Perform one-way ANOVA.

The one-way ANOVA tests the null hypothesis that two or more groups have the same population mean. The test is applied to samples from two or more groups, possibly with differing sizes.

sample1, sample2, …array_like

The sample measurements for each group.


The computed F-value of the test.


The associated p-value from the F-distribution.


Raised if each of the input arrays is constant array. In this case F-value is either infinite or isn’t defined, so np.inf or np.nan is returned for F-value


The ANOVA test has important assumptions that must be satisfied in order for the associated p-value to be valid.

  1. The samples are independent.

  2. Each sample is from a normally distributed population.

  3. The population standard deviations of the groups are all equal. This property is known as homoscedasticity.

If these assumptions are not true for a given set of data, it may still be possible to use the Kruskal-Wallis H-test (scipy.stats.kruskal) although with some loss of power.

If each group is made of constant values, and

  • There exist at least two groups with different values

    the function returns (np.inf, 0)

  • All values in all groups are the same, function returns (np.nan, np.nan)

The algorithm is from Heiman[2], pp.394-7.



R. Lowry, “Concepts and Applications of Inferential Statistics”, Chapter 14, 2014,


G.W. Heiman, “Understanding research methods and statistics: An integrated introduction for psychology”, Houghton, Mifflin and Company, 2001.


G.H. McDonald, “Handbook of Biological Statistics”, One-way ANOVA.


>>> import scipy.stats as stats

[3] Here are some data on a shell measurement (the length of the anterior adductor muscle scar, standardized by dividing by length) in the mussel Mytilus trossulus from five locations: Tillamook, Oregon; Newport, Oregon; Petersburg, Alaska; Magadan, Russia; and Tvarminne, Finland, taken from a much larger data set used in McDonald et al. (1991).

>>> tillamook = [0.0571, 0.0813, 0.0831, 0.0976, 0.0817, 0.0859, 0.0735,
...              0.0659, 0.0923, 0.0836]
>>> newport = [0.0873, 0.0662, 0.0672, 0.0819, 0.0749, 0.0649, 0.0835,
...            0.0725]
>>> petersburg = [0.0974, 0.1352, 0.0817, 0.1016, 0.0968, 0.1064, 0.105]
>>> magadan = [0.1033, 0.0915, 0.0781, 0.0685, 0.0677, 0.0697, 0.0764,
...            0.0689]
>>> tvarminne = [0.0703, 0.1026, 0.0956, 0.0973, 0.1039, 0.1045]
>>> stats.f_oneway(tillamook, newport, petersburg, magadan, tvarminne)
(7.1210194716424473, 0.00028122423145345439)

Previous topic


Next topic