on the threshold ≥ 0.135 g (3) and a set of motion features was computed for every bout of activity (4). Finally, the average and distribution of motion features across all bouts of activity were computed (5). acc = acceleration
As the dataset includes multiple observations (both legs) per patient and exhibits linearity as evaluated by exploratory data analysis, a generalized linear mixed model (GLMM) to account for intra-patient correlation by using individual patients as a random effect was chosen. Given the numerous independent variables of interest, including demographic, clinical, and activity-related features, a rigorous approach to model selection and validation to prevent overfitting was required. Therefore, we employed regularization with Least Absolute Shrinkage and Selection Operator (LASSO), which penalizes the GLMM model via L1-norm and in effect shrinks the weight of non-contributing features to zero.
First, multicollinearity among predictors was mitigated by excluding variables with a variance inflation factor (VIF) exceeding 5 (removing AB per hour and SOFA) [ 21 ]. Next, standardization (z-score normalization) of the remaining prediction variables (age, sex, baseline RFM muscle mass, mSOFA, calorie deficit, protein deficit, overall intensity, %active, AB-intensity log-mean , AB-duration log-mean , AB-intensity log-SD , AB-duration log-SD ) was performed to ensure equal weights and comparable units. To allow testing on unseen data, a stratified split was executed to divide the data into training (80%) and test (20%) sets. The training set was further used for optimizing the hyperparameter of GLMM-LASSO using a machine learning approach with nested cross-validation (Fig. 2 ) [ 22 ]. Model performance was evaluated on the test set using mean squared error, root mean squared error, mean absolute error, R-squared (squared correlation method, R2) and a plot depicting actual versus predicted values.
Nested-cross validation of a regularized GLMM model . After standardization and a stratified 80/20 split, the training data set was partitioned into 4 folds (outer loop). Within each outer fold, an inner loop of 2 folds was used for hyperparameter tuning. The hyperparameter (lambda) that minimized the mean squared error in the inner loop was selected. The model with this optimal lambda was then evaluated on the validation fold of the outer loop. This process was repeated for all 4 outer folds, resulting in an optimal lambda for each fold. The final model was chosen using the average of the optimal lambdas from all outer folds. Finally, the performance of this final model was assessed using the unseen test set. GLMM = generalized mixed effects model; lasso = least absolute shrinkage and selection operator
To illustrate the level of uncertainty of the model coefficients, bootstrapping with 10,000 resamples was performed to estimate the bias-corrected and accelerated (BCa) confidence intervals for the model coefficients.
Additionally, and to test the relevance of leg movement on TM as a muscle group unaffected by thigh movement, we used a linear regression model for the prediction of TM atrophy at day 10 including all demographic, clinical and nutritional variables as well as %active as independent variables. To compare %active between healthy individuals and the neurointensive care unit (NICU) cohort, a two-tailed t-test was performed. Further, we identified patients with unilateral upper motor neuron damage and corresponding motor deficits to investigate the contribution of upper motor neuron lesion on muscle atrophy. To compare the magnitude of muscle atrophy and to account for within-subject correlation, we used Generalized Estimating Equations (GEE) with post hoc pairwise comparisons and Bonferroni adjustment.
Summary statistics for continuous variables are presented as means with standard deviation (SD) for normally distributed data and as medians with interquartile ranges (IQR) for non-normally distributed data, with normality assessed using Quantile–Quantile plots and Shapiro–Wilk test. Categorical variables are summarized as frequencies and percentages.
All analyses were performed using R (2023.06.1 + 524) using ‘stats’, ‘psych’, ‘ggplot2’, ‘dplyr’, ‘lme4’, ‘nlme’, ‘geepack’, ‘multcomp’, ‘emmeans’, ‘MASS’, ‘svglite’ ‘glmmLasso’,‘caret’ and ‘boot’, packages. ChatGPT (version 4) was used for error handling, repetitive programming, and overall optimization of code in R.
Out of 407 patients screened, 53 with a total of 91 available accelerometer datasets were enrolled in this study (Fig. 3 ). Clinical baseline characteristics are presented in Table 1 . Of all patients included in the analysis, mean age was 59.2 years (SD 15.9) and 31 (58.5%) were male. Cerebrovascular diseases were the most frequent ICU admission diagnoses (86.8%, 46/53). Mean ICU length of stay was 17.0 days (IQR 8.0), while the mean duration of mechanical ventilation was 15.6 days (SD 9.2). During the observation period, patients met 62.6% (SD 18.4) of the caloric goals and 57.9% (SD 21.6) of protein goals according to the ESPEN guidelines.
