The Ansari-Bradley test (, ) is a non-parametric test for the equality of the scale parameter of the distributions from which two samples were drawn. The null hypothesis states that the ratio of the scale of the distribution underlying x to the scale of the distribution underlying y is 1.
Notes
The p-value given is exact when the sample sizes are both less than 55 and there are no ties, otherwise a normal approximation for the p-value is used.
A non-parametric test for the equality of two scale parameters
Examples
import numpy as np
from scipy.stats import ansari
rng = np.random.default_rng()
For these examples, we'll create three random data sets. The first
two, with sizes 35 and 25, are drawn from a normal distribution with
mean 0 and standard deviation 2. The third data set has size 25 and
is drawn from a normal distribution with standard deviation 1.25.
First we apply `ansari` to `x1` and `x2`. These samples are drawn
from the same distribution, so we expect the Ansari-Bradley test
should not lead us to conclude that the scales of the distributions
are different.
ansari(x1, x2)
With a p-value close to 1, we cannot conclude that there is a
significant difference in the scales (as expected).
Now apply the test to `x1` and `x3`:
ansari(x1, x3)
The probability of observing such an extreme value of the statistic
under the null hypothesis of equal scales is only 0.03087%. We take this
as evidence against the null hypothesis in favor of the alternative:
the scales of the distributions from which the samples were drawn
are not equal.
We can use the `alternative` parameter to perform a one-tailed test.
In the above example, the scale of `x1` is greater than `x3` and so
the ratio of scales of `x1` and `x3` is greater than 1. This means
that the p-value when ``alternative='greater'`` should be near 0 and
hence we should be able to reject the null hypothesis:
ansari(x1, x3, alternative='greater')
As we can see, the p-value is indeed quite low. Use of
``alternative='less'`` should thus yield a large p-value:
ansari(x1, x3, alternative='less')
See :
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