scikit_posthocs.test_hartley

scikit_posthocs.test_hartley(data: _Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | complex | bytes | str | _NestedSequence[complex | bytes | str] | DataFrame, val_col: str | None = None, group_col: str | None = None, n_perm: int = 100000, sort: bool = False) → tuple[float, float, int]

Hartley’s maximum F-ratio test of homogeneity of variances.

Tests the null hypothesis that the variances in each of the groups are equal, against the alternative that at least one differs [1].

Parameters:

  • data (Union[List, numpy.ndarray, DataFrame]) – An array, any object exposing the array interface or a pandas DataFrame with data values.

  • val_col (str = None) – Name of a DataFrame column that contains dependent variable values (test or response variable). Values should have a non-nominal scale. Must be specified if data is a pandas DataFrame object.

  • group_col (str = None) – Name of a DataFrame column that contains independent variable values (grouping or predictor variable). Must be specified if data is a pandas DataFrame object.

  • n_perm (int = 100000) – Positive integer number of Monte Carlo samples used to approximate the null distribution of the maximum F-ratio statistic.

  • sort (bool = False) – If True, sort data by group_col.

Returns:

P value, F-max statistic, and degrees of freedom (of the minimum-variance group).

Return type:

tuple[float, float, int]

Notes

Hartley’s test requires a (nearly) balanced design; a warning is issued otherwise. The p value is approximated by Monte Carlo simulation of k independent chi-squared(df) variables (df taken from the minimum-variance group, following PMCMRplus), rather than PMCMRplus’s exact pmaxFratio distribution (which has no scipy equivalent). Missing observations and groups containing only missing observations are excluded. At least two groups with two finite observations each are required. If all group variances are zero, a ValueError is raised; a single zero-variance group gives an infinite F-ratio and a zero p value.

References

Examples

>>> import scikit_posthocs as sp
>>> x = [[1,2,3,5,1], [12,31,54,62,12], [10,12,6,74,11]]
>>> sp.test_hartley(x)