Rigor MCP vs Hindsight

Rigor MCP tools 37

• one_sample_t_testTest 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.
• two_sample_t_testTest 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.
• paired_t_testTest whether the mean difference between paired observations (e.g. before/after measurements on the same subjects, or matched pairs) is zero. a[i] and b[i] must be the two measurements of the same pair -- use two_sample_t_test instead if the two samples are independent (different subjects in each group). Returns the t-statistic, degrees of freedom (n-1), two-tailed p-value, a confidence interval for the mean difference, a citation, and assumption warnings.
• one_proportion_z_testTest whether an observed proportion (successes out of n) differs from a hypothesized proportion p0 -- e.g. "is this coin fair (p0=0.5) given 55 heads in 100 flips?" Uses the normal approximation, which degrades for small n or p0 near 0 or 1; a warning is included when that assumption looks shaky. Returns the z-statistic, two-tailed p-value, a confidence interval for the true proportion, a citation, and warnings.
• two_proportion_z_testTest whether two independent proportions differ -- the standard test behind comparing conversion rates between two groups (e.g. an A/B test). Returns the z-statistic, two-tailed p-value, a confidence interval for the difference in proportions, a citation, and warnings.
• chi_square_goodness_of_fitTest whether observed category counts match an expected distribution -- e.g. "are these six days-of-week signup counts evenly distributed, or skewed towards weekends?" Returns the chi-squared statistic, degrees of freedom (len-1), p-value, a citation, and a warning if any expected count is below 5 (the usual threshold below which this approximation gets unreliable).
• chi_square_independenceTest whether the row and column variables of a contingency table are independent (e.g. "does group membership relate to outcome?"). Returns the chi-squared statistic, degrees of freedom, p-value, a citation, and a warning if any expected cell count is below 5 (consider cramers_v afterwards for effect size).
• one_way_anovaTest whether three or more independent groups have different means -- e.g. comparing average order value across three marketing channels. A significant result means at least one group differs from the others, not which one -- follow up with pairwise two_sample_t_test calls (correcting for multiple comparisons via bonferroni_correction or benjamini_hochberg_correction) to find which. Returns the F-statistic, between/within degrees of freedom, p-value, a citation, and a warning if within-group df is small.
• levene_testTest whether two or more groups have equal population variances (homogeneity of variance) -- use this to decide equal_var for two_sample_t_test, or to sanity-check one_way_anova's equal-variance assumption. Uses the Brown-Forsythe variant (deviations from each group's median), more robust to non-normal data than the original mean-based Levene's test. Returns the same shape as one_way_anova (it's computed as one internally, on absolute deviations from each group's median).
• fisher_exact_testTest whether the row and column variables of a 2x2 contingency table are independent -- exact (via the hypergeometric distribution over all tables with the same margins), unlike chi_square_independence's chi-squared approximation. Use this instead whenever chi_square_independence warns an expected cell count is below 5, or whenever the sample is small. 2x2 tables only. Returns the sample odds ratio as ``statistic`` (can be inf/0 for a zero cell), a two-tailed p-value, a citation, and warnings.
• mcnemar_testTest whether two paired proportions are equal -- e.g. the same subjects' yes/no answers before and after an intervention, or two raters' calls on the same items. Use this instead of two_proportion_z_test whenever the "two groups" are actually the same subjects measured twice; two_proportion_z_test assumes independent groups and gets the standard error wrong for paired data. Yates continuity-corrected chi-squared, 1 df -- use mcnemar_exact_test instead when there are few discordant pairs (this warns when there are). Returns that chi-squared statistic, a p-value, and a confidence interval for the difference in marginal proportions.
• mcnemar_exact_testExact version of mcnemar_test: an exact binomial test (p=0.5) on the discordant pairs instead of the chi-squared approximation -- the small-sample-safe alternative mcnemar_test's own warning points to, the same relationship fisher_exact_test has to chi_square_independence. ``statistic`` is b-c (the raw discordant-pair imbalance); the p-value is two-tailed.
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Hindsight tools

No tool names declared yet. Check the project README from the listing page.