Test whether a sample's mean differs from a hypothesized value mu0. Returns the t-statistic, degrees of freedom, two-tailed p-value, a confidence interval for the mean, and any assumption warnings.

Test whether two independent samples have different means. Defaults to Welch's t-test (does not assume equal variances); pass equal_var=true for the classic pooled-variance test.

Test whether the mean difference between paired observations (e.g. before/after on the same subjects) is zero.

Test whether an observed proportion (successes out of n) differs from a hypothesized proportion p0.

Test whether two independent proportions differ -- the standard test behind comparing conversion rates between two groups (e.g. an A/B test).

Test whether observed category counts match an expected distribution.

Test whether the row and column variables of a contingency table are independent (e.g. "does group membership relate to outcome").

Test whether three or more independent groups have different means.

Standardized mean difference between two samples (pooled SD). Rough guidance: ~0.2 small, ~0.5 medium, ~0.8 large -- context-dependent. Returns {"value": float or null, "warnings": [...]}. value is null only when both samples have zero variance and unequal means, where the effect size is mathematically infinite -- see the warning for which direction and use the raw mean difference instead.

Effect size for a difference between two proportions (arcsine transform).

Effect size for a chi-squared test of independence, normalized to [0, 1].

How many observations per group are needed to detect a given Cohen's d with a two-sample t-test at the target power. Returns a continuous value and a rounded-up integer to actually use.

Statistical power to detect a given Cohen's d with n observations per group, using a two-sample t-test.

How many observations per group are needed to detect a difference between two proportions (e.g. conversion rates) at the target power.

Statistical power to detect a difference between two proportions with n observations per group.

Adjust a batch of p-values for multiple comparisons, controlling the family-wise error rate. Conservative; use when any false positive among the batch is costly.

Adjust a batch of p-values for multiple comparisons, controlling the false discovery rate. Less conservative than Bonferroni; the standard choice when testing many hypotheses at once.