Computes the O’Brien transform on input data (any number of arrays).

Used to test for homogeneity of variance prior to running one-way stats. Each array in *args is one level of a factor. If f_oneway is run on the transformed data and found significant, the variances are unequal. From Maxwell and Delaney [R351], p.112.


args : tuple of array_like

Any number of arrays.


obrientransform : ndarray

Transformed data for use in an ANOVA. The first dimension of the result corresponds to the sequence of transformed arrays. If the arrays given are all 1-D of the same length, the return value is a 2-D array; otherwise it is a 1-D array of type object, with each element being an ndarray.


[R351](1, 2) S. E. Maxwell and H. D. Delaney, “Designing Experiments and Analyzing Data: A Model Comparison Perspective”, Wadsworth, 1990.


We’ll test the following data sets for differences in their variance.

>>> x = [10, 11, 13, 9, 7, 12, 12, 9, 10]
>>> y = [13, 21, 5, 10, 8, 14, 10, 12, 7, 15]

Apply the O’Brien transform to the data.

>>> from scipy.stats import obrientransform
>>> tx, ty = obrientransform(x, y)

Use scipy.stats.f_oneway to apply a one-way ANOVA test to the transformed data.

>>> from scipy.stats import f_oneway
>>> F, p = f_oneway(tx, ty)
>>> p

If we require that p < 0.05 for significance, we cannot conclude that the variances are different.