Friedman test

Let’s work out another non-parametric hypothesis test – analogous to repeated measures ANOVA, the Friedman test. The way it works is exemplified by analysing ten runners who participated in a training program. The following are the measured heart rates at regular intervals. Your task is to inspect if there is a significant difference in the heart rate of patients across the three time points.

H_Rate <-  matrix(c(150, 143, 142,
                  140, 143, 140,
                  160, 158, 165,
                  145, 140, 138,
                  138, 130, 128,
                  122, 120, 125,
                  132, 131, 128,
                  152, 155, 150,
                  145, 140, 140,
                  140, 137, 135),
                nrow = 10,
                byrow = TRUE,
                dimnames = list(1:10, c("INITIAL", "ONE WEEK", "TWO WEEKS")))

INITIAL ONE WEEK TWO WEEKS
1      150      143       142
2      140      143       140
3      160      158       165
4      145      140       138
5      138      130       128
6      122      120       125
7      132      131       128
8      152      155       150
9      145      140       140
10     140      137       135

The null hypothesis, H₀: HR1 = HR2 = HR3 (mean heart rates across the intervals are all equal)
The alternative hypothesis, H_A: There is a difference (at least one) during the interval.

The following command can execute the Friedman test,

friedman.test(H_Rate)

	Friedman rank sum test

data:  H_Rate
Friedman chi-squared = 5.8421, df = 2, p-value = 0.05388

The p-value is 0.053, which is greater than the significance value of 0.05; the evidence is not sufficient to reject the null hypothesis.