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 1,763, and the WITHIN groups sum of squares was calculated to be 15,859. (NOTE: These are not the mean sum of squares) Calculate the F-statistic to two decimal places.

Explanation / Answer

Here,

SSW = 15859

As there are k = 4 groups, N = 40 participants

df1 = N - k = 40 - 4 = 36

Hence,

MSW = SSW/df1 = 15859/36 = 440.5277778

Also,

SSB = 1763

So

df2 = k - 1 = 3, then

MSB = 1763/3 = 587.6666667

THus,

F = MSB/MSW = 587.6666667/440.5277778 = 1.334005927

F = 1.33 [ANSWER]

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