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.

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) or the Alexander-Govern test (scipy.stats.alexandergovern) although with some loss of power.

The length of each group must be at least one, and there must be at least one group with length greater than one. If these conditions are not satisfied, a warning is generated and (np.nan, np.nan) is returned.

If all values in each group are identical, and there exist at least two groups with different values, the function generates a warning and returns (np.inf, 0).

If all values in all groups are the same, function generates a warning and returns (np.nan, np.nan).

The algorithm is from Heiman , pp.394-7.

Perform one-way ANOVA.

import numpy as np
from scipy.stats import f_oneway

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]
f_oneway(tillamook, newport, petersburg, magadan, tvarminne)

a = np.array([[9.87, 9.03, 6.81],
              [7.18, 8.35, 7.00],
              [8.39, 7.58, 7.68],
              [7.45, 6.33, 9.35],
              [6.41, 7.10, 9.33],
              [8.00, 8.24, 8.44]])
b = np.array([[6.35, 7.30, 7.16],
              [6.65, 6.68, 7.63],
              [5.72, 7.73, 6.72],
              [7.01, 9.19, 7.41],
              [7.75, 7.87, 8.30],
              [6.90, 7.97, 6.97]])
c = np.array([[3.31, 8.77, 1.01],
              [8.25, 3.24, 3.62],
              [6.32, 8.81, 5.19],
              [7.48, 8.83, 8.91],
              [8.59, 6.01, 6.07],
              [3.07, 9.72, 7.48]])
F, p = f_oneway(a, b, c)
F

p