The Analysis of Variance
A tool named after variance and built entirely from variance estimates -- yet the thing it actually tests is whether group means are equal
Traces ANOVA from Fisher's 1918 coinage of the word 'variance' through its development at Rothamsted and formalization in Statistical Methods for Research Workers (1925), including the Snedecor naming story behind the letter F. Derives the sum-of-squares identity SST = SSB + SSW and then the real mechanism -- E[MSW] = sigma^2 always, while E[MSB] = sigma^2 plus an extra term that is exactly zero under equal means -- showing precisely why a ratio of two variance estimates tests location, not spread. Covers the assumptions that make the exact F-test valid (independence, Normality, homogeneity of variance) and what to use instead when each breaks down, explains -- in broad terms -- how Levene's test repurposes the identical between/within machinery on absolute deviations to test variances instead of means, and closes with a fully worked, hand-computable three-treatment ANOVA table (verified numerically) so the reader can build one from raw data unaided.
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