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A study investigated the effects of physical fatigue on the performance of profe

ID: 3257877 • Letter: A

Question

A study investigated the effects of physical fatigue on the performance of professional tennis players. Researchers measured the number of unforced errors committed by a random sample of 12 professional tennis players during the first three sets of a match. They hypothesized that increased fatigue would be associated with a greater number of errors. The following is an F-table for this hypothetical study using the one-way within-subjects ANOVA.

(a) Complete the F-table.

Source of Variation SS df MS Fobt Between groups       12    Between persons       5    Within groups (error) 44          Total            

Explanation / Answer

dfbetween groups = k - 1 = 3 - 1 = 2

dfbetween persons = N - 1 = 12 - 1 = 11

dfwithin groups = dfbetween groups x dfbetween persons =2*11 =22

dftotal =22+11+2 = 35

SSbetween groups = dfbetween groups x MSbetween groups = 2*12 = 24

SSbetween persons = dfbetween persons x MSbetween persons = 11*5 = 55

SStotal = SSbetween groups + SSbetween persons + SSwithin groups = 24 + 55 +44 = 123

MSwithin groups = SSwithin groups/dfwithin groups = 44/22 = 2

Fbetween groups = MSbetween groups/MSwithin groups = 12/2 = 6

Fbetween persons = MSbetween persons/MSwithin groups = 5/2 = 2.5

Source of
Variation

SS df MS Fobt Between
groups 24 2 12 6 Between
persons 55 11 5 2.5 Within
groups (error) 44 22 2    Total 123 45