Repeated Measures Design PDF

1 REPEATED MEASURE DESIGN SUBMITTED TO DR. MUSARRAT JABEEN SUBMITTED BY HAJRA JAVED (008503/MSCP/F24) LAIBA IKRAM (006272/MSCP/F24) ALISHBHA SHER (007354/MSCP/F24) AMBER MASOOD (008502/MSCP/F24) ATTIQA SIDDI...

1 REPEATED MEASURE DESIGN SUBMITTED TO DR. MUSARRAT JABEEN SUBMITTED BY HAJRA JAVED (008503/MSCP/F24) LAIBA IKRAM (006272/MSCP/F24) ALISHBHA SHER (007354/MSCP/F24) AMBER MASOOD (008502/MSCP/F24) ATTIQA SIDDIQUE (007352/MSCP/F24) ALEENA KHAN (007351/MSCP/F24) DATE 23rd NOVEMBER 2024 PSYCHOLOGY DEPARTMENT FACULTY OF SOCIAL SCIENCES INTERNATIONAL ISLAMIC UNIVERSITY ISLAMABAD  2 Repeated Measure Design Definition A Repeated Measures design is an experimental design where the same group of participants takes part in all conditions of Independent Variable. In other words, each participant experiences every condition of the experiment and the subjects serve as their own controls. This design is also called a within-groups or within-subjects design. Example Consider the experimenter testing how different types of exercise (yoga and jogging) affect memory. Instead of dividing participants into two separate groups, all the participants try yoga first before taking a memory test. Then, all the participants try jogging before taking a memory test. Next, the experimenter compares the test scores to determine which type of exercise had the most significant effect on performance on the memory tests. Uses of Repeated Measure Design There are some conditions when to use repeated measures design; Conduct an experiment when few participants are available Since the same participants take part in all conditions, fewer people are needed to conduct the experiment. This helps reduce the variation in results and allows researchers to make statistical inference or conclusions with fewer participants.  3 Conduct experiment more efficiently Repeated measures designs make experiments to be completed faster and more efficient because fewer groups need to be trained to complete the whole experiment. There are many experiments where each condition takes few minutes but the time spent training participants to do those tasks can be just as long, or even longer. So, the training process can take up a significant portion of the total experiment time. Study changes in participant’s behavior over time Repeated measures designs allow researchers to monitor how participants' behavior changes over time. This can be for long-term studies (like tracking changes over years) or short- term studies (like seeing how practice affects performance). Characteristics of Repeated Measure Design The following are the characteristics of repeated measure design; 1. The subject participates in all conditions of the experiment i.e., repeated measurements are taken from same subjects. 2. The subjects serve as their own controls because they participate in both the experimental and control conditions. 3. This design study changes in participants’ behavior over time. Steps Involved in Repeated Measure Design Following steps are involved in administering a simple repeated measure design;  4 1. In the first step, a sample of participants is randomly selected from population. 2. In second step, all participants receive the same treatments usually called the conditions. 3. In third step, each participant is undergone through a pretest in a control condition. 4. In fourth step, each participant is given all possible treatments and scores are analyzed. 5. In fifth step, a posttest is conducted and scores are examined. 6. In sixth step, scores are analyzed using statistical methods. Threats to internal validity of Repeated Measure Design Within-subjects designs have more statistical power than between-subjects designs, but without a control group, there are a number of potential threats to their internal validity. Maturation effects A maturation effect occurs when changes in a score over time are due to naturally occurring internal processes such as changes in cognition or getting smarter as you get older. For example, if a teacher wants to test the effectiveness of new curriculum and tests first graders' math skills at the start and end of the year, improvements might be because the kids are growing, not just because of a new teaching method. History effects Whereas maturation effects involve an internal process, history effects involve an external event that occurs between the two measurements. For example, consider a researcher testing whether a particular chemical increases anxiety. The researcher measures New York City residents' anxiety on September 5, 2001, gives them the drug, and measures them again 20 days later. Scores  5 are likely to have increased because of the terrorist attacks on September 11 – an external event. History effects can also include things like weather changes or new laws that impact people's mood or stress. Testing effects A testing effect occurs when the pretest itself influences the post-test. The most typical example of testing effects is a practice effect. Participants’ performance in repeated measure design may change across conditions simply because of repeated testing (not because of the independent variable); these changes are called practice effects. It threatens the internal validity when the conditions of independent variable are presented in the same order to all participants. There are two forms of practice effect i.e., positive and negative practice effect. In positive practice effect, repeating the same experience can lead to improvements in performance (e.g., efficiency, speed etc.). While a negative practice effect leads to fatigue where participants perform worse after repeated