Exact sample size per variant for an A/B test on a conversion rate (two independent proportions): baseline rate, minimum detectable effect (relative or absolute), alpha, power, one or two-sided, several variants with optional Bonferroni, and unequal allocation. Uses the pooled/unpooled normal formula (same as R power.prop.test) and also reports the figure Evan Miller's calculator gives, so the two can be reconciled.

How many days an A/B test must run: from a known sample size per variant, or from baseline rate and MDE (computed as in calculate_sample_size), plus daily visitors and the share of traffic in the test. Returns exact days and the recommended whole weeks (to cover weekday effects).

Is an A/B test result statistically significant? From visitors and conversions per group: two-proportion z-test (pooled), one or two-sided p-value, Wald confidence interval for the difference, relative lift, Pearson chi-square with and without Yates correction (R prop.test), Fisher exact p for the same 2x2 table, and a sample ratio mismatch (SRM) check against the planned split.

Exact p-value for a contingency table of counts. 2x2: Fisher exact test (two-sided, greater or less, as R fisher.test). Larger r x c tables (for example 3 variants x converted/not, or 4 x 4 survey tables): Fisher-Freeman-Halton exact test by a network algorithm. Also returns Pearson chi-square and how many cells have expected counts below 5, so you can see when the chi-square approximation is unsafe.

What peeking does to an A/B test: the real false positive rate if you check a fixed-horizon test K times and stop at the first p < alpha (for example about 14% at 5 looks with alpha 0.05), and the Pocock and O'Brien-Fleming group sequential boundaries (z and nominal p per look) that keep the overall rate at alpha, for up to 10 equally spaced looks.