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# 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”.

## References

[1]

Sprent, P. and Smeeton, N.C. (2000), “Applied Nonparametric Statistical Methods, Third Edition”. Chapter 6, Section 6.3.2.