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Advanced Frequentist Tools

Five tools that extend basic testing, each answering a limitation of the t-test.

ANOVA: comparing more than two groups

Running a t-test on every pair of kk groups means (k2)\binom{k}{2} tests and an inflated error rate. ANOVA tests them jointly, asking whether any group mean differs, by comparing variance between groups against variance within them:

The F statistic
F=variance between groupsvariance within groupsF = \frac{\text{variance between groups}}{\text{variance within groups}}

Variation between groups against variation within them, which is what lets one test compare several means at once.

A large FF means group membership explains more variation than noise does. ANOVA tells you something differs but not what, so a significant result is followed by post-hoc pairwise tests, themselves corrected for multiplicity.

Typical use: do returns differ across market regimes, sectors, or times of day?

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