A study comparing the resting heart rate of four different types of elite athlet

Question

A study comparing the resting heart rate of four different types of elite athletes recruited: 10 cyclists, 10 triathletes, 10 soccer players, and 10 baseball players. The resting heart rate of each athlete was measured, and the following hypothesis was tested using ANOVA: "Type of sport is a factor in elite athletes' resting heart rate." The BETWEEN groups sum of squares was calculated to be 1,324.8, and the WITHIN groups sum of squares was calculated to be 14,193.2. (NOTE: These are not the mean sum of squares) Calculate the F-statistic to two decimal places.

Explanation / Answer

There are total of 4 groups and 40 observations. So,

k = 4, N = 40

Between group degrees of freedom = k - 1 = 4 - 1 = 3

Within group degrees of freedom = N - k = 40 - 4 = 36

So,

Between group mean square = 1324.8 / 3 = 441.6

Within group mean square = 14193.2 / 36 = 394.256

Hence,

F - statistic = 441.6 / 394.256 = 1.12

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