testing. If performance is being measured multiple times, it is possible that performance will decrease in later conditions simply because the participant is getting tired, feeling demotivated and experience boredom. Techniques to manage or overcome threats to internal validity In order to overcome the practice effect, counterbalancing technique is used. In this technique, when there are two possible conditions A and B, the participant sample is divided in two halves; one half completing the conditions in one order and the other half completing the conditions in the reverse order. If you  6 have three conditions, the process is exactly the same and you would divide the subjects into 6 groups, treated as orders ABC, ACB, BAC, BCA, CAB and CBA. The maturation effects can be ruled out by the addition of control group. Comparing the experimental group to the control group helps determine if changes are due to the treatment or natural maturation. Also, Shorten the study or measurement duration to reduce the effects of natural changes. Using a control group can help in reducing the history effects, as changes in the experimental group can be compared to the control group who didn’t experience the external event. By taking multiple measurements throughout the study, the researcher can monitor if external events are influencing the results at specific times. But addition of a control group (would make them mixed designs because they now have a mix of both within-subjects and between-subjects independent variables). Types of Repeated Measures Designs Crossover design This is the type of repeated measures designs in which participants experience multiple conditions in a counterbalanced order (systematic variation of the sequence in which participants are exposed to different treatments or conditions).  7 Sequence Period 1 Period 2 1 A B 2 B A Each participant act as their own control group, thus allowing for direct comparison between treatments. It involves a single group of participants. Participants alternate between experimental conditions and a washout period is included to diminish carry-over affect (residual effect of the prior given treatment) before starting the next treatment. A pre-test is conducted on participants before giving them any treatment and then post- test is conducted after each treatment phase to evaluate the treatment effectiveness. For example. Researcher wants to test the effects of two drugs Drug A and Drug B on the blood pressure. He gives half of the participants Drug A first and then after the washout period the researcher gives Drug B to these participants. As for the other half of the participants, researcher gives them Drug B first, and then gives them Drug A after the washout period. Split plot design In Split plot repeated measures design, one groups of participants (or experimental units) are exposed to multiple conditions or treatments over time. It combines two factors; one is whole plot factor (multiple conditions or treatment) and the other is sub-plot factor (repeated measurement of participants across different time points). A pre-test is conducted to measure the participants’ performance or behaviour before giving any treatment. Then, the intervention (whole plot) is given  8 to the participants and then the same participants are measured multiple times at different time points (sub plot factor). At the end, post-test is conducted by the researcher to observe any changes that might have occurred as a result of the treatment. For example. Let’s say a researcher wants to check the effects of two different exercise programs (strength training program and cardiovascular training program) on physical fitness of participants. Here the whole plot is two different exercise programs (or conditions) and the sub plot is that researcher examines the participants at different time points such as, after 1 week, 2 weeks and 3 weeks of doing the exercise program. The researcher then measures how the outcomes such as performance, physical fitness or behaviour of participants changed over time or across different conditions such as, strength training program and cardiovascular training program. Longitudinal design This type of repeated measure designs focuses on one treatment, condition or a natural progression of a variable with repeated measures at multiple time points. In this research design, there is one group of participants and the same group of participants is measured repeatedly over time at pre-defined intervals to observe how they change and develop over the time. For example. A researcher used longitudinal repeated measure design to study the effect of new exercise program (program XYZ) on the physical fitness level of the participants. For this purpose, researcher selects a single group of participants and all participants are engaged in the same exercise program. Then researcher assesses their physical fitness level repeatedly at regular intervals over time to track progress and long-term effect.  