23.2 Factorial Experiments
23.2.1 Repeated measure design
https://en.wikipedia.org/wiki/Repeated_measures_design
23.2.1.1 One-way repeated measures ANOVA
https://www.yongxi-stat.com/one-way-repeat-measure-anova/
Mauchly Spherical Test: https://en.wikipedia.org/wiki/Mauchly%27s_sphericity_test
Greenhouse–Geisser correction, Huynh-Feldt Correction https://personal.utdallas.edu/~herve/abdi-GreenhouseGeisser2010-pretty.pdf
\[Y_{ij} = \mu + \alpha_i + S_j + \varepsilon_{ij}\]
23.2.2 Two-way ANOVA
\[Y_{ijk} = \mu + \alpha_i + \beta_j + (\alpha\beta)_{ij} + \varepsilon_{ijk}\]Source | SS | df | MS | F |
---|---|---|---|---|
Factor \(A\) | \(SS_A\) | \(a-1\) | \(MS_A=\frac{SS_A}{a-1}\) | \(F_A=\frac{MS_A}{MS_E}\) |
Factor \(B\) | \(SS_B\) | \(b-1\) | \(MS_B=\frac{SS_B}{b-1}\) | \(F_B=\frac{MS_B}{MS_E}\) |
\(A \times B\) | \(SS_{AB}\) | \((a-1)(b-1)\) | \(MS_{AB}=\frac{SS_{AB}}{(a-1)(b-1)}\) | \(F_{AB}=\frac{MS_{AB}}{MS_E}\) |
Error | \(SS_E\) | \(ab(r-1)\) | \(MS_E=\frac{SS_E}{ab(r-1)}\) | |
Total | \(SS_T\) | \(n-1\) |
23.2.3 mixed-design ANOVA
https://en.wikipedia.org/wiki/Mixed-design_analysis_of_variance https://www.yongxi-stat.com/mix-two-way-anova/