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	$SS_T$	$n-1$

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/

23.2.4 Three-way ANOVA

https://en.wikipedia.org/wiki/Single-subject_design