Repeated measures designs involve multiple observations of the same participants. Between-subjects factors assign participants to different groups, while within-subjects factors expose participants to all conditions. These approaches have unique advantages and considerations for controlling individual differences and statistical power.

Mixed designs combine both factor types, allowing researchers to examine complex relationships. Understanding the differences between these approaches is crucial for selecting the most appropriate design for a study, considering research questions, practical constraints, and potential confounds.

Types of Factors

Between-Subjects and Within-Subjects Factors

• Between-subjects factors assign each participant to only one level of the factor
  • Participants in different groups receive different treatments (drug vs. placebo)
  • Reduces the impact of individual differences on the results
  • Requires a larger sample size to achieve the same statistical power as within-subjects designs
• Within-subjects factors expose each participant to all levels of the factor
  • Participants serve as their own control, reducing the impact of individual differences
  • Requires fewer participants to achieve the same statistical power as between-subjects designs
  • May introduce order effects or carryover effects that need to be controlled (counterbalancing)

Mixed and Split-Plot Designs

• Mixed design incorporates both between-subjects and within-subjects factors
  • Allows for the examination of both types of effects and their interactions
  • Can be more efficient than a purely between-subjects or within-subjects design
  • Requires careful consideration of the order of conditions and counterbalancing
• Split-plot design is a type of mixed design where the levels of one factor are assigned to larger groups (plots) and the levels of another factor are assigned within each plot
  • Commonly used in agricultural research where large plots of land are divided into subplots (fertilizer type as between-subjects factor, crop variety as within-subjects factor)
  • Can reduce the impact of variability between plots on the within-subjects factor

Effects and Interactions

Main Effects and Interaction Effects

• Main effects represent the overall effect of a single factor, averaged across the levels of other factors
  • Indicates whether there is a significant difference between the levels of a factor (drug vs. placebo)
  • Can be examined for both between-subjects and within-subjects factors
• Interaction effects occur when the effect of one factor depends on the level of another factor
  • Indicates that the factors do not operate independently (drug effectiveness may depend on dosage)
  • Can provide insights into the complex relationships between variables
  • Requires a factorial design with multiple factors to detect

Interpreting and Reporting Effects

• Main effects and interaction effects are typically reported using F-tests and p-values
  • A significant main effect suggests that the levels of the factor differ significantly
  • A significant interaction effect suggests that the factors interact with each other
• Effect sizes (eta-squared, partial eta-squared) provide a standardized measure of the magnitude of the effect
  • Helps to assess the practical significance of the findings
  • Allows for comparisons across studies and meta-analyses

Considerations

Individual Differences and Statistical Power

• Individual differences can introduce variability into the data, reducing the ability to detect true effects
  • Within-subjects designs help to control for individual differences by having each participant serve as their own control
  • Between-subjects designs require larger sample sizes to account for individual differences
• Statistical power is the probability of detecting a true effect when it exists
  • Depends on the sample size, effect size, and chosen significance level (alpha)
  • Within-subjects designs typically have higher statistical power than between-subjects designs due to the reduction in individual differences
  • Researchers should conduct power analyses to determine the appropriate sample size for their study

Choosing the Appropriate Design

• The choice between a between-subjects, within-subjects, or mixed design depends on several factors:
  • Research question and hypotheses
  • Nature of the variables and manipulations
  • Practical constraints (time, resources, sample availability)
  • Potential confounds and sources of bias (order effects, carryover effects)
• Researchers should carefully consider the trade-offs between different designs and choose the one that best addresses their research goals while minimizing potential confounds
  • Between-subjects designs are often preferred when order effects or carryover effects are a concern
  • Within-subjects designs are preferred when individual differences are a major concern or when sample sizes are limited
  • Mixed designs offer a compromise between the two, allowing for the examination of both between-subjects and within-subjects effects