# rigor

<!-- mcp-name: io.github.mrnh/rigor-mcp -->

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:

```sh
$ 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:

```sh
$ 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).

## Install

```sh
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:

```sh
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:

```sh
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):

```sh
pip install rigor-mcp
rigor-mcp
```

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

Register it with Claude Code:

```sh
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:

```sh
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

```sh
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](LICENSE).

[![rigor MCP server](https://glama.ai/mcp/servers/mrnh/rigor/badges/card.svg)](https://glama.ai/mcp/servers/mrnh/rigor)