[3] Tests for Variance#

pysht.variance provides classical one-, two-, and multi-sample procedures for scalar population variances.

Question

Function

Is one variance equal to a reference value?

chisquare_1samp

Are two normal-population variances equal?

f_2samp

Are several normal-population variances equal?

bartlett

Are several group spreads equal around their means?

levene

Are several group spreads equal around their medians?

brown_forsythe

See the classical-variance validation ledger for assumptions, scale handling, and SciPy comparisons.

Functions#

Tests for one, two, and multiple population variances.

The chi-square, F, and Bartlett procedures are normal-theory tests. Levene’s test and its Brown–Forsythe median-centered variant are less sensitive to departures from normality, but their reported F distributions are still finite-sample approximations.

pysht.variance.bartlett(*samples)[source]#

Test homogeneity of normal population variances across groups.

Bartlett’s statistic is especially sensitive to non-normality. Every sample must have positive sample variance; otherwise its logarithmic statistic is undefined and a ValueError is raised.

References

Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proceedings of the Royal Society A, 160, 268–282.

Parameters:

samples (ArrayLike)

Return type:

HypothesisTestResult

pysht.variance.brown_forsythe(*samples)[source]#

Run the Brown–Forsythe median-centered test for equal variances.

References

Brown, M. B. and Forsythe, A. B. (1974). Robust tests for the equality of variances. Journal of the American Statistical Association, 69, 364–367.

Parameters:

samples (ArrayLike)

Return type:

HypothesisTestResult

pysht.variance.chisquare_1samp(x, *, variance=1.0, alternative='two-sided', confidence_level=0.95)[source]#

Test one normal population variance against a positive value.

Parameters:
x

One-dimensional sample containing at least two finite real values.

variance

Positive variance under the null hypothesis.

alternative

"two-sided", "less", or "greater".

confidence_level

Confidence coefficient for the interval obtained by inverting the chi-square pivot.

Parameters:

  • x (ArrayLike)

  • variance (float)

  • alternative (str)

  • confidence_level (float)

Return type:

HypothesisTestResult

Notes

Exact chi-square calibration requires independent normal observations. A constant sample is handled as the boundary statistic zero rather than as an arithmetic error.

References

Snedecor, G. W. and Cochran, W. G. (1996). Statistical Methods, 8th ed.

pysht.variance.f_2samp(x, y, *, alternative='two-sided', confidence_level=0.95)[source]#

Test equality of two normal population variances with an F ratio.

The statistic is the unbiased sample variance of x divided by that of y. Both sample variances must be strictly positive; constant samples are rejected explicitly because the ratio and its confidence interval are then degenerate.

References

Snedecor, G. W. and Cochran, W. G. (1996). Statistical Methods, 8th ed.

Parameters:

  • x (ArrayLike)

  • y (ArrayLike)

  • alternative (str)

  • confidence_level (float)

Return type:

HypothesisTestResult

pysht.variance.levene(*samples)[source]#

Run Levene’s mean-centered test for homogeneity of variances.

References

Levene, H. (1960). Robust tests for equality of variances. In Contributions to Probability and Statistics, 278–292.

Parameters:

samples (ArrayLike)

Return type:

HypothesisTestResult