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

\[Y_{ij} = \mu + \alpha_i + S_j + \varepsilon_{ij}\]

#aov(response ~ factor + Error(Subject/factor), data=data)

https://en.wikipedia.org/wiki/Pseudoreplication

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 \(SS_T\) \(n-1\)