Question

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

1	2	3	4
53 49 21 42 51 34 44	44 31 36 34 39 30 12	46 42 46 37 36 34 47	25 31 30 27 33 28 31

a) Compute the preliminary statistics below.
SS_BG = _________ ; df_BG = __________
SS_BS = _________ ; df_BS = ___________
SS_E = __________ ; df_E = ___________
SS_T = __________ ; df_T = ___________

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =_______________ ; test statistic = ______________
Decision: ---Select---Reject H0 or 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 OR No
2 vs. 3: difference =___________ ; significant: ---Select---Yes OR No

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

Answer 1

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	359.86	6	59.98	0.87	0.5350	2.66
Columns	848.39	3	282.80	4.11	0.0220	3.16
Error	1239.86	18	68.88
Total	2448.11	27

a)

SS_BG = ____848.39_____ ; df_BG = ____3______

SS_BS = ____359.86_____ ; df_BS = ____6_______
SS_E = ______1239.86____ ; df_E = _____18______
SS_T = ____ 2448.11 ______ ; df_T = _______27____

b)

critical value=3.16

test stat=4.11

decision: reject Ho

c) eta squared = 848.39/2448.11=0.347 (medium)

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

e)

test stat = mean difference/√(MSE/n)
1 vs. 3: difference = _____0.86_____ ; significant: ---Select---NO
2 vs. 3: difference =_____-8.86______ ; significant: ---Select---NO

f)

Test statistic, F'=   (X̅I - X̅j)²/(MSE*√(1ni+1/nj))

1 vs. 3: test statistic = ______0.0200______ ; significant: --- NO
1 vs. 2: test statistic = ______2.563______ ; significant: --- No