Methods and implementation status

The candidate API has 72 canonical public functions. Its 51-function compatibility core covers 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.lrt_1samp. Another 21 validated research methods have no SHT counterpart. 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; the pySHT-native catalog records research additions beyond SHT; and 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 interpoint, energy, and kernel permutation tests; Ball remains withheld
[8] Normality	pysht.normality	univariate Shapiro/moment tests and omnibus multivariate tests
[9] Rectangular uniformity	pysht.uniformity	interpoint, normal-quantile, and nearest-neighbor tests
[10] Special domains	pysht.simplex	simplex uniformity and compositional distribution equality
[11] Independence	pysht.independence	distance- and kernel-based pairwise or mutual independence tests
[12] Circular data	pysht.circular	circular uniformity and multi-sample equality tests

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.