# scipy.stats.alexandergovern¶

scipy.stats.alexandergovern(*args, nan_policy='propagate')[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.

Parameters
sample1, sample2, …array_like

The sample measurements for each group. There must be at least two samples.

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

Defines how to handle when input contains nan. The following options are available (default is ‘propagate’):

• ‘propagate’: returns nan

• ‘raise’: throws an error

• ‘omit’: performs the calculations ignoring nan values

Returns
statisticfloat

The computed A statistic of the test.

pvaluefloat

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

Warns
AlexanderGovernConstantInputWarning

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

`f_oneway`

one-way ANOVA

Notes

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.

References

1

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, www.jstor.org/stable/1165140. Accessed 12 Sept. 2020.

Examples

```>>> 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 sigificance 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)
AlexanderGovernResult(statistic=4.65087071883494,
pvalue=0.19922132490385214)
```

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.