Question

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

1	2	3	4
53 49 38 42 51 34 44	44 29 36 34 39 30 12	46 37 39 37 36 34 47	25 22 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 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) 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) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 2: test statistic =  ; significant:  ---Select--- Yes No
2 vs. 4: test statistic =  ; significant:  ---Select--- Yes No

Answer 1

One-way ANOVA: Y versus Treatment

Source	DF	SS	MS	F	P
Between	3	1139.5	379.8	7.88	0.001
Error	240	1157.4	48.2
Total	27	2297

S = 6.945 R-Sq = 49.61% R-Sq(adj) = 43.31%

a) Compute the preliminary statistics below.
SS_BG = NA ; df_BG = NA
SS_BS =1139.5 ; df_BS = 3
SS_E =  1157.4 ; df_E = 24
SS_T = 2297 ; df_T = 27

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² =1139.5/ 2297= 0.4961; medium effect

d) Make an interpretation based on the results.

At least one week differs on the GRE verbal score.

####

Multiple Comparisons
Dependent Variable:Y
	(I) Between	(J) Between	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
						Lower Bound	Upper Bound
Tukey HSD	1	2	12.4286*	3.71200	.013	2.1886	22.6685
		3	5.0000	3.71200	.543	-5.2399	15.2399
		4	16.4286*	3.71200	.001	6.1886	26.6685
	2	1	-12.4286*	3.71200	.013	-22.6685	-2.1886
		3	-7.4286	3.71200	.215	-17.6685	2.8114
		4	4.0000	3.71200	.706	-6.2399	14.2399
	3	1	-5.0000	3.71200	.543	-15.2399	5.2399
		2	7.4286	3.71200	.215	-2.8114	17.6685
		4	11.4286*	3.71200	.025	1.1886	21.6685
	4	1	-16.4286*	3.71200	.001	-26.6685	-6.1886
		2	-4.0000	3.71200	.706	-14.2399	6.2399
		3	-11.4286*	3.71200	.025	-21.6685	-1.1886
Scheffe	1	2	12.4286*	3.71200	.025	1.2763	23.5809
		3	5.0000	3.71200	.618	-6.1523	16.1523
		4	16.4286*	3.71200	.002	5.2763	27.5809
	2	1	-12.4286*	3.71200	.025	-23.5809	-1.2763
		3	-7.4286	3.71200	.286	-18.5809	3.7237
		4	4.0000	3.71200	.763	-7.1523	15.1523
	3	1	-5.0000	3.71200	.618	-16.1523	6.1523
		2	7.4286	3.71200	.286	-3.7237	18.5809
		4	11.4286*	3.71200	.043	.2763	22.5809
	4	1	-16.4286*	3.71200	.002	-27.5809	-5.2763
		2	-4.0000	3.71200	.763	-15.1523	7.1523
		3	-11.4286*	3.71200	.043	-22.5809	-.2763

e) Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference = 5.0000 ; significant: No
1 vs. 2: difference = 12.4286 ; significant:  Yes

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 2: test statistic = 12.4286 ; significant:  Yes
2 vs. 4: test statistic = 4.0000 ; significant: No