Question

Answer the one-way ANOVA questions using the data below. Use α = 0.05.

1	2	3	4
53 49 47 42 30 34 44	44 44 36 34 39 30 12	46 42 39 37 36 31 47	25 35 45 27 33 28 31

a) Compute the preliminary statistics below.
SS_BG =  ;   df_BG =  
SS_WG =  ;   df_WG =  
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 mean is different from another.None of the means differed from one another.   

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

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

Answer 1

a) Compute the preliminary statistics below.

Tests of Between-Subjects Effects
Dependent Variable:Res
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	511.714a	3	170.571	2.562	.078
Intercept	38628.571	1	38628.571	580.258	.000
Factor	511.714	3	170.571	2.562	.078
Error	1597.714	24	66.571
Total	40738.000	28
Corrected Total	2109.429	27

SS_BG = 511714 ;   df_BG = 3
SS_WG = 1597714 ;   df_WG = 24
SS_T = 2109429 ; df_T = 27

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value = F(005, 3, 24)=3.0088 ; test statistic =  2.562
Decision: Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = 511.714/2109.429=0.2426 ;   small effect

d) Make an interpretation based on the results.

None of the means differed from one another.   

e) Conduct Tukey's Post Hoc Test for the following comparisons:

Multiple Comparisons
Dependent Variable:Res
	(I) Factor	(J) Factor	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
						Lower Bound	Upper Bound
Tukey HSD	1	2	8.5714	4.36124	.229	-3.4595	20.6024
		3	3.0000	4.36124	.901	-9.0310	15.0310
		4	10.7143	4.36124	.093	-1.3167	22.7452
	2	1	-8.5714	4.36124	.229	-20.6024	3.4595
		3	-5.5714	4.36124	.586	-17.6024	6.4595
		4	2.1429	4.36124	.960	-9.8881	14.1738
	3	1	-3.0000	4.36124	.901	-15.0310	9.0310
		2	5.5714	4.36124	.586	-6.4595	17.6024
		4	7.7143	4.36124	.312	-4.3167	19.7452
	4	1	-10.7143	4.36124	.093	-22.7452	1.3167
		2	-2.1429	4.36124	.960	-14.1738	9.8881
		3	-7.7143	4.36124	.312	-19.7452	4.3167
Scheffe	1	2	8.5714	4.36124	.301	-4.5314	21.6743
		3	3.0000	4.36124	.924	-10.1029	16.1029
		4	10.7143	4.36124	.139	-2.3886	23.8171
	2	1	-8.5714	4.36124	.301	-21.6743	4.5314
		3	-5.5714	4.36124	.657	-18.6743	7.5314
		4	2.1429	4.36124	.970	-10.9600	15.2457
	3	1	-3.0000	4.36124	.924	-16.1029	10.1029
		2	5.5714	4.36124	.657	-7.5314	18.6743
		4	7.7143	4.36124	.392	-5.3886	20.8171
	4	1	-10.7143	4.36124	.139	-23.8171	2.3886
		2	-2.1429	4.36124	.970	-15.2457	10.9600
		3	-7.7143	4.36124	.392	-20.8171	5.3886

2 vs. 3: difference =   ; significant: No  
1 vs. 3: difference =   ; significant: No  

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