statsmodels.stats.nonparametric.jonckheere_terpstra

statsmodels.stats.nonparametric.jonckheere_terpstra(samples, alternative='larger')

Jonckheere-Terpstra test for ordered k-sample alternatives.

The order of samples defines the ordered alternative. Under the "larger" alternative, later samples tend to take larger values than earlier samples. Under the "smaller" alternative, later samples tend to take smaller values.

Parameters:

samplessequence of array_like

Sequence containing at least two one-dimensional samples of numeric, finite observations, in the order implied by the alternative hypothesis.

alternative{“two-sided”, “larger”, “smaller”}

Defines the alternative hypothesis. The following options are available:

• "two-sided": the ordered trend is non-zero

• "larger": later samples tend to have larger values

• "smaller": later samples tend to have smaller values

Returns:

resJonckheereTerpstraResult

A NamedTuple with the Jonckheere-Terpstra statistic, pvalue and related quantities. The key fieleds are``statistic`` and pvalue. See JonckheereTerpstraResult for the full list of fields.

See also

JonckheereTerpstraResult

Results class for the Jonckheere-Terpstra test

scipy.stats.kendalltau

Kendall’s tau, the asymptotically equivalent trend statistic used here for the pooled observations and ordered group labels.

scipy.stats.mannwhitneyu

Mann-Whitney U test, the pairwise two-sample building block summed by the Jonckheere-Terpstra statistic.

scipy.stats.kruskal

Kruskal-Wallis H-test, a k-sample test against an unordered (omnibus) alternative rather than an ordered trend.

scipy.stats.page_trend_test

Page’s L test for an ordered alternative in related (repeated-measures) samples, as opposed to the independent samples assumed here.

Notes

The Jonckheere-Terpstra statistic is the sum of pairwise Mann-Whitney type counts over all ordered pairs of groups. Ties between groups contribute one half to the raw statistic.

The p-value is computed from the asymptotic normal approximation, which is equivalent to the large-sample Kendall trend test applied to the pooled observations and their ordered group labels.

References

[1]

Terpstra, T. J. “The asymptotic normality and consistency of Kendall’s test against trend, when ties are present in one ranking.” Indagationes Mathematicae 14 (1952): 327-333.

[2]

Jonckheere, A. R. “A distribution-free k-sample test against ordered alternatives.” Biometrika 41 (1954): 133-145.