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.

Source of Variation	SS	df	MS	Fobt
Between groups			10
Between persons			3
Within groups (error)	44
Total

(a) Complete the F-table.

Source of Variation	SS	df	MS	Fobt
Between groups			10
Between persons			3
Within groups (error)	44
Total

Make a decision to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)

Retain the null hypothesis

OR

Reject the null hypothesis.    

(b) Estimate effect size using partial omega-squared: ω_P². (Round your answer to two decimal places.)
ω_P² = ___?

Answer 1

Answer Date: 23/01/2019 a) The complete ANOVA table is, First, compute sum ofsquares, degree of freedom, mean square and F-statistics The degree of freedom for between groups is, The degree of freedom for between persons is, dsp n-1 -12-1

The null and alternative hypothesis is, H a: at least one μ is unequal. The F statistics is 5.00 The F-critical value is, From the F distribution at 5% level of significance table, show degree of freedom treatment 2 and degree of freedom error 22 as result the F-critical value is 3.44. The F-critical value is 3.44 Decision The F-test statistics is 5.00 is greater than F-critical value which is 3.44, the null hypothesis is rejected at 5% level of significance. There is sufficient evidence that the mean effects of physical fatigue among three sets of match. The result is statistically significant.

b) The effect size using partial omega-squared is, 2 SS ω = or-osTreatment-djTreatment XMS Error) SSTotal N- dfreame)xMSEror 20 (3x2) 97(36-3)x 2 0.09 The effect size using partial omega-squared is 0.09