Rigor

Verified statistical inference for AI agents.

LLMs are decent at reciting statistics but bad at doing it reliably — a t-statistic or a required sample size is a number recalled from training data, not computed and checked. rigor is the alternative: classical hypothesis testing (parametric and non-parametric), correlation and regression, effect sizes, power/sample-size calculation, multiple-comparisons correction, and always-valid sequential testing for results checked more than once before they're final, computed from scratch and returned as a cited, assumption- checked answer -- plus a decision helper for picking the right tool and a batch tool for running/correcting many comparisons at once, since "which test do I even use," "I forgot to correct for multiple comparisons," and "I peeked at the dashboard and stopped early" are their own common failure modes, distinct from getting a single formula wrong.

A concrete case where this matters. The one sample-size number everyone half-remembers is Cohen (1988)'s own worked example: d=0.5, alpha=.05, power=.80 -> n≈64 per group. It's in every textbook and slide deck, so it's also what gets pattern-matched to when a similar-looking question comes up. Ask instead for d=0.46, power=.85 -- a modest, realistic revision, not a trick:

$ rigor power ttest-2samp --effect-size 0.46 --power 0.85
Required n per group = 84.86 (round up: 85)

85, not "about 64" -- a third more participants to recruit than the half-remembered number suggests, from a question that looks like the famous one. The formula itself isn't hard (power.py runs the same bisection search either direction, in a few lines); the failure mode is that recalling a nearby-looking answer feels indistinguishable from computing the right one, right up until the number's wrong.

A second concrete case. An agent (or person) watching a live experiment's dashboard and checking the p-value every time new data comes in, stopping the moment it clears 0.05, is a textbook way to fool yourself -- and it's the default way anyone actually monitors a running experiment, fixed-sample design or not:

$ rigor sequential peeking-inflation --n-looks 10
Naive repeated peeking, 10 looks, nominal alpha=0.05
  estimated true alpha = 0.1918 (+/- 0.0028 MC SE, 20000 trials)

Checking 10 times at a nominal 5% level is really running at closer to 19% -- roughly one in five "significant" results would be noise even with zero real effect. rigor sequential proportion / rigor sequential mean compute an always-valid p-value instead (mSPRT, Johari et al. 2017): checkable after every new observation with the false-positive rate actually staying at the nominal level, no pre-committed sample size and no correction for "how many times have I looked" required.

Built as an MCP server: a scan of the current MCP ecosystem (Context7 for coding docs, several physics/engineering/chemistry/geo servers, even Bentley's STAAD integration) found statistics/experimental design as one of the few common agent needs nobody had covered yet.

The statistics themselves (rigor/distributions.py, inference.py, nonparametric.py, correlation.py, regression.py, effect_size.py, power.py, corrections.py, plus the decision/batch helpers in advisor.py and batch.py) are pure standard library, no dependencies. The package as a whole does depend on the official mcp SDK, since the MCP server is a first-class part of what it ships, not an add-on -- see Install.

Install

pip install rigor-mcp

(the PyPI distribution is rigor-mcp since plain rigor was already taken by an unrelated package; the importable package and the CLI command are both still just rigor.) This gets you both console commands, rigor (CLI) and rigor-mcp (MCP server) -- deliberately one install, no extras to get right, since uvx rigor-mcp (how most MCP clients would actually invoke this) has no way to request an extra.

