9.1 Fundamentals of repeated measures experiments
4 min read•august 7, 2024
Repeated measures experiments involve testing the same participants under different conditions. This design reduces the impact of individual differences and requires fewer participants. However, it can lead to confounds like and .
To address these issues, researchers use techniques and check for . Understanding these fundamentals helps design more effective experiments and interpret results accurately. Repeated measures are crucial for studying changes over time and within individuals.
Repeated Measures Design Fundamentals
Definition and Characteristics
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- involves each participant being exposed to all levels of the independent variable (IV) and measured on the dependent variable (DV) under each level
- refers to the same participants being tested under all conditions of the experiment (levels of IV)
- is a type of research design that involves repeated observations of the same variables over long periods of time (months or years)
- Time-series design involves measuring the DV at multiple time points before and after the introduction of the IV to assess its impact over time
Advantages and Disadvantages
- Repeated measures designs require fewer participants than between-subjects designs since each participant is exposed to all levels of the IV
- Within-subjects designs reduce the impact of individual differences on the results by having each participant serve as their own control
- Longitudinal studies allow researchers to track changes over time and establish temporal order between variables (causality)
- Time-series designs are useful for evaluating the effectiveness of interventions or treatments in real-world settings (clinical trials)
- Repeated measures designs are susceptible to confounds such as carryover effects, practice effects, and that can threaten internal validity
- Within-subjects designs may not be feasible or ethical for certain research questions that involve irreversible treatments or long-term exposure to conditions
- Longitudinal studies are time-consuming, expensive, and prone to participant attrition over time which can lead to biased results
- Time-series designs often lack a control group which makes it difficult to rule out alternative explanations for observed changes in the DV over time
Potential Confounds in Repeated Measures
Carryover and Order Effects
- Carryover effects occur when the effect of one level of the IV persists and influences performance on subsequent levels of the IV
- For example, if a participant learns a skill in one condition, that learning may carry over and improve their performance in later conditions
- refer to the possibility that the order in which the levels of the IV are presented can influence the results
- For example, participants may perform better on a task if they complete the easiest condition first and the hardest condition last (ascending difficulty) compared to the reverse order (descending difficulty)
Practice and Fatigue Effects
- Practice effects occur when participants' performance improves over time due to familiarity with the task or measurement instruments
- For example, participants may get better at a memory task across trials simply because they have had more practice with the task
- Fatigue effects occur when participants' performance declines over time due to boredom, tiredness, or decreased motivation
- For example, participants may put less effort into a task or make more errors as the experiment goes on because they become fatigued or lose interest
Addressing Confounds and Assumptions
Counterbalancing Techniques
- Counterbalancing involves varying the order in which the levels of the IV are presented across participants to control for order effects
- exposes each participant to all possible orders of the conditions (Latin Square design)
- involves creating a subset of orders that control for first-order carryover effects (balanced Latin Square design)
- presents the levels of the IV in opposite orders for half of the participants (A-B-C vs. C-B-A)
- assigns participants to orders randomly with the constraint that each order is used an equal number of times
Sphericity and Compound Symmetry
- Sphericity is the assumption that the variances of the differences between all pairs of conditions are equal
- Violations of sphericity can lead to an increased Type I error rate (rejecting the null hypothesis when it is true)
- is used to assess sphericity and corrections (Greenhouse-Geisser, Huynh-Feldt) are applied if violated
- is a more stringent assumption that requires both equal variances and equal covariances between all pairs of conditions
- Compound symmetry is a sufficient but not necessary condition for sphericity (if CS is met, sphericity is also met)
- Multilevel modeling (mixed effects models) can be used to analyze repeated measures data without assuming CS or sphericity
Key Terms to Review (23)
Anova for repeated measures: ANOVA for repeated measures is a statistical technique used to analyze data when the same subjects are measured multiple times under different conditions or over time. This method helps determine if there are significant differences in the means of the measurements, taking into account the correlations among repeated observations from the same subjects. It is particularly useful for experiments designed to assess the effects of treatments or interventions across several time points or conditions, allowing researchers to control for individual differences in responses.
