scipy.stats.

fligner#

scipy.stats.fligner(*samples, center='median', proportiontocut=0.05, axis=0, nan_policy='propagate', keepdims=False)[source]#

Perform Fligner-Killeen test for equality of variance.

Fligner’s test tests the null hypothesis that all input samples are from populations with equal variances. Fligner-Killeen’s test is distribution free when populations are identical [2].

Parameters:
sample1, sample2, …array_like

Arrays of sample data. Need not be the same length.

center{‘mean’, ‘median’, ‘trimmed’}, optional

Keyword argument controlling which function of the data is used in computing the test statistic. The default is ‘median’.

proportiontocutfloat, optional

When center is ‘trimmed’, this gives the proportion of data points to cut from each end. (See scipy.stats.trim_mean.) Default is 0.05.

axisint or None, default: 0

If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If None, the input will be raveled before computing the statistic.

nan_policy{‘propagate’, ‘omit’, ‘raise’}

Defines how to handle input NaNs.

  • propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.

  • omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.

  • raise: if a NaN is present, a ValueError will be raised.

keepdimsbool, default: False

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.

Returns:
statisticfloat

The test statistic.

pvaluefloat

The p-value for the hypothesis test.

See also

bartlett

A parametric test for equality of k variances in normal samples

levene

A robust parametric test for equality of k variances

Fligner-Killeen test for equality of variance

Extended example

Notes

As with Levene’s test there are three variants of Fligner’s test that differ by the measure of central tendency used in the test. See levene for more information.

Conover et al. (1981) examine many of the existing parametric and nonparametric tests by extensive simulations and they conclude that the tests proposed by Fligner and Killeen (1976) and Levene (1960) appear to be superior in terms of robustness of departures from normality and power [3].

Beginning in SciPy 1.9, np.matrix inputs (not recommended for new code) are converted to np.ndarray before the calculation is performed. In this case, the output will be a scalar or np.ndarray of appropriate shape rather than a 2D np.matrix. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or np.ndarray rather than a masked array with mask=False.

References

[1]

Park, C. and Lindsay, B. G. (1999). Robust Scale Estimation and Hypothesis Testing based on Quadratic Inference Function. Technical Report #99-03, Center for Likelihood Studies, Pennsylvania State University. https://cecas.clemson.edu/~cspark/cv/paper/qif/draftqif2.pdf

[2]

Fligner, M.A. and Killeen, T.J. (1976). Distribution-free two-sample tests for scale. Journal of the American Statistical Association. 71(353), 210-213.

[3]

Park, C. and Lindsay, B. G. (1999). Robust Scale Estimation and Hypothesis Testing based on Quadratic Inference Function. Technical Report #99-03, Center for Likelihood Studies, Pennsylvania State University.

[4]

Conover, W. J., Johnson, M. E. and Johnson M. M. (1981). A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics, 23(4), 351-361.

Examples

>>> import numpy as np
>>> from scipy import stats

Test whether the lists a, b and c come from populations with equal variances.

>>> a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]
>>> b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]
>>> c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]
>>> stat, p = stats.fligner(a, b, c)
>>> p
0.00450826080004775

The small p-value suggests that the populations do not have equal variances.

This is not surprising, given that the sample variance of b is much larger than that of a and c:

>>> [np.var(x, ddof=1) for x in [a, b, c]]
[0.007054444444444413, 0.13073888888888888, 0.008890000000000002]

For a more detailed example, see Fligner-Killeen test for equality of variance.

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