Methods and implementation status#

pySHT exposes 51 canonical functions covering 52 of the 54 public statistical routine identities in SHT 0.1.9. mvar1.1998AS and mvar1.LRT are algebraically the same test and share pysht.mean_variance.as_1samp. mean2.2014CLX and cov1.2012Fisher are validation-blocked and have no public callable. The two R callable adapters are unnecessary in Python, and no compatibility aliases are added.

The API reference is authoritative for callable names and signatures. The R migration crosswalk records every legacy entry point, while the searchable method names and acronyms glossary expands author tokens, years, and spelling variants.

Scientific categories#

SHT category

pySHT module

Public scope

[0] Utilities

—

R adapters are replaced by ordinary Python callables

[1] Univariate mean

pysht.mean

t tests and one-way ANOVA

[2] Multivariate mean

pysht.mean

classical, high-dimensional, unequal-covariance, randomized, Bayesian, and multi-group tests; mean CLX remains validation-blocked

[3] Variance

pysht.variance

one-, two-, and multi-sample variance or spread tests

[4] Covariance

pysht.covariance

validated one-, two-, and multi-sample covariance tests, including a Bayesian procedure; Fisher remains withheld

[5] Mean and variance

pysht.mean_variance

one- and two-sample joint tests for univariate normal parameters

[6] Mean and covariance

pysht.mean_covariance

one- and two-sample joint multivariate tests

[7] Equality of distributions

pysht.equaldist

exact or Monte Carlo two-sample permutation testing

[8] Normality

pysht.normality

Shapiro and moment-based univariate goodness-of-fit tests

[9] Rectangular uniformity

pysht.uniformity

interpoint-distance and normal-quantile tests

[10] Special domains

pysht.simplex

probability-simplex uniformity against Dirichlet alternatives

Module qualification is part of a function’s identity. For example, the public covariance CLX test belongs to pysht.covariance, while the distinct mean CLX and one-sample Fisher identities are not public. Python names use lowercase snake_case; mathematical capitalization remains in method titles and statistic labels.

A consistent method contract#

Every procedure documents:

  1. the null and alternative hypotheses;

  2. sampling and dimensional assumptions;

  3. the statistic and finite-sample denominators;

  4. the null, randomization, or Bayes-factor calibration;

  5. supported alternatives and confidence intervals;

  6. numerical edge cases and mathematical invariants;

  7. result fields and their units; and

  8. primary references and independent validation evidence.

An asymptotic p-value remains an approximation even when a function is public. The test chooser explains how to select among methods, and the validation center records the evidence and advertised regimes behind each implementation.