Question

Answer the within-subjects ANOVA questions using the data below. Use α = 0.01.

1	2	3	4
53 49 47 42 51 39 44	44 39 36 34 39 30 29	46 42 39 37 36 34 26	44 35 30 27 33 28 31

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

Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 4: test statistic =   ; significant:  ---Select--- Yes No  
2 vs. 3: test statistic =   ; significant:  ---Select--- Yes No

Answer 1

Anova: Single Factor

SUMMARY
Groups	Count	Sum	Average	Variance
1	7	325	46.42857	25.28571
2	7	251	35.85714	28.47619
3	7	260	37.14286	40.14286
4	7	228	32.57143	32.95238

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	740.8571	3	246.9524	7.786787	0.000843	4.718051
Within Groups	761.1429	24	31.71429
Total	1502	27

effect size = (SSbetween groups) / (SSTotal) = 740.8571/ 1502 = 0.493, effect size is large.

Scheffe's Post Hoc Test

treatments pair	Scheffé T -statistic	Scheffé p-value	Scheffé inferfence
1 vs 2	3.5119	0.017341	* p<0.05
1 vs 3	3.0848	0.042538	* p<0.05
1 vs 4	4.6034	0.001447	** p<0.01
2 vs 3	0.4271	0.979901	insignificant
2 vs 4	1.0915	0.756237	insignificant
3 vs 4	1.5187	0.522777	insignificant

1 vs. 4: test statistic = 4.6034 ; significant:Yes
2 vs. 3: test statistic = 0.4271  ; significant:   No