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# scipy.stats.alexandergovern

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

  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’, ‘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.

    axis int 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.

    keepdims bool, 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:
    res AlexanderGovernResult

      An object with attributes:

      statisticfloat

        The computed A statistic of the test.

      pvaluefloat

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

  Warns:
    `ConstantInputWarning`

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

  See also

  `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.

  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]

  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 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)
      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.