scipy.stats.alexandergovern(*samples, nan_policy='propagate', axis=0, keepdims=False)[source]#

Performs the Alexander Govern test.

The Alexander-Govern approximation tests the equality of k independent means in the face of heterogeneity of variance. The test is applied to samples from two or more groups, possibly with differing sizes.

sample1, sample2, …array_like

The sample measurements for each group. There must be at least two samples, and each sample must contain at least two observations.

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.

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.

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.


An object with attributes:


The computed A statistic of the test.


The associated p-value from the chi-squared distribution.


Raised if an input is a constant array. The statistic is not defined in this case, so np.nan is returned.

See also


one-way ANOVA


The use of this test relies on several assumptions.

  1. The samples are independent.

  2. Each sample is from a normally distributed population.

  3. Unlike f_oneway, this test does not assume on homoscedasticity, instead relaxing the assumption of equal variances.

Input samples must be finite, one dimensional, and with size greater than one.

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.



Alexander, Ralph A., and Diane M. Govern. “A New and Simpler Approximation for ANOVA under Variance Heterogeneity.” Journal of Educational Statistics, vol. 19, no. 2, 1994, pp. 91-101. JSTOR, Accessed 12 Sept. 2020.


>>> from scipy.stats import alexandergovern

Here are some data on annual percentage rate of interest charged on new car loans at nine of the largest banks in four American cities taken from the National Institute of Standards and Technology’s ANOVA dataset.

We use alexandergovern to test the null hypothesis that all cities have the same mean APR against the alternative that the cities do not all have the same mean APR. We decide that a significance level of 5% is required to reject the null hypothesis in favor of the alternative.

>>> atlanta = [13.75, 13.75, 13.5, 13.5, 13.0, 13.0, 13.0, 12.75, 12.5]
>>> chicago = [14.25, 13.0, 12.75, 12.5, 12.5, 12.4, 12.3, 11.9, 11.9]
>>> houston = [14.0, 14.0, 13.51, 13.5, 13.5, 13.25, 13.0, 12.5, 12.5]
>>> memphis = [15.0, 14.0, 13.75, 13.59, 13.25, 12.97, 12.5, 12.25,
...           11.89]
>>> alexandergovern(atlanta, chicago, houston, memphis)

The p-value is 0.1992, indicating a nearly 20% chance of observing such an extreme value of the test statistic under the null hypothesis. This exceeds 5%, so we do not reject the null hypothesis in favor of the alternative.