9 Intervals Performance Month 0 (Baseline) Pre-test to measure initial fitness level Month 3 First follow up fitness assessment Month 6 Second follow up fitness assessment Month 12 Final assessment to evaluate outcomes Approaches to Repeated Measure Data Repeated measures data involve multiple measurements from the same subject over time or space, analyzed using repeated measures ANOVA, mixed models, or marginal models. These methods vary in assumptions and data handling but may yield similar outcomes in certain designs. Each person may have as little as two measurements or as many as twenty, and time may or may not be a significant role. Approach 1: Repeated Measure ANOVA Description. Repeated Measure ANOVA is a method which is used to analyze data when the same outcome is measured multiple times for each individual. The data is organized in wide formats where each individual has one row and their repeated measures are in different columns. Each measurement is treated as a separate variable in a multivariate approach. Analysis. It is often taught in statistics courses as part of ANOVA methods and is conducted as a MANOVA (Multivariate Analysis of Variance), where each measurement is treated as a separate variable, and multiple dependent variables and residuals are analyzed together. In  10 software like SPSS, this is performed using the Repeated Measures General Linear Model (GLM) procedure. The Repeated Measures General Linear Model (GLM) in SPSS analyzes data from participants tested multiple times or under different conditions. It accounts for correlations in repeated data, handles missing values, and tests for main effects and interactions between variables. Example. A researcher assesses weight loss from three diets (A, B, C) over 8 weeks in 10 participants, measured at Week 1, Week 4, and Week 8. Data is in wide format, and Repeated Measures ANOVA shows a significant main effect of time, indicating overall weight loss. However, no post-hoc tests are available, and missing data reduces statistical power Advantages. The advantages of Repeated Measure ANOVA are given below: 1. This approach has conceptual simplicity, meaning it is easy to understand and implement, making it particularly appealing for basic repeated measures designs. It is simple and clear, working well for straightforward experimental settings where the variables and conditions are clearly defined, and the design is easy to manage. 2. This approach is suitable for experiments as it works well in controlled experimental conditions, where measurements are taken under distinct setups, such as testing the effect of different treatments. Disadvantages. The disadvantages of Repeated Measure ANOVA are given below: 1. This approach has strict assumptions, requiring balanced data, meaning that every individual must have all measurements. If any measurement is missing, the entire  11 individual is removed from the analysis. Additionally, it assumes equal correlations between measurements (known as sphericity) and equal variances across the measurements. 2. One limitation of this approach is that it does not allow for detailed comparisons, or post-hoc tests, between individual time points or conditions. This restricts the ability to explore and analyze the specific differences between conditions in greater detail. Approach 2: The Marginal Model Description. The Marginal Model treats repeated responses as multilevel data, where the outcome is a single variable and another variable indicates the condition or time measurement. This approach requires the data to be in a long format, or stacked data, which means that each subject has multiple rows of data in the spreadsheet. The unit of analysis is changed from the subject level to each measurement occasion. Analysis. In the Marginal Model (also known as the population-averaged model), the model equation is written like any linear model, with a single response and a single residual. Unlike the Repeated Measures ANOVA, the Marginal Model does not assume residuals are independent with constant variance. The residuals for each individual can be correlated, and these correlations can vary. The residuals across different individuals are assumed to be independent. Generalized Estimating Equations (GEE) handle correlated data by accounting for relationships within repeated measures, estimating the population's average response. Generalized Linear Models (GLM) extend linear regression to different data types and distributions, offering flexibility in analyzing correlated data.  12 Example. A researcher investigates how three treatments (A, B, C) affect blood pressure in 10 patients at three time points: before treatment (Week 0), after one month (Week 1), and after three months (Week 3). The data is organized in a long format, with each patient having three rows for each time point. Using Generalized Estimating Equations (GEE), the researcher analyzes correlations between repeated measurements for each patient, accounts for unequal variances across time, and conducts post-hoc tests to compare blood pressure at specific time points (e.g., Week 0 vs. Week 3), providing a clear understanding of treatment effects. Advantages. The advantages of Marginal Model are given below: 1. This model allows flexible specification of correlations between repeated measurements, accounting for stronger correlations between closer time points, leading to a more accurate data representation. 2. It does not require equal variances or correlations, unlike Repeated Measures ANOVA, allowing for better fitting when these assumptions are not met. 3. A univariate approach enables the use of post-hoc tests on the repeated measures factor, offering greater flexibility in data analysis. Disadvantages. The disadvantages of Marginal Model are given below: 1. Requires long format data, where each subject has multiple rows for each measurement occasion. 2. Involves complexity in implementation due to the need to understand multilevel data (i.e., how measurements are related within and between subjects) and  13 correlation structures, making it more challenging than simpler methods like ANOVA. 