scipy.stats.ansari

scipy.stats.ansari(x, y)

Perform the Ansari-Bradley test for equal scale parameters.

The Ansari-Bradley test ([1], [2]) is a non-parametric test for the equality of the scale parameter of the distributions from which two samples were drawn.

Parameters

x, yarray_like

Arrays of sample data.

Returns

statisticfloat

The Ansari-Bradley test statistic.

pvaluefloat

The p-value of the hypothesis test.

See also

fligner

A non-parametric test for the equality of k variances

mood

A non-parametric test for the equality of two scale parameters

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.

References

1

Ansari, A. R. and Bradley, R. A. (1960) Rank-sum tests for dispersions, Annals of Mathematical Statistics, 31, 1174-1189.

2

Sprent, Peter and N.C. Smeeton. Applied nonparametric statistical methods. 3rd ed. Chapman and Hall/CRC. 2001. Section 5.8.2.

Examples

>>> from scipy.stats import ansari

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.

>>> np.random.seed(1234567890)
>>> x1 = np.random.normal(loc=0, scale=2, size=35)
>>> x2 = np.random.normal(loc=0, scale=2, size=25)
>>> x3 = np.random.normal(loc=0, scale=1.25, size=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)
AnsariResult(statistic=511.0, pvalue=0.35506083719834347)

With a p-value of 0.355, 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)
AnsariResult(statistic=452.0, pvalue=0.006280278681971285)

With a p-value of 0.00628, the test provides strong evidence that the scales of the distributions from which the samples were drawn are not equal.