Screening and study inclusion. ICU = Intensive Care Unit;
Muscular atrophy as measured with ultrasound was more pronounced in RFM compared to TM (-19.5% (SD 12.0) versus -15.3% (SD 11.1) at day 10) (Fig. 4 A). Active movement of NICU patients as indicated by proportion of active movement (%active) over time is infrequent, particular at early stages of the ICU stay. While mean %active stays low over the entire time, some patients exhibit higher activity starting around day 3. (Fig. 4 B). Compared to healthy individuals, NICU patients demonstrate a significant reduction in active movement (%active: healthy individuals 13.3 (SD 0.8) vs. NICU patients 0.84 (SD 1.08), p < 0.001) (Supplementary Tables 2 and 4 ). No adverse events were observed in association with the placement of accelerometers in the ICU setting (Supplementary Table 3 ).
Active movement and muscle atrophy during ICU treatment. Muscle atrophy at days 3, 5 7 and 10 relative to day 0 for RFM and TM ( A ). Proportion of active movement (%active) over time ( B ). ICU = Intensive Care Unit;
The machine learning model based on a total of 12 demographic, clinical, nutritional and accelerometer-derived variables selected baseline RFM muscle mass (beta − 5.1, 95% confidence interval (95% CI) − 7.9 to − 3.8) and %active (beta 1.6, 95% CI 0.1 to 4.9) to explain 79% (R 2 = 79%) of the occurring variance in muscle wasting in an unseen test data set (Fig. 5 , A and B). Thus, for every standard deviation increase in baseline RFM (2.6 mm), RFM thickness at day 10 is estimated to decrease by another 5.1 percentage points (49.5% relative change). In contrast, a standard unit increase in %active (1.1%) is projected to result in 1.6 percentage points less RFM atrophy at day 10 (relative change 15.5%). Ignoring movement features as predictors for RFM muscle atrophy results in substantially worse model performance (R 2 = 55%) (Fig. 5 C, Supplementary Table 6 ). RFM atrophy was not significantly different between immobile limbs with upper motor neuron lesions (UMNL) and immobile limbs without UMNL. However, muscle atrophy was markedly decreased in limbs with active movement (Supplementary Fig. 2 ). Thigh-fixed accelerometer data did not contribute significantly to a model predicting TM atrophy (Supplementary Table 5 ).
Prediction of MRF muscle atrophy with and without movement features. Standardized coefficients and 95% confidence intervals (asterisks indicate significant predictors) of the regularized regression models with (model movement+ , A ) and without movement features (model movement− , C ). Out of all demographic (age, sex), clinical (baseline RFM muscle mass, mSOFA), nutritional (calorie deficit, protein deficit) and movement variables (intensity, %active, AB-intensity log-mean , AB-duration log-mean , AB-intensity log-SD , AB-duration log-SD ), the depicted 10/12 independent variables for model model movement+ and 4/6 independent variables for model movement− were selected for the final models, respectively. Significant predictors in model movement+ included baseline RFM muscle mass (beta − 5.1, 95% confidence interval (95% CI) − 7.9 to − 3.8) and %active (beta 1.6, 95% CI 0.1 to 4.9). For model movement- , only baseline RFM muscle was found as a statistically significant predictor (beta − 4.6, 95% CI − 7.6 to − 3.9). Scatter plots with regression line of predicted versus actual muscle wasting (grey dots: training data; black dots: unseen test data) for model movement+ ( B ) and model movement- ( D ), respectively (R 2 : 0.79 vs. 0.55, RMSE: vs. 8.4 vs. 10.7 mm; MAE: 6.2 vs. 8.0 mm). mSOFA = SOFA without GCS;
In this prospective cohort study, we used thigh-fixed accelerometers to establish movement features as predictive biomarkers for muscle atrophy in neurocritical care patients. Proportion of active movement (%active) demonstrated a significant protective effect against muscle wasting and improved the precision of muscle atrophy prediction in an unseen test data set. To the best of our knowledge, this is the first quantifiable and validated measure that provides information on the relative importance of inactivity for muscle atrophy in critically ill patients.
