Analysis of Variance (ANOVA)

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# Analysis of Variance (ANOVA) ## 4.1 One-Way ANOVA Compare means of $k$ groups: $$ y_{ij} = \mu + \alpha_i + \varepsilon_{ij} $$ **Hypothesis:** $H_0: \alpha_1 = \cdots = \alpha_k = 0$ vs $H_1$: at least one $\alpha_i \neq 0$ ### ANOVA Table Source SS df MS F Treatment $SS_{trt}$ $k-1$ $MS_{trt}$ $MS_{trt}/MS_{err}...

Analysis of Variance (ANOVA)

4.1 One-Way ANOVA

Compare means of

k

groups:

y_{ij} = \mu + \alpha_i + \varepsilon_{ij}

Hypothesis:

H_0: \alpha_1 = \cdots = \alpha_k = 0

H_1

: at least one

\alpha_i \neq 0

ANOVA Table

Source	SS	df	MS	F
Treatment	$SS_{trt}$	$k-1$	$MS_{trt}$	$MS_{trt}/MS_{err}$
Error	$SS_{err}$	$n-k$	$MS_{err}$
Total	$SS_{tot}$	$n-1$

4.2 Two-Way ANOVA

y_{ijk} = \mu + \alpha_i + \beta_j + (\alpha\beta)_{ij} + \varepsilon_{ijk}

Tests: main effects of factor A, factor B, and their interaction. Join Discord PreviousHypothesis TestingNextModel Diagnostics

What this note is really saying

Analysis of Variance (ANOVA)

4.1 One-Way ANOVA

ANOVA Table

4.2 Two-Way ANOVA

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