Question

It is commonly believed that repeatedly taking the Graduate Record quiz (GRE) leads to better scores, even without studying to improve one's scores. A higher education researcher obtains a sample of participants and gives them the GRE verbal quiz every Saturday morning for three weeks. Below are the GRE verbal score of the participants. Note that the scores were transformed to have a mean of 50. What can the researcher conclude with an α of 0.01?

week 1	week 2	week 3
55 48 54 55 45 54 49 58	55 49 58 62 51 55 46 51	59 55 62 68 56 67 52 60

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

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

d) 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.     

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

f) Regardless of the H₀ decision in b), conduct Scheffe's post hoc test for the following comparisons:
1 vs. 2: test statistic =  ; significant:  ---Select--- Yes No
1 vs. 3: test statistic =  ; significant:  ---Select--- Yes No

Answer 1

a) It is one-way ANOVA within-subjects

b) From the given data

critical value (F Critical )= 5.78042 ;

test statistic (F) = 5.23

Since F Value < F critical value so we fail to reject H0
Decesion: Fail to reject H0

c)

d) Correct answer: No week is different on GRE verbal score

e)

e) Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:
1 vs. 3: difference = 7.625 ; significant: NO
1 vs. 2: difference = 6.50 ; significant: No

f) Regardless of the H₀ decision in b), conduct Scheffe's post hoc test for the following comparisons:
1 vs. 2: test statistic = 0.907; significant: No
1 vs. 3: test statistic = 0.024; significant: No