It is crucial to distinguish between immobility and inactivity, especially within the ICU context, as inactivity can occur despite mobilization efforts due to a lack of active patient participation (passive movement). To address this, we excluded periods such as physiotherapy, intrahospital transports, and patient positioning, from our analysis. Therefore, we consider the movement features as surrogates for activity rather than measures of mobility. Importantly, and as a limitation of this approach, movement sensors are unable to capture any muscle activity without movement via isometric contractions (active immobility).
The relevance of inactivity, as compared to immobility, as the variable of interest in this context is further exemplified by clinical trials on electrical muscle stimulation (EMS) and interventions focusing on early (passive) mobilization. The current evidence highlights the efficacy of EMS [ 23 , 24 ], whereas mobilization trials demonstrated limited efficacy and raised safety concerns [ 25 , 26 , 27 , 28 , 29 , 30 , 31 ]. While the latter often involve passive mobilization without genuine patient activity, EMS generates muscle activity without requiring mobility. Considering the data, a reasonable strategy to prevent muscle atrophy in critically ill patients may involve first measuring the extent of active movement with accelerometers to identify those at risk, and subsequently promoting activity (with or without mobilization) based on the patient's stability.
The pathophysiology of mechanical unloading leading to atrophy has so far only been systematically studied and quantified outside the ICU. Studies with cast immobilization of the lower extremity for two weeks in healthy adults and examination of astronauts after 8 days of space flight revealed a 5% and 6% decrease in quadriceps muscle mass, respectively [ 32 , 33 ]. A recent meta-analysis analyzing the general ICU population estimated muscle atrophy to be around 16% at day 10 for RFM [ 34 ]. In comparison, our data demonstrate a more pronounced rate of RFM atrophy, showing a 19.5% decrease by day 10. While additional factors such as CIP, CIM, and CIPNM certainly contribute to the higher rate of atrophy in ICU patients, the residual activity in cast immobilization (via isometric contractions) and during space flight (via active movement with reduced muscle activity) may also account for the observed differences.
Given that no or passive movement was described in more than 70% of patients in the first 48 h, and still more than 40% after two weeks, in the TEAM trial [ 26 ], it is plausible to assume that inactivity also significantly contributes to ICUAW in the general ICU population. Yet, as disorders of consciousness and focal-neurological deficits are major barriers to mobilization and activity [ 26 ], this might be even more relevant for neurointensive care patients. Although our accelerometer data are not directly comparable to the ICU mobility scale used in the TEAM trial, it indicates extremely infrequent periods of active movement for most patients over a 10-day observation period, reaching only 6% (0.84/13.3) of the activity level of healthy individuals. These numbers are parallelled by data from González-Seguel et al., who found mechanically ventilated patients to be inactive during the ICU stay in over 96% of the time [ 35 ]. This, coupled with the prominence of movement features as predictors of muscle atrophy in our prospective cohort, further strengthens the significance of inactivity in (neuro-) critical care. Other studies within the ICU have investigated accelerometry primarily in the context of sleep, circadian rhythm, and sedation levels. However, these studies exhibit limitations, such as narrow observation periods and the absence of well-defined thresholds for activity measurement [ 36 , 37 , 38 , 39 ].
Accelerometer-derived data have also been validated as biomarkers for muscle atrophy outside the ICU setting. In a study with almost 500 elderly participants, Sanchez-Sanchez et al. investigated the association of physical activity as measured with hip-worn accelerometers and sarcopenia. Here, higher physical activity correlated with better performance in sarcopenia-related scores [ 40 ]. Similarly, Foong et al. showed a positive association of accelerometer-derived physical activity with muscle mass and muscle strength [ 41 ].
The exercise stimulus, as the ultimate determinant for activity, can be delineated into two primary variables: volume and intensity. In exercise physiology, the volume of exercise is traditionally quantified by the number of repetitions performed, while intensity is commonly measured by the force exerted during exercise [ 42 ]. In our ICU cohort, we utilized proportion of active movement (%active) and AB-duration log-mean as proxies for exercise volume. For critically ill patients, the force generated cannot be measured pragmatically. We therefore introduced movement intensity (resultant acceleration magnitude) as a surrogate of exercise intensity. The LASSO regularization used to address the high number and potential co-linearity of parameters revealed %active as an approximation of exercise volume as a relevant predictor, while surrogates of intensity were not selected. Thus, intensity may either be irrelevant considering the uniform force generated by patients moving against gravity and not against resistance, or movement intensity is not a valid biomarker of the exercise intensity.