3. Assumes independence of residuals across individuals, which may not always hold true in real-world scenarios. Approach 3: The Linear Mixed Model Description. The Linear Mixed Model (LMM) is a statistical method used for analyzing data where multiple measurements are made from the same individuals, typically in repeated measures or clustered data. Like the marginal model, it requires the data to be in long format, where each subject has multiple rows for different time points or conditions. However, LMM takes a different approach by adding random effects for individuals, which allows it to account for non- independence among repeated observations. This model controls for individual differences by estimating the variance for each individual’s random effects, which helps to explain variations in the data that may not be captured by fixed effects alone. The model equation incorporates additional parameters for random effects, represented as extra residual terms, with the model estimating their variance. Analysis. The Linear Mixed Model (LMM) includes both fixed effects (such as treatment conditions or time) and random effects (such as individual differences), providing a more nuanced understanding of the data. It estimates random effects by introducing additional residual terms to the model. This allows for better handling of individual variations in outcomes. For example, the simplest form the random intercept model controls for the fact that some individuals consistently  14 have higher or lower values than others, thus separating this variability from the general residual error. One specific application of LMM is the individual growth curve model, which models how each individual’s outcome changes over time, allowing researchers to investigate not only the effect of predictors on the value of the dependent variable but also on how these values change over time. Example. A researcher is studying the effect of three study strategies (Strategy A, B, and C) on students' test scores over a semester, with data collected from 30 students at four time points: before the study period (Week 0), after four weeks (Week 4), eight weeks (Week 8), and twelve weeks (Week 12). Each student's test scores are recorded at each time point. For example, Student 1's test scores are 60% at Week 0, 70% at Week 4, 75% at Week 8, and 80% at Week 12, while Student 2's test scores are 65% at Week 0, 72% at Week 4, 78% at Week 8, and 85% at Week 12. The researcher employs a linear mixed model (LMM) with fixed effects for study strategy and time, and random effects for individual students. This approach captures variability in baseline scores and score changes over time, assessing strategy effectiveness while accounting for individual differences. Advantages. The advantages of Linear Mixed Model are given below: 1. The linear mixed model can handle clustered and repeated measures data, making it adaptable for various types of research designs. 2. It can be used with unbalanced data, allowing for missing observations without excluding participants.  15 3. Time can be treated either as continuous or categorical, based on the research design. 4. The model combines random effects (e.g., individual differences) and fixed effects (e.g., treatments) while handling complex relationships, such as crossed random factors, where data points are influenced by multiple overlapping groups. Disadvantages. The disadvantages of Linear Mixed Model are given below: 1. The main drawback of mixed models is their flexibility, which can lead to mis- specification and inaccurate results, especially for beginners with limited understanding. 2. Additionally, mixed models require careful specification, including a strong understanding of the data structure, random effects, and correlation structures. Improper specification can result in misleading conclusions. MANOVA MANOVA is an extension of ANOVA that examines multiple dependent variables (DVs) simultaneously to determine if the groups (based on independent variables) differ significantly across these variables. Repeated Measures and MANOVA. In repeated measures designs, the same subjects are measured under different conditions or across multiple time points. MANOVA can be adapted to analyze repeated measures data by treating the repeated measurements as multiple dependent variables.  16 For example. If participants are tested on a variable across three time points (e.g., pre-test, mid-test, post-test), MANOVA can examine if there are significant differences across time points (treating these as separate DVs). MANOVA (multivariate analysis of variance) is a type of multivariate analysis used to analyze data that involves more than one dependent variable at a time. MANOVA allows us to test hypotheses regarding the effect of one or more independent variables on two or more dependent variables. The obvious difference between ANOVA and the “Multivariate Analysis of Variance” (MANOVA) is the “M”, which stands for multivariate. In basic terms, MANOVA is an ANOVA with two or more continuous response variables. Like ANOVA, MANOVA has both the one-way flavor and a two-way flavor. The number of factor variables involved distinguishes the one-way MANOVA from a two-way MANOVA. When comparing the two or more continuous response variables by the single factor, a one-way MANOVA is appropriate (e.g., comparing ‘test score’ and ‘annual income’ together by ‘level of education’). The two-way MANOVA also entails two or more continuous response variables, but compares them by at least two factors (e.g., comparing ‘test score’ and ‘annual income’ together by both ‘level of education’ and ‘zodiac sign’). Limitations of MANOVA. The limitations of MANCOVA are given below 1. MANOVA assumes that the differences between repeated measures (like time points) are consistent. If they’re not, the results might be wrong.  