Question

Answer the within-subjects ANOVA questions using the data below. Use α = 0.05.

1	2	3	4
53 49 47 37 51 34 44	44 39 36 34 39 30 34	23 42 39 37 36 34 47	25 35 34 27 33 28 31

a) Compute the corresponding effect size(s) and indicate magnitude(s).
η² =  ;  ---Select--- na trivial effect small effect medium effect large effect

b) Make an interpretation based on the results.

At least one week differs on the GRE verbal score.

No week is different on GRE verbal score.    

c) Regardless of the H₀ decision, conduct Tukey's post hoc test for the following comparisons:
2 vs. 3: difference =  ; significant:  ---Select--- Yes No
1 vs. 4: difference =  ; significant:  ---Select--- Yes No

d) Regardless of the H₀ decision, conduct Scheffe's post hoc test for the following comparisons:
1 vs. 2: test statistic =______ ; significant:  ---Select--- Yes No
1 vs. 4: test statistic = ______ ; significant:  ---Select--- Yes No

Answer 1

ANOVA
Source of Variation	SS	df	MS	F-stat	p-value	F-critical
Rows	298.71	6	49.79	1.62	0.19919	2.66
Columns	750.43	3	250.14	8.13	0.001	3.160
Error	553.57	18	30.75
Total	1602.71	27

a)

η2 = 750.43/1602.71 = 0.47 (large)

b)

1) At least one week differs on the GRE verbal score.

c)

Level of significance   0.05
no of treatments   4
df error   18
MSE   30.7540
q-statistic value   3.997

critical value = q*√(MSE/n)   
if absolute difference of means > critical value,means are significnantly different ,otherwise not                      
                      

2 vs. 3: difference = No, ; not significant:  
1 vs. 4: difference = yes ; significant: