`scipy.stats._stats_py:obrientransform`

source: build-install/usr/lib/python3.14/site-packages/scipy/stats/_stats_py.py:2519

Signature

def obrientransform(*samples, nan_policy = propagate)

Summary

Compute the O'Brien transform on input data (any number of arrays).

Extended Summary

Used to test for homogeneity of variance prior to running one-way stats. Each array in *samples is one level of a factor. Significant results of f_oneway on the transformed data suggest that the variances of the underlying distributions are unequal. See Maxwell and Delaney ^[1], p.112.

Parameters

*samples : array_like

Any number of arrays.

nan_policy : {'propagate', 'omit', 'raise'}

Defines how to handle input NaNs.

propagate: if a NaN is present in a sample, all elements of the transformed sample will be NaN.
omit: NaNs will be omitted when computing reducing statistics for the transform, but NaNs in the sample will remain NaNs in the transformed sample.
raise: if a NaN is present, a ValueError will be raised.

Returns

obrientransform : tuple of arrays: Transformed arrays for use in ANOVA.

Raises

: ValueError: If the mean of the transformed data is not equal to the original variance, indicating a lack of convergence in the O'Brien transform.

Examples

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)

✓

✗

np.float64(0.13141394770403342)

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