Besides proportion of active movement, baseline muscle mass was predictive of muscle atrophy. This finding is in line with studies in healthy participants. Here, higher age with lower baseline muscle mass showed significantly less pronounced atrophy. However, older participants with lower baseline muscle mass suffered from greater loss of muscle strength after immobilization [ 43 , 44 , 45 ]. Furthermore, variations in atrophy can be observed across muscle and fiber types. Anti-gravity muscles with high proportions of slow type 1 fibers, such as RFM, seem to exhibit a selective vulnerability [ 45 ], which is in line with our data demonstrating pronounced atrophy of RFM over TM.
The strengths of our study include the selection of a neurointensive care population devoid of frailty, specifically targeting individuals at high risk of muscle atrophy without pre-existing muscle wasting. However, the study's focus on neurocritical care may limit its generalizability and further research is needed to confirm the applicability of our results to more diverse patient populations. The extent of neurogenic atrophy mediated via various damage to the lower motor neuron was not explicitly measured in our study but can be assumed to be minimal given the demographics of our cohort. As that general ICU cohorts also experience lower motor neuron lesions due to critical illness or its treatments, this confounder is likely to be similar across groups. For UMNL, we do not expect neurogenic atrophy, as it does not result in direct muscle denervation. Supporting this pathophysiological hypothesis, we could not observe any difference in the extent of muscle atrophy between immobile limbs with upper motor neuron lesions (UMNL) and immobile limbs without UMNL. However, muscle atrophy was markedly decreased in limbs with active movement, suggesting no role for UMNL as a mediator for atrophy. We ensured high data quality by filtering out passive mobilization and prospectively collecting clinical data. Furthermore, our analysis is underpinned by a strong statistical framework leveraging machine learning to identify the most important predictors and using unseen data to validate these findings. Further limitations of our study are primarily rooted in the fact that muscle morphology does not necessarily equate to function. We used muscle ultrasound, a widely adopted and validated surrogate for ICUAW [ 34 , 46 , 47 ], instead of the Medical Research Council Sum Score (MRC-SS), as the latter is often deemed infeasible in the general ICU cohort, and even more so in neurocritical care. Additionally, we decided against including measures of the upper extremities because muscle volume is challenging to determine via ultrasound due to variability in muscle thickness relative to positioning, difficult anatomical landmarks, and less pronounced atrophy compared to the lower extremities. Instead, we focused on the RFM as the established sonographic gold standard, along with the TM as a muscle group unrelated to the movement captured by the accelerometers.
Active movement, as a surrogate of muscle activity, can be quantified using non-invasive, thigh-fixed accelerometers and adds value for the prediction of muscle atrophy in neurocritical care patients. Establishing movement-derived biomarkers enables better phenotyping of ICUAW, thereby providing a foundation for tailored interventions and should be included as covariates in trials on ICUAW in the future. Studies addressing the external validity of these findings beyond the neurointensive care unit are warranted.
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. Matlab code for analyzing motion features is available at https://github.com/DSGZ-MotionLab/ICU_motion_analysis/ .
Activity bout
Acute physiology and chronic health evaluation II
Bias-corrected and accelerated
Body mass index
Confidence interval
Critical illness myopathy
Critical illness polyneuropathy
Critical illness polyneuromyopathy
Energy expenditure
Electrical muscle stimulation
European Society of Parenteral and Enteral Nutrition
Glasgow Coma Scale
Generalized Estimating Equations
Generalized linear mixed model
Glasgow Outcome Scale—Extended
High/low pass filter
Intensive care unit
Intensive care unit acquired weakness
Least Absolute Shrinkage and Selection Operator
Length of stay
Metabolism and nutrition in neurointensive care
Medical Research Council Sum Score
Modified SOFA
Nerve conduction studies
Neurointensive care unit
Nutrition risk in the critically ill
Post intensive care syndrome
Premorbid modified Rankin scale
Quantile–Quantile
Rectus femoris muscle
Signal magnitude area
Sequential organ failure assessment
Temporalis muscle
Upper motor neuron lesion
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The authors thank the staff of the neurological and neurosurgical intensive care units at LMU Munich for their great interest and cooperation.