Carryover effects: Carryover effects refer to the influence that a prior treatment or condition has on the response to a subsequent treatment in repeated measures experiments. This phenomenon can lead to changes in participants' behavior or performance that are not solely attributed to the current treatment, but rather to the lingering effects of previous exposures. Understanding carryover effects is essential for designing experiments that accurately measure the impact of different conditions without confounding variables.
Complete counterbalancing: Complete counterbalancing is a technique used in experimental design, particularly in repeated measures experiments, where all possible orders of treatment conditions are presented to participants. This method ensures that each condition is equally represented and helps control for order effects, where the sequence of conditions could influence participants' responses. By systematically varying the order of conditions for each participant, complete counterbalancing minimizes biases that may arise from exposure to treatments in a particular sequence.
Compound Symmetry: Compound symmetry refers to a specific type of covariance structure often assumed in repeated measures designs, where the variances are equal across measurements and the covariances between any two measurements are also equal. This structure suggests that the repeated observations on the same subjects are correlated, but with a constant degree of correlation across all pairs of measurements. Understanding this concept is essential as it impacts how researchers analyze data from repeated measures experiments and interpret the effects of different treatments or conditions.
Counterbalancing: Counterbalancing is a technique used in experimental design to control for potential confounding variables by systematically varying the order of conditions for participants. This helps to ensure that any effects observed in an experiment can be attributed to the independent variable rather than the order in which conditions were presented. It's particularly crucial in repeated measures designs where participants are exposed to multiple conditions.
Fatigue effects: Fatigue effects refer to the decline in performance or changes in behavior observed in participants as a result of prolonged exposure to a specific experimental condition or repeated testing. This phenomenon can significantly influence the outcomes of repeated measures experiments, where the same subjects are measured multiple times under different conditions. Understanding fatigue effects is essential for accurately interpreting results and ensuring the validity of the study's conclusions.
Greenhouse-geisser correction: The greenhouse-geisser correction is a statistical adjustment used in repeated measures ANOVA to correct for violations of sphericity, which is the assumption that the variances of the differences between all combinations of related groups are equal. This correction provides a more accurate estimate of the degrees of freedom, leading to more reliable F-tests when analyzing data from experiments with repeated measures. This adjustment is crucial for maintaining the validity of statistical inferences drawn from such data.
Huynh-Feldt Correction: The Huynh-Feldt correction is a statistical adjustment used in repeated measures ANOVA to correct for violations of sphericity, which occurs when the variances of the differences between all combinations of related groups are not equal. This correction helps ensure that the results of the analysis are more reliable and accurate by adjusting the degrees of freedom, leading to more valid F-ratios and p-values. When using repeated measures designs, applying this correction becomes crucial for interpreting the effects across multiple factors.
Increased Statistical Power: Increased statistical power refers to the likelihood that a statistical test will correctly reject a false null hypothesis, thereby detecting an effect when there is one. Higher statistical power reduces the risk of Type II errors, which occur when a study fails to identify a true effect. This concept is particularly important in the context of repeated measures experiments, as they are designed to account for individual differences and can lead to more reliable results, allowing researchers to detect smaller effects with greater confidence.
Longitudinal Study: A longitudinal study is a research design that involves repeated observations of the same variables over a long period of time, allowing researchers to track changes and developments within the same subjects. This approach is essential for understanding how variables evolve and can help establish cause-and-effect relationships, making it valuable for many areas of research, including psychology, medicine, and social sciences.
Mauchly's Test: Mauchly's Test is a statistical procedure used to assess the assumption of sphericity in repeated measures ANOVA and other statistical models. It evaluates whether the variances of the differences between all possible pairs of groups are approximately equal, which is crucial for ensuring valid results when conducting analyses that involve repeated measurements or multiple factors. If this assumption is violated, it can lead to inaccurate conclusions regarding the significance of effects in multifactor experiments.
