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Sample size: 2 × 2 designs, A/B tests and repeated trials - #47
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Before: the sample size page had no 2 × 2 designs, so there was no plan for a before-and-after study with a control group. It never mentioned A/B tests, and it didn't say what to do when people do each condition several times.
After: a new design, "Two factors at once, like a 2 × 2 design", asks two things: whether each factor is between people, within people or one of each, and whether the question is about the interaction or a main effect. In plain words, an interaction is described by its shape: the effect disappears, halves or reverses. A/B tests are pointed to the two-group or yes/no design, and repeated trials are planned on each person's average.
How: every effect in a 2 × 2 design has 1 df, so its test is a t-test on one contrast, with λ = N·f² in every layout and df2 = N − 4, N − 2 or N − 1. The between-subjects case matches G*Power's "fixed effects, special" (128 people for f = .25). Mixed and within designs match 2000-run simulations in R. The page's R code is base R and is checked in CI like the other designs.