SStotal SSbetwee 0333 = 124.0334 45. The following table summarizes the results

Question

SStotal SSbetwee 0333 = 124.0334 45. The following table summarizes the results of a two-factor ANOVA evaluating an independent-measures experiment with two levels of factor A, three levels of factor B, and n 8 participants in each treatment condition a. Fill in all missing values in the table. (Hint: Start with the df column.) -Source Between Treatments 124 df MS t0 Factor A Factor B A x B 10 20 10.0 a5D Within Treatments Total 21 41 46. The following data were obtained from a two factor indenendent-measures experiment with n- 5 particinants in each

Explanation / Answer

Factor A (rows) a = 2

Factor B (Columns) b = 3

Replicates n = 8

Total N = 8 * 3 * 2 = 48

Therefore Total df = N-1 = 47

df Between Treatments = a + b - 2 = 2 + 3 -2 = 3

df of Factor A = a -1 = 2 - 1 = 1

df of Factor B = b -1 = 3 -1 = 2

df of A x B = 2 * 1 = 2

df Within Treatments = N - (ab) = 48 - (2*3) = 42

df Total = Sum of df of A + B + AB + Error = 1 + 2 + 2 + 42 = 47 so this is correct

FOR FACTOR A

Now it is given that F of Factor A = 10 and MS error = 4

F (Factor A) = MS Factor A/MS error. Therefore MS factor A = MS error * F = 10*4 = 40

And MS factor A = SS factor A/df A. Therefore SS factor A = MS factor A * df A= 40/1 = 40

FOR FACTOR B

SS Between Treatments = SS factor A + SS factor B. Therefore SS factor B = 124 - 40 = 84

MS factor B = SS factor B/df B= 84 / 2 = 41

F factor B = MS factor B/MS error = 41/4 = 10.25

FOR FACTOR AB

Given SS AB = 20. Therefore MS AB = SS AB/df AB= 20/2 = 10

Therefore F AB = MS AB/MS error = 10/4 = 2.5

FOR WITHIN TREATMENTS

MS within = SS Within/ df error. Therefore SS within = 4 * 42 = 168

Therefore SS total = SS A + SS B + SS AB + SS error = 40 + 84 + 20 + 168 = 312

The ANOVA Table is as Below

SS df MS F Between 124 3 A 40 1 40 10 B 84 2 42 10.5 AB 20 2 10 2.5 Within 168 42 4 Total 312 47

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