Mixed-effects models: Mixed-effects models are statistical models that incorporate both fixed effects, which are constant across individuals, and random effects, which account for individual differences. These models are particularly useful in repeated measures experiments where multiple observations are made from the same subjects, allowing researchers to understand how individual variability impacts the overall outcome while controlling for the correlation of repeated measures.
Order Effects: Order effects refer to the potential changes in participants' responses that arise from the sequence in which treatments or conditions are presented in a repeated measures design. These effects can skew results and lead to inaccurate conclusions if not properly controlled. They can arise from factors like fatigue, practice, or carryover effects, making it essential to consider their impact when designing experiments and analyzing data.
Partial counterbalancing: Partial counterbalancing is a technique used in experimental design to control for the potential effects of order or sequence when participants are exposed to multiple conditions. Instead of using a full counterbalancing method that considers all possible orders, partial counterbalancing only ensures that each condition appears in each position within the sequence a certain number of times, reducing the impact of order effects while keeping the study manageable.
Power analysis: Power analysis is a statistical method used to determine the likelihood that a study will detect an effect of a specified size, assuming that the effect actually exists. It connects sample size, significance level, and the expected effect size to help researchers ensure their study is adequately equipped to draw meaningful conclusions.
Practice effects: Practice effects refer to the improvements in participants' performance on a task that result from repeated testing rather than true changes in ability or learning. These effects are particularly important to consider in repeated measures experiments, as they can confound the results and lead to misleading conclusions about the effectiveness of an intervention or treatment.
Random counterbalancing: Random counterbalancing is a technique used in experimental design to control for potential order effects by randomly assigning the sequence in which participants experience different conditions. This method helps to ensure that any differences observed in the dependent variable are less likely to be attributed to the order in which treatments are presented. By varying the presentation order across participants, researchers can minimize bias and enhance the internal validity of repeated measures experiments.
Reduced participant variability: Reduced participant variability refers to the decrease in differences among participants in an experiment, leading to more consistent results and stronger conclusions. This concept is particularly important in repeated measures experiments, where the same participants are tested under different conditions. By minimizing the variability among participants, researchers can better isolate the effects of the independent variable being studied.
Repeated measures design: Repeated measures design is a type of experimental design where the same participants are exposed to multiple conditions or treatments, allowing researchers to observe changes over time or across different conditions. This approach helps control for individual differences since each participant acts as their own control, making it easier to detect effects of the treatments being studied. Such designs are particularly useful when studying phenomena that require the same subjects to be evaluated under varying situations.
Reverse counterbalancing: Reverse counterbalancing is a method used in repeated measures experiments to control for order effects by presenting conditions in a sequence that is the reverse of an earlier sequence. This technique helps to ensure that any potential influence of the order in which treatments are administered is balanced across participants. By using this approach, researchers can enhance the validity of their findings by minimizing bias due to sequencing.
Sample size estimation: Sample size estimation is the process of determining the number of participants needed for a study to achieve reliable and valid results. It involves considering various factors such as the expected effect size, the level of significance, and the statistical power required to detect differences or relationships in repeated measures experiments. Proper sample size estimation is crucial to ensure that studies are adequately powered to provide meaningful insights.
Sphericity: Sphericity is a statistical assumption in repeated measures designs that requires the variances of the differences between all combinations of related groups to be equal. This concept is crucial in understanding the validity of various statistical tests, particularly when analyzing data from multifactor ANOVA and repeated measures, as violations can lead to incorrect conclusions about the effects being studied.
Within-subjects design: Within-subjects design is an experimental setup where the same participants are exposed to all conditions of the experiment, allowing for comparisons across different treatment levels. This design is crucial because it controls for participant variability, enhances statistical power, and often requires fewer participants, making it a practical choice for researchers.