Open Access funding enabled and organized by Projekt DEAL. MLS was supported by the Deutsche Forschungsgemeinschaft (TRR 274) and Stiftungen zugunsten der Medizinischen Fakultät (LMU Munich).
Moritz L. Schmidbauer, Timon Putz, Max Wuehr and Konstantinos Dimitriadis have contributed equally to this work.
Department of Neurology, LMU University Hospital, LMU Munich, Munich, Germany
Moritz L. Schmidbauer, Timon Putz, Leon Gehri, Luka Ratkovic, Andreas Maskos, Julia Zibold, Johanna Bauchmüller, Sophie Imhof, Max Wuehr & Konstantinos Dimitriadis
Department of Anaesthesiology, LMU University Hospital, LMU Munich, Munich, Germany
Thomas Weig
German Center for Vertigo and Balance Disorders (DSGZ), LMU University Hospital, LMU Munich, Munich, Germany
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Conceptualization, methodology, validation: MLS, MW, KD. Data curation, formal analysis, visualization, software: MLS, MW. Investigation: TP, LG, LR, AM. Writing—original draft: MLS, TP, MW. Writing—review and editing: LG, LR, AM, JZ, TW, KD. Resources: MW, TW, KD. Project administration, supervision, funding acquisition: MLS, KD. All authors reviewed the manuscript.
Correspondence to Moritz L. Schmidbauer .
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Approval for this study was granted by the local ethics committee (LMU Munich, approval number: 22-0173, data of approval: 11.04.2022). This study was conducted in accordance with the Declaration of Helsinki and ethical guidelines for medical and health research involving human subjects. Written informed consent was obtained from all patients or next of kin.
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Supplementary Figure 1. Accelerometer placement. Figure 2. Influence of movement and upper motor neuron lesion on muscle atrophy. Table 1. Reliability of RFM ultrasound measurements. Table 2. Negative and positive controls. Table 3. Adverse events of accelerometer placement. Table 4. Accelerometer data. Table 5. Linear regression model for TM atrophy. Table 6. Performance metrics of models with and without movement features.
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Schmidbauer, M.L., Putz, T., Gehri, L. et al. Accelerometer-derived movement features as predictive biomarkers for muscle atrophy in neurocritical care: a prospective cohort study. Crit Care 28 , 288 (2024). https://doi.org/10.1186/s13054-024-05067-y
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DOI : https://doi.org/10.1186/s13054-024-05067-y
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Present the findings in your results and discussion section. Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps. Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test.
Hypothesis testing involves five key steps, each critical to validating a research hypothesis using statistical methods: Formulate the Hypotheses: Write your research hypotheses as a null hypothesis (H 0) and an alternative hypothesis (H A). Data Collection: Gather data specifically aimed at testing the hypothesis.
A hypothesis test consists of five steps: 1. State the hypotheses. State the null and alternative hypotheses. These two hypotheses need to be mutually exclusive, so if one is true then the other must be false. 2. Determine a significance level to use for the hypothesis. Decide on a significance level.
In hypothesis testing, the goal is to see if there is sufficient statistical evidence to reject a presumed null hypothesis in favor of a conjectured alternative hypothesis.The null hypothesis is usually denoted \(H_0\) while the alternative hypothesis is usually denoted \(H_1\). An hypothesis test is a statistical decision; the conclusion will either be to reject the null hypothesis in favor ...
A hypothesis test is a statistical inference method used to test the significance of a proposed (hypothesized) relation between population statistics (parameters) and their corresponding sample estimators. In other words, hypothesis tests are used to determine if there is enough evidence in a sample to prove a hypothesis true for the entire population. The test considers two hypotheses: the ...
Hypothesis testing is a crucial procedure to perform when you want to make inferences about a population using a random sample. These inferences include estimating population properties such as the mean, differences between means, proportions, and the relationships between variables. This post provides an overview of statistical hypothesis testing.