17 2. You need a lot of participants for reliable results. Small samples can make the results unstable. 3. If some participants miss a test or time point, MANOVA often excludes them, which can weaken your study. 4. If your experiment has too many groups, variables, or complicated structures, MANOVA becomes difficult to use and might not work well. 5. The results can be hard to interpret, especially if you’re comparing many variables at once. MANCOVA MANCOVA (Multivariate Analysis of Covariance) can be applied to repeated measures data, but it’s less common than other methods like mixed-effects models or repeated-measures ANOVA. MANCOVA is an extension of MANOVA that examines multiple dependent variables (DVs) simultaneously, while also controlling for the effect of covariates (continuous variables that might influence the DVs). It helps determine if groups differ significantly across DVs after accounting for the covariates. Repeated Measures and MANCOVA. In repeated measures designs, the same participants are measured under different conditions or across time points. MANCOVA can be used for such data by treating the repeated measures as multiple dependent variables and including covariates to control for their effects on the DVs. For Example. Participants’ performance is measured at three time points (pre-test, mid-test, post-test), and IQ is included as a covariate to account for its influence on performance scores.  18 MANCOVA examines whether there are significant differences across time points after controlling for IQ. In MANCOVA, we assess for statistical differences on multiple continuous dependent variables by an independent grouping variable, while controlling for a third variable called the covariate; multiple covariates can be used, depending on the sample size. Covariates are added so that it can reduce error terms and so that the analysis eliminates the covariates’ effect on the relationship between the independent grouping variable and the continuous dependent variables. ANOVA and ANCOVA, the main difference between the MANOVA and MANCOVA, is the “C,” which again stands for the “covariance.” Both the MANOVA and MANCOVA feature two or more response variables, but the key difference between the two is the nature of the IVs. While the MANOVA can include only factors, an analysis evolves from MANOVA to MANCOVA when one or more covariates are added to the mix. Limitations of MANCOVA. The limitations of MANCOVA are given below 1. MANCOVA assumes covariates (e.g., age, IQ) and dependent variables (e.g., test scores) have a simple, straight-line relationship. If this isn’t the case, results might be inaccurate. 2. It assumes that the differences between repeated measures (e.g., pre-test to post-test) are consistent. If not, the results can be incorrect unless adjusted. 3. MANCOVA works best with a large number of participants. A small sample size can lead to unstable or unreliable results. 4. If participants miss some measurements, MANCOVA excludes them, which can weaken the results.  19 5. Setting up and interpreting MANCOVA can be challenging, especially with many covariates and dependent variables, as too many covariates may make the model overly specific and reduce its generalizability. The Paired t-Test A paired t-test is a statistical test used to compare the means of two related groups or measurements. It is commonly applied in repeated measures designs, where the same participants are measured under different conditions or at multiple time points. A paired t-test is a method used to test whether the mean difference between pairs of measurements is zero or not. You can use the test when your data values are paired measurements. For example, you might have before-and-after measurements for a group of people. Also, the distribution of differences between the paired measurements should be normally distributed. What are some other names for the paired t-test? The paired t-test is also known as the dependent samples t-test, the paired-difference t-test, the matched pairs t-test and the repeated-samples t-test. For the paired t-test, we need two variables. One variable defines the pairs for the observations. The second variable is a measurement. Sometimes, we already have the paired differences for the measurement variable. Other times, we have separate variables for “before” and “after” measurements for each pair and need to calculate the differences. We also have an idea, or hypothesis, that the differences between pairs is zero. For example, a group of people with dry skin use a medicated lotion on one arm and a non-medicated lotion on their other arm. After a week, a doctor measures the redness on each arm. We want to  20 know if the medicated lotion is better than the non-medicated lotion. We do this by finding out if the arm with medicated lotion has less redness than the other arm. Since we have pairs of measurements for each person, we find the differences. Then we test if the mean difference is zero or not. Assumptions. To apply the paired t-test to test for differences between paired measurements, the following assumptions need to hold: 1. Subjects must be independent. Measurements for one subject do not affect measurements for any other subject. 2. Each of the paired measurements must be obtained from the same subject. For example, the before-and-after weight for a smoker in the example above must be from the same person. 3. The measured differences are normally distributed. Limitations of the paired t-test. The limitations of paired t -test are given below 1. It can only compare two time points or conditions (e.g., before vs after). 2. The differences between paired values must be normally distributed. 