What's in it

• rigor/distributions.py — t, chi-squared, and F distributions built from scratch on stdlib (regularized incomplete gamma/beta), verified against exact closed-form identities (t(1) = Cauchy, chi2(2) = scaled exponential, t² = F(1, df)) rather than trusted transcription.
• rigor/inference.py — one-/two-sample and paired t-tests, one-/two-proportion z-tests, chi-squared goodness-of-fit and independence, Fisher's exact test (2x2, exact via the hypergeometric distribution — the small-sample alternative chi_square_independence's own low-expected-count warning points to), McNemar's test and McNemar's exact test (2x2, for paired proportions -- e.g. the same subjects' before/after answers -- which two_proportion_z_test's independent-groups assumption gets wrong; the exact version is via the binomial distribution on the discordant pairs, the same small-sample relationship Fisher's exact test has to chi_square_independence), one-way ANOVA, and Levene's (Brown-Forsythe) test for equal variances. Each returns a TestResult: statistic, degrees of freedom, two-tailed p-value, a confidence interval, a citation, and assumption warnings (e.g. small-n normality reliance, low expected cell counts).
• rigor/nonparametric.py — Mann-Whitney U, Wilcoxon signed-rank, and Kruskal-Wallis: the non-parametric alternative to two_sample_t_test/paired_t_test/one_way_anova respectively, for when a parametric test's own assumption warnings make its result suspect. Rank-based, with tie correction; also returns TestResult.
• rigor/correlation.py — Pearson (linear) and Spearman (monotonic, via ranks) correlation, each returned as a TestResult (H0: no association) with a confidence interval via the Fisher z-transform.
• rigor/regression.py — simple (single-predictor) ordinary least squares regression: slope, intercept, R², and a significance test + CI for the slope.
• rigor/effect_size.py — Cohen's d, Hedges' g, Cohen's h, Cramér's V, eta²/omega² (for one_way_anova), and rank-biserial correlation (for mann_whitney_u).
• rigor/power.py — power and required sample size for the one-/two-sample t-test and two-proportion z-test (the one-sample formula covers paired_t_test too, since a paired t-test is a one-sample t-test on the differences). The two directions (given n, find power; given power, find n) are exact numerical inverses of each other by construction (bisection on the same underlying power function), and sanity-checked against the Cohen (1988) d=0.5/α=.05/power=.80 textbook reference case (n≈64).
• rigor/corrections.py — Bonferroni and Benjamini-Hochberg (FDR) multiple-comparisons correction.
• rigor/advisor.py — recommend_test: a decision helper, not a statistic. Answer a few characteristics of the data/question (continuous/proportion/categorical/ordinal, how many groups, paired, small-or-skewed, association-not-difference, checked-repeatedly) and get back which tool to call, what to call instead if this test's assumptions look shaky, and what to run alongside it -- compiling the cross-references every other module's docstrings already carry into one callable answer, so an agent doesn't need to have already read all of them to find the relevant one. checked_repeatedly=True routes to a sequential_* tool where one exists (two independent groups, continuous or proportion), and otherwise says so explicitly rather than silently ignoring the flag.
• rigor/batch.py — pairwise_group_comparisons: runs every pairwise comparison across 2+ groups (two_sample_t_test or mann_whitney_u, your choice) and applies Bonferroni/BH correction to the whole batch in one call, instead of the agent orchestrating k*(k-1)/2 separate calls plus a correction call by hand and risking forgetting the correction step. The natural follow-up one_way_anova/kruskal_wallis already recommend in their own docstrings once a result comes back significant.
• rigor/sequential.py — always-valid (peeking-safe) sequential testing via the mixture sequential probability ratio test (mSPRT): every other test in this package assumes a fixed sample size decided in advance and checked once; this one is designed to be re-checked after every new observation (e.g. a live A/B test dashboard) without inflating the false-positive rate the way naively re-running a fixed-sample test at each check does. Closed-form (Robbins 1970; Johari, Koomen, Pekelis & Walsh 2017), covering two-sample means and two proportions, plus naive_peeking_inflation -- a seeded Monte Carlo demonstration of exactly the failure mode this exists to avoid. The always-valid guarantee itself (not just a single p-value's correctness) is checked by simulation in tests/test_sequential.py. One deliberately counterintuitive choice: complete separation at a small n (e.g. 0/5 vs. 5/5) reports no actionable evidence (p=1), not the maximal evidence a one-shot Fisher's exact test would call it -- because this test gets checked after every single observation, and small-n complete separation happens under the null purely by chance often enough (~40% at n=1 per arm) that treating it as proof would defeat the always-valid guarantee itself. Caught by the guarantee simulation during development, not by inspection.
• rigor/cli.py — a CLI over all of the above (rigor.py at the repo root is a thin shim so python3 rigor.py ... also works from a plain checkout, without installing anything).
• rigor/mcp_server.py — an MCP tool wrapper exposing all 37 operations to any MCP client (Claude Code, Claude Desktop, etc.). Smoke-tested end-to-end over stdio against a real client — tool discovery plus representative calls checked against known reference values, including the full round-trip still landing the Cohen (1988) case at n=63 and Fisher's original "lady tasting tea" case at p≈0.4857.

