Question

Answer the one-way ANOVA questions using the data below. Use α = 0.01.

1	2	3	4
53 49 47 44 51 34 44	44 39 36 36 39 30 12	46 42 39 37 36 34 30	25 35 30 40 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 Tukey's Post Hoc Test for the following comparisons:
3 vs. 4: difference =   ; significant:  ---Select--- Yes No  
2 vs. 4: difference =   ; significant:  ---Select--- Yes No  

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

Answer 1

SUMMARY
Groups	Count	Sum	Average	Variance
1	7	322	46	39.33333
2	7	236	33.71429	109.5714
3	7	264	37.71429	27.57143
4	7	222	31.71429	23.90476

ANOVA Table

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	839.4286	3	279.8095	5.585551	0.004728	4.718
Within Groups	1202.286	24	50.09524
Total	2041.714	27

effect size η² = SS_{Between Groups}/SS_Total = 839.43/2041.71 = 0.41 , effect size is large.

Tukey's Post Hoc Test for comparisons:

treatments pair	Tukey HSD Q statistic	Tukey HSD p-value	Tukey HSD inferfence
1 vs 2	4.5925	0.016833	* p<0.05
1 vs 3	3.0973	0.154755	insignificant
1 vs 4	5.3401	0.004795	** p<0.01
2 vs 3	1.4952	0.698457	insignificant
2 vs 4	0.7476	0.899995	insignificant
3 vs 4	2.2429	0.406343	insignificant

Conduct Tukey's Post Hoc Test for the following comparisons:
3 vs. 4: difference = 2.2429  ; significant: No  
2 vs. 4: difference = 0.7476 ; significant: No  

f) Scheffe's Post Hoc Test for comparisons:

treatments pair	Scheffé test statistic	Scheffé p-value	Scheffé inferfence
1 vs 2	3.2474	0.030443	* p<0.05
1 vs 3	2.1901	0.215792	insignificant
1 vs 4	3.7761	0.009696	** p<0.01
2 vs 3	1.0573	0.773477	insignificant
2 vs 4	0.5286	0.963094	insignificant
3 vs 4	1.5859	0.486136	insignificant

Scheffe's Post Hoc Test for the following comparisons:
2 vs. 3: test statistic = 1.0573 ; significant: No  
3 vs. 4: test statistic = 1.5859  ; significant: No