3. Extreme values can affect the results. 4. It works only with ratio/ interval data like test scores or weight, not ranked or categorical data. 5. It requires complete data from all participants. Advantages of Repeated Measures Design Increased Statistical Power  21 One of the key strengths of repeated measures designs is their ability to reduce variability caused by individual differences. Since the same participants are used across all experimental conditions, differences due to factors like age, ability, or IQ are eliminated. This enhanced control over variability leads to greater statistical power, allowing researchers to detect significant effects even with smaller sample sizes. Longitudinal Insights Repeated measures designs are particularly valuable in studies requiring data collection over time. They enable researchers to track changes or trends within the same participants, providing a comprehensive understanding of how interventions or treatments impact subjects. This is especially useful in medical, psychological, and educational research, where long-term outcomes are critical. Efficient Use of Data Compared to independent groups designs, repeated measures studies require fewer participants to achieve robust results. By using the same participants across conditions, researchers gather more data points per subject, optimizing data collection and making studies more efficient, especially when resources are limited. Control Over Individual Differences Individual differences, such as personality traits, cognitive abilities, or physical health, remain consistent across experimental conditions in repeated measures designs. This control ensures that the observed differences in outcomes are more likely due to the manipulation of the independent variable rather than variations between participants.  22 Cost-Effectiveness Repeated measures designs are cost-effective as they reduce the need for recruiting large participant pools. With fewer participants required, resources such as time, money, and materials can be allocated more efficiently, making this approach ideal for studies with tight budgets. Simplified Recruitment Recruiting participants can often be a challenging and time-consuming process. However, since repeated measures designs require fewer participants, recruitment becomes quicker and easier, enabling researchers to start their studies without prolonged delays. Disadvantages of Repeated Measures Design The disadvantages of repeated measure design are given below Order Effects One of the primary challenges in repeated measures designs is order effects, where the sequence in which conditions are presented can influence participants' performance. For instance, participants might become bored or fatigued over time, leading to decreased performance, or they may improve due to practice and familiarity with the task. These issues can compromise the validity of the results. Complexity in Analysis Analyzing data from repeated measures designs can be more complex due to the inherent correlation between repeated measures. Specialized statistical techniques, such as repeated measures ANOVA or linear mixed models, are often required to account for this correlation and ensure accurate interpretations.  23 Assumption Violations Certain statistical analyses for repeated measures, like ANOVA, rely on assumptions such as sphericity (equal variance of differences between conditions). When these assumptions are violated, results may be biased or invalid, requiring adjustments such as applying corrections like Greenhouse-Geisser or Huynh-Feldt estimates. Participant Fatigue Repeated exposure to multiple conditions can lead to fatigue, which negatively impacts participants’ focus and performance. This fatigue can introduce unintended variability in the results, particularly in tasks that require sustained attention or effort. Material Variability To avoid familiarity or practice effects, different materials are often required for each condition in repeated measures designs. However, this introduces the risk of variability between materials, which may affect participants’ performance and obscure the true effect of the independent variable. Time-Intensive Studies using repeated measures designs often require more time to conduct because participants must engage with all conditions. This increased time commitment can be challenging for both researchers and participants, potentially leading to scheduling difficulties or attrition. Confounding Variables Differences in the design, such as task difficulty or material presentation, might inadvertently influence the results. These unintended confounding factors can obscure the effect of the independent variable, making it essential to carefully control all experimental conditions.  24 References Martin, K. G. (2024, January 4). Approaches to repeated measures data. Medium. https://medium.com/@kgm_52135/approaches-to-repeated-measures-data-43f7c7026c5d Medium. (n.d.). Everything about MANOVA and MANCOVA. Nerd for Tech. Retrieved from https://medium.com/nerd-for-tech/everything-about-manova-and-mancova-4c1c237af464 JMP. (n.d.). Paired t-test. JMP Statistical Knowledge Portal. Retrieved from https://www.jmp.com/en_us/statistics-knowledge-portal/t-test/paired-t-test.html Typeset.io. (n.d.). What are the advantages and disadvantages of repeated measures? https://typeset.io/search/what-are-the-advantages-ad-disadvantages-of-repeated-measure- 3cte9ugdfv Owen, D. S. (2011, December 1). The advantages and disadvantages of repeated measures. https://dsowen.wordpress.com/2011/12/01/the-advantages-and-disadvantages-of- repeated-measures/ LibreTexts. (n.d.). Statistics. https://stats.libretexts.org/