Usage

CLI, once installed:

rigor ttest one-sample --data 5.1,4.9,5.3,5.0,4.8,5.2 --mu0 5.0
rigor corr pearson --x 1,2,3,4,5 --y 2,4,5,4,5
rigor regress --x 1,2,3,4,5 --y 3,5,7,9,11
rigor nonparam mann-whitney --a 1,2,3 --b 4,5,6
rigor power ttest-2samp --effect-size 0.5 --power 0.8
rigor recommend --outcome-type continuous --n-groups 3   # which test fits?
rigor posthoc --groups "1,2,3|4,5,6|7,8,9" --labels A,B,C  # pairwise + correction
rigor mcnemar --table "794,86;150,570"    # paired proportions, e.g. before/after
rigor sequential proportion --successes1 55 --n1 500 --successes2 40 --n2 500 --tau 0.05
                # ^ peeking-safe -- rerun as n1/n2 grow, no correction needed
rigor sequential peeking-inflation --n-looks 10   # ...vs. naively checking 10 times
rigor --help   # full list of subcommands (ttest, ztest, chi2, fisher, mcnemar,
                # mcnemar-exact, anova, levene, nonparam, corr, regress,
                # effect-size, power, correct, recommend, posthoc, sequential)

or straight from a checkout without installing anything:

python3 rigor.py ttest one-sample --data 5.1,4.9,5.3,5.0,4.8,5.2 --mu0 5.0

MCP server, over stdio (the transport local clients like Claude Code expect):

pip install rigor-mcp
rigor-mcp

or from a checkout: pip install mcp && python3 -m rigor.mcp_server.

Register it with Claude Code:

claude mcp add rigor -- rigor-mcp

(or, from a checkout: claude mcp add rigor -- python3 -m rigor.mcp_server, run from this repo's root or with an absolute module path). For interactive poking with the MCP Inspector, run it as a script rather than the installed command — which means the package root has to be put on the path by hand, since the Inspector imports the file directly:

pip install "mcp[cli]"
PYTHONPATH=. mcp dev rigor/mcp_server.py

A transport-level edge case, handled

cohens_d correctly returns +inf/-inf for zero-variance samples (per its own documented contract), but non-finite floats serialize to JSON null over MCP's structured content — which used to fail the tool's own number-typed output schema and crash the call. The MCP cohens_d tool now returns {"value": float | null, "warnings": [...]} instead of a bare float, so that case is reported explicitly (null value, a warning naming the direction) rather than blowing up. That fix is specific to tools with a bare-scalar output schema — every tool that returns a dict (all the TestResult-based ones, plus simple_linear_regression) has been confirmed over real stdio to pass a non-finite field straight through as JSON's non-standard Infinity, since a generic dict return doesn't get a strict per-field number schema. Of the bare-float tools, cohens_d is the only one that can actually produce a non-finite value.

Tests

python3 -m unittest discover -s tests -v

203 tests: 182 exercise the statistics/decision logic directly (including, for sequential.py, a simulation check that the always-valid guarantee itself holds under repeated peeking, not just that a single p-value comes out right -- and, during development, a simulation catching a real bug: an early draft treated small-n complete separation as maximal evidence rather than the small-sample noise it usually is, which broke that same guarantee); 18 spawn mcp_server.py as a real MCP client would and check results over the wire (skipped automatically if mcp isn't installed); 3 check that server.json's metadata (version, description length, name length) hasn't drifted from pyproject.toml's or the MCP Registry's own limits (the two files aren't otherwise linked -- see test_release_metadata.py).

License

MIT — see LICENSE.