Migrating from SHT for R#

pySHT is an independently validated successor to SHT, not a line-by-line translation. The compatibility baseline is SHT 0.1.9 at commit 4e29cda1257f86dd0237d37329af358b54d04f2b. A primary paper and the stated hypotheses take precedence whenever the legacy implementation disagrees with the mathematics.

The pinned R namespace contains 56 exports: 54 statistical routine identities and two dynamic adapters. The public pySHT API has 51 canonical functions covering 52 of those 54 identities: mvar1.1998AS and mvar1.LRT share one algebraically identical implementation, while mean2.2014CLX and cov1.2012Fisher are validation-blocked and have no public Python mapping. The adapters are unnecessary in Python.

Complete statistical crosswalk#

[1] Tests for univariate mean#

SHT 0.1.9	pySHT
`mean1.ttest`	`pysht.mean.ttest_1samp`
`mean2.ttest`	`pysht.mean.ttest_2samp`
`meank.anova`	`pysht.mean.anova_oneway`

[2] Tests for multivariate mean#

SHT 0.1.9	pySHT
`mean1.1931Hotelling`	`pysht.mean.hotelling_1samp`
`mean1.1958Dempster`	`pysht.mean.dempster_1samp`
`mean1.1996BS`	`pysht.mean.bs_1samp`
`mean1.2008SD`	`pysht.mean.sd_1samp`
`mean2.1931Hotelling`	`pysht.mean.hotelling_2samp`
`mean2.1958Dempster`	`pysht.mean.dempster_2samp`
`mean2.1965Yao`	`pysht.mean.yao_2samp`
`mean2.1980Johansen`	`pysht.mean.johansen_2samp`
`mean2.1986NVM`	`pysht.mean.nvm_2samp`
`mean2.1996BS`	`pysht.mean.bs_2samp`
`mean2.2004KY`	`pysht.mean.ky_2samp`
`mean2.2008SD`	`pysht.mean.sd_2samp`
`mean2.2011LJW`	`pysht.mean.ljw_2samp`
`mean2.2014CLX`	Validation-blocked; no public pySHT callable
`mean2.2014Thulin`	`pysht.mean.thulin_2samp`
`mean2.mxPBF`	`pysht.mean.lyl_2samp`
`meank.2007Schott`	`pysht.mean.schott_ksamp`
`meank.2009ZX`	`pysht.mean.zx_ksamp`
`meank.2019CPH`	`pysht.mean.cph_ksamp`

[3] Tests for variance#

SHT 0.1.9	pySHT
`var1.chisq`	`pysht.variance.chisquare_1samp`
`var2.F`	`pysht.variance.f_2samp`
`vark.1937Bartlett`	`pysht.variance.bartlett`
`vark.1960Levene`	`pysht.variance.levene`
`vark.1974BF`	`pysht.variance.brown_forsythe`

[4] Tests for covariance#

SHT 0.1.9	pySHT
`cov1.2012Fisher`	Withheld: corrected private implementation has not passed reproducible release gates
`cov1.2015WL`	`pysht.covariance.wl_1samp`
`cov2.2012LC`	`pysht.covariance.lc_2samp`
`cov2.2013CLX`	`pysht.covariance.clx_2samp`
`cov2.2015WL`	`pysht.covariance.wl_2samp`
`cov2.mxPBF`	`pysht.covariance.lyl_2samp` (published known-zero-mean model)
`covk.2001Schott`	`pysht.covariance.schott_2001_ksamp`
`covk.2007Schott`	`pysht.covariance.schott_2007_ksamp`

The exported-but-pkgdown-hidden cov2.mxPBF is included because it is in the 0.1.9 namespace. The source-only cov1.mxPBF is excluded: it is marked @noRd, absent from NAMESPACE, and is not one of the 54 public tests.

[5] Simultaneous tests for mean and variance#

SHT 0.1.9	pySHT	Note
`mvar1.1998AS`	`pysht.mean_variance.as_1samp`	Arnold–Shavelle form
`mvar1.LRT`	`pysht.mean_variance.as_1samp`	Same algebra as the preceding R routine
`mvar2.1930PN`	`pysht.mean_variance.pn_2samp`	Lower likelihood-ratio tail corrected
`mvar2.1976PL`	`pysht.mean_variance.pl_2samp`	Fisher combination
`mvar2.1982Muirhead`	`pysht.mean_variance.muirhead_2samp`	Upper rejection tail corrected
`mvar2.2012ZXC`	`pysht.mean_variance.zxc_2samp`	Stable exact calculation
`mvar2.LRT`	`pysht.mean_variance.lrt_2samp`	Asymptotic LRT

[6] Simultaneous tests for mean and covariance#

SHT 0.1.9	pySHT
`sim1.2017Liu`	`pysht.mean_covariance.llzs_1samp`
`sim1.LRT`	`pysht.mean_covariance.lrt_1samp`
`sim2.2018HN`	`pysht.mean_covariance.hn_2samp`

[7] Tests for equality of distributions#

SHT 0.1.9	pySHT
`eqdist.2014BG`	`pysht.equaldist.bg_2samp`

Only exact and corrected Monte Carlo permutation calibration are available. The invalid legacy asymptotic branch is outside the compatibility target.