HYPOTHESIS TESTING. A clinical trial begins with an assumption or belief, and then proceeds to either prove or disprove this assumption. In statistical terms, this belief or assumption is known as a hypothesis. Counterintuitively, what the researcher believes in (or is trying to prove) is called the "alternate" hypothesis, and the opposite ...
Test Statistic: z = x¯¯¯ −μo σ/ n−−√ z = x ¯ − μ o σ / n since it is calculated as part of the testing of the hypothesis. Definition 7.1.4 7.1. 4. p - value: probability that the test statistic will take on more extreme values than the observed test statistic, given that the null hypothesis is true. It is the probability ...
The above image shows a table with some of the most common test statistics and their corresponding tests or models.. A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently supports a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic.Then a decision is made, either by comparing the ...
Components of a Formal Hypothesis Test. The null hypothesis is a statement about the value of a population parameter, such as the population mean (µ) or the population proportion (p).It contains the condition of equality and is denoted as H 0 (H-naught).. H 0: µ = 157 or H0 : p = 0.37. The alternative hypothesis is the claim to be tested, the opposite of the null hypothesis.
Step 1: Using the value of the mean population IQ, we establish the null hypothesis as 100. Step 2: State that the alternative hypothesis is greater than 100. Step 3: State the alpha level as 0.05 or 5%. Step 4: Find the rejection region area (given by your alpha level above) from the z-table.
First, the technical definition of power is 1−β. It represents that given an alternative hypothesis and given our null, sample size, and decision rule (alpha = 0.05), the probability is that we accept this particular hypothesis. We visualize the yellow area below. Second, power is really intuitive in its definition.
Hypothesis testing is a technique that is used to verify whether the results of an experiment are statistically significant. It involves the setting up of a null hypothesis and an alternate hypothesis. There are three types of tests that can be conducted under hypothesis testing - z test, t test, and chi square test.
Hypothesis testing is the process that an analyst uses to test a statistical hypothesis. The methodology depends on the nature of the data used and the reason for the analysis.
Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population. It involves formulating two competing hypotheses, the null hypothesis (H0) and the alternative hypothesis (Ha), and then collecting data to assess the evidence. ...
Hypothesis Testing Steps. There are 5 main hypothesis testing steps, which will be outlined in this section. The steps are: Determine the null hypothesis: In this step, the statistician should ...
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses, by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
Aug 5, 2022. --. 6. Photo by Andrew George on Unsplash. Student's t-tests are commonly used in inferential statistics for testing a hypothesis on the basis of a difference between sample means. However, people often misinterpret the results of t-tests, which leads to false research findings and a lack of reproducibility of studies.
A hypothesis test is a procedure used in statistics to assess whether a particular viewpoint is likely to be true. They follow a strict protocol, and they generate a 'p-value', on the basis of which a decision is made about the truth of the hypothesis under investigation.All of the routine statistical 'tests' used in research—t-tests, χ 2 tests, Mann-Whitney tests, etc.—are all ...
3. One-Sided vs. Two-Sided Testing. When it's time to test your hypothesis, it's important to leverage the correct testing method. The two most common hypothesis testing methods are one-sided and two-sided tests, or one-tailed and two-tailed tests, respectively. Typically, you'd leverage a one-sided test when you have a strong conviction ...
Hypothesis testing in statistics refers to analyzing an assumption about a population parameter. It is used to make an educated guess about an assumption using statistics. With the use of sample data, hypothesis testing makes an assumption about how true the assumption is for the entire population from where the sample is being taken.
Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps. 1. Formulate the null hypothesis H_0 (commonly, that the observations are the result of pure chance) and the alternative hypothesis H_a (commonly, that the observations show a real effect combined with a component of chance ...
Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data.
Definition and Scope of Value Hypothesis. Let's get into the step-by-step process, but first, we need to understand the basics of the Value Hypothesis: ... MVP Testing. Build a minimum viable product (MVP)—a basic version of your product with essential functions. This lets you test your value proposition with actual users and get feedback ...
Background Physical inactivity and subsequent muscle atrophy are highly prevalent in neurocritical care and are recognized as key mechanisms underlying intensive care unit acquired weakness (ICUAW). The lack of quantifiable biomarkers for inactivity complicates the assessment of its relative importance compared to other conditions under the syndromic diagnosis of ICUAW. We hypothesize that ...