A study comparing the resting heart rate of four different t

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 1,122.9, and the WITHIN groups sum of squares was calculated to be 16,185.1. (NOTE: These are not the mean sum of squares) Calculate the F-statistic to two decimal places.

Solution

Answer: F = 1.436

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Solutions / Discussion:

Note: The following notation varies from book-to-book.

g = # of groups = 4 (cyclists, triathletes, soccer players, and baseball players)
dfB = g-1 = 4-1 = 3

N = total sample size = 10 + 10 + 10 + 10 = 40
dfW = N-g = 40 - 4 = 36

Given: SSB = 1,735.7 and SSW = 14,526.2

MSB = SSB / dfB
MSB = 1,735.7/3 = 579.2333

MSW = SSW / dfW
MSW = 14,526.2 / 36 = 403.5056

F = MSB / MSW
F = 579.2333 / 403.5056
F = 1.436

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