[8] Goodness-of-fit: normal distribution#

SHT 0.1.9	pySHT
`norm.1965SW`	`pysht.normality.shapiro_wilk`
`norm.1972SF`	`pysht.normality.shapiro_francia`
`norm.1980JB`	`pysht.normality.jarque_bera`
`norm.1996AJB`	`pysht.normality.adjusted_jarque_bera`
`norm.2008RJB`	`pysht.normality.robust_jarque_bera`

[9] Goodness-of-fit: uniform distribution#

SHT 0.1.9	pySHT
`unif.2017YMi`	`pysht.uniformity.ym_interpoint`
`unif.2017YMq`	`pysht.uniformity.ym_quantile`

[10] Tests on special domains#

SHT 0.1.9	pySHT
`simplex.uniform`	`pysht.simplex.uniformity`

The two adapter exports#

usek1d and useknd accept an R function and a list of samples. Python users call an ordinary callable directly and pass multi-group samples positionally, so pySHT deliberately provides no adapter aliases:

from pysht.variance import brown_forsythe

result = brown_forsythe(group_a, group_b, group_c)

Argument translation#

R convention	Python convention
`mu0`	`popmean`
`Sigma0`	`popcov`
`var0`	`variance`
`var.equal`	`equal_var`
`alternative="two.sided"`	`alternative="two-sided"`
`dlist=list(x, y, z)`	positional groups: `function(x, y, z)`
`method`, `nreps`	descriptive lowercase options, `calibration`, `n_resamples`
ambient R random state	`rng=None`, an integer seed, or a NumPy `Generator`
`m` for random projections	`n_projections` or `n_subspaces`, as applicable
`nthreads`	no counterpart; the current runtime is NumPy/SciPy only
matrices `X`, `Y`	arrays `x`, `y`; rows remain observations

Short R option initials such as "L" and "T" are not accepted. Use the documented lowercase word, such as "bai-saranadasa", "hotelling", "clime", or "monte-carlo". Public controls are keyword-only when a positional value would be ambiguous.

Result translation#

R `htest` component	pySHT field
`statistic`	`result.statistic`
`p.value`	`result.pvalue` or the read-only `result.p_value` alias
`alternative`	`result.alternative`
`method`	`result.method`
`data.name`	`result.data_name`
named parameters	`result.df`, `result.estimates`, or `result.diagnostics`
`conf.int`	`result.confidence_interval`, `result.confidence_level`

print(result) gives an htest-style summary, but the Python object is immutable. Resampling results retain counts, exactness, Monte Carlo standard error, and a binomial tail-probability interval.

The two LYL functions return BayesFactorTestResult, not an object pretending to be a frequentist htest. They expose the maximum and component log Bayes factors and intentionally have no p-value. pySHT never exponentiates the maximum internally or supplies an automatic evidence threshold. Their default gamma is derived from alpha=2.01, sample size, and dimension. Unlike the legacy covariance kernel’s implicit centering, the Python covariance function uses the primary paper’s known-zero-mean, no-intercept model.

Deliberate correctness differences#

The corrected Fisher covariance implementation whitens by the supplied null covariance, but remains private until reproducible null and power gates pass; the legacy code calculated that transform and then ignored it.
Li–Chen uses literal scale-equivariant U-statistics.
Wu–Li equality tests account for both directions instead of applying a one-sided maximum to a two-sided hypothesis.
Pearson–Neyman and Muirhead use the rejection tails implied by their likelihood-ratio statistics.
Cao–Park–He evaluates each group in both variance-estimator branches rather than reusing a stale loop index.
Adjusted and robust Jarque–Bera default calls are defined, and finite-sample Monte Carlo calibration reports its simulation uncertainty.
Random projections and subspaces are drawn once and held fixed across the observed and permuted statistics.
Zhang–Xu–Chen and all Bayes-factor kernels use log-domain arithmetic where direct exponentiation would underflow or overflow.
Biswas–Ghosh uses floating-point tie handling, exact enumeration when feasible, stable distance normalization, and no legacy asymptotic branch.

See the method-name glossary for expanded surnames and the validation ledgers for the evidence behind these departures.