What does one-way ANOVA test?

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Answer

${\mu}_{1}\; = \;{\mu}_{2}$
$F_{k - 1, \;N - k}$
$Assumptions: (1) i.i.d. within groups; (2) normally distributed; (3) equal variances (Welch's ANOVA relaxes this).$
$If F is significant, follow-up with post-hoc tests (Tukey HSD, Bonferroni) to identify which groups differ.$
$Non-parametric alternative: Kruskal-Wallis.$

Check yourself — multiple choice

Only two groups
H0: all k group means equal; F = between/within variance; follow up with Tukey HSD; Kruskal-Wallis is non-parametric alt
Same as t-test
Only regression

One-way ANOVA: F-test of equal means; post-hoc Tukey; K-W is non-param alt.

#hypothesis-testing#parametric-tests

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