Friedman test for repeated samples#
In [1], 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
(scipy.stats.friedmanchisquare.)
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
np.float64(10.57142857142857)
res.pvalue
np.float64(0.005063414171757498)
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”.