# scipy.stats.fligner

scipy.stats.fligner(*args, center='median', proportiontocut=0.05)

  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’.

    proportiontocut float, 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.

  Returns
    statistic float

      The test statistic.

    pvalue float

      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

  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].

  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 biding data. Technometrics, 23(4), 351-361.

  Examples

  Test whether or not the lists a, b and c come from populations with equal variances.

      >>> from scipy.stats import fligner
      >>> 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 = 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]

scipy.stats.binomtest scipy.stats.median_test