repeatedmeasures

Repeated measures refer to data collected from the same individuals across multiple conditions or over time. This within-subjects approach contrasts with between-subjects designs, where each participant provides data under a single condition. The main advantage is reduced error variance due to controlling for individual differences, which can increase statistical power. Potential drawbacks include carryover or practice effects that may confound results, as well as greater sensitivity to time-related factors.

Common analyses include repeated measures ANOVA for one within-subject factor with several levels, and more complex designs such as two-way or higher RM-ANOVA. These methods assume that residuals are normally distributed and, crucially, that sphericity holds—the condition-specific differences have equal variances. Mauchly’s test assesses sphericity; when violated, corrections like Greenhouse-Geisser or Huynh-Feldt adjust degrees of freedom to protect against inflated Type I error. If normality assumptions are questionable, non-parametric alternatives such as Friedman's test can be used.

Linear mixed-effects models (LMM) or generalized linear mixed models (GLMM) offer a flexible alternative, especially with missing data, unbalanced time points, or when random subject effects need explicit modeling. These models can handle complex covariance structures and accommodate both fixed and random factors.

Key design considerations include counterbalancing and randomization to mitigate order effects, as well as appropriate data visualization (for example, profile plots) to inspect patterns across time or conditions. Data structures involve within-subject factors (time, treatment level, or condition) and possible between-subject factors, with attention to the correlation among repeated measures. Repeated measures are widely used in psychology, medicine, education, and neuroscience to study change and treatment effects within the same individuals.