scipy.stats.friedmanchisquare(*samples, axis=0, nan_policy='propagate', keepdims=False)[source]#

Compute the Friedman test for repeated samples.

The Friedman test tests the null hypothesis that repeated samples of the same individuals have the same distribution. It is often used to test for consistency among samples obtained in different ways. For example, if two sampling techniques are used on the same set of individuals, the Friedman test can be used to determine if the two sampling techniques are consistent.

sample1, sample2, sample3…array_like

Arrays of observations. All of the arrays must have the same number of elements. At least three samples must be given.

axisint 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.

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.

keepdimsbool, 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.


The test statistic, correcting for ties.


The associated p-value assuming that the test statistic has a chi squared distribution.


Due to the assumption that the test statistic has a chi squared distribution, the p-value is only reliable for n > 10 and more than 6 repeated samples.

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.



P. Sprent and N.C. Smeeton, “Applied Nonparametric Statistical Methods, Third Edition”. Chapter 6, Section 6.3.2.


In [2], the pulse rate (per minute) of a group of seven students was measured before exercise, immediately after exercise and 5 minutes after exercise. Is there evidence to suggest that the pulse rates on these three occasions are similar?

We begin by formulating a null hypothesis \(H_0\):

The pulse rates are identical on these three occasions.

Let’s assess the plausibility of this hypothesis with a Friedman test.

>>> from scipy.stats import friedmanchisquare
>>> before = [72, 96, 88, 92, 74, 76, 82]
>>> immediately_after = [120, 120, 132, 120, 101, 96, 112]
>>> five_min_after = [76, 95, 104, 96, 84, 72, 76]
>>> res = friedmanchisquare(before, immediately_after, five_min_after)
>>> res.statistic
>>> res.pvalue

Using a significance level of 5%, we would reject the null hypothesis in favor of the alternative hypothesis: “the pulse rates are different on these three occasions”.