# 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.

```{index} single: migration from R
```
```{index} single: SHT 0.1.9; function crosswalk
```

## 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:

```python
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](../methods/names-and-acronyms.md) for expanded
surnames and the [validation ledgers](../validation/index.md) for the evidence
behind these departures.