ToistomittausANOVA

ToistomittausANOVA, or repeated-measures ANOVA, is a statistical technique used to analyze data where the same subjects are observed under multiple conditions or across multiple time points. It extends the classic one-way ANOVA to account for the correlation between measurements taken on the same subjects, reducing error variance and increasing statistical power.

Designs in ToistomittausANOVA involve a within-subject factor, such as time, treatment order, or experimental conditions. The design can be one-factor (one within-subject factor with several levels) or factorial with multiple within-subject factors. The primary outputs are F statistics for main effects and interactions.

Assumptions include that the dependent variable is approximately normally distributed within each condition, and that sphericity holds. Sphericity means the variances of the differences between conditions are equal. When sphericity is violated, corrections such as Greenhouse-Geisser or Huynh-Feldt are applied to adjust the degrees of freedom and p-values.

Analysis partitions variance into within-subject and between-subject components, treating subject variability as a random effect. Post hoc comparisons or simple-effects analyses may follow significant effects to explore specific condition differences.

Practical considerations include data organization, with formats suitable for software like SPSS, R (packages such as ez, afex, or aov), or Python. Interpretation centers on whether differences exist across time or conditions and whether interactions between factors are present.

Limitations involve sensitivity to sphericity violations and non-normal data. For complex data or missing values, linear mixed-effects models offer a flexible alternative that can accommodate more elaborate covariance structures.