Question

Researchers gave a family planning survey was given to the head(s) of household in a local community. In particular, one question asked the head(s) of households to indicate if they think the community has a great need, some need, or no need of family planning counseling. In addition, they were asked to indicate how many children are in the household. Researchers want to know if the number of children in the household is impacted by family planning counseling. What can they conclude with α = 0.01?

great need	some need	no need
0 0 2 3 1 2 0 1	6 2 3 1 1 4 3 5	9 4 3 2 9 4 5 4

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA  

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 of the family planning opinions differs on the number of children in the household.None of the family planning opinions differ on the number of children in the household.   

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

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

Answer 1

a) What is the appropriate test statistic?
Ans: One-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value = 3.4668 ; test statistic = 7.911
Decision: Reject H0.

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = 60.083/139.833=0.4297 ;  ---Select- medium effect

d) Make an interpretation based on the results.

At least one of the family planning opinions differ on the number of children in the household.

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

Multiple Comparisons
Dependent Variable:Children
	(I) Planning	(J) Planning	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
						Lower Bound	Upper Bound
Tukey HSD	1	2	-2.0000	.97437	.124	-4.4560	.4560
		3	-3.8750*	.97437	.002	-6.3310	-1.4190
	2	1	2.0000	.97437	.124	-.4560	4.4560
		3	-1.8750	.97437	.157	-4.3310	.5810
	3	1	3.8750*	.97437	.002	1.4190	6.3310
		2	1.8750	.97437	.157	-.5810	4.3310
Scheffe	1	2	-2.0000	.97437	.147	-4.5657	.5657
		3	-3.8750*	.97437	.003	-6.4407	-1.3093
	2	1	2.0000	.97437	.147	-.5657	4.5657
		3	-1.8750	.97437	.182	-4.4407	.6907
	3	1	3.8750*	.97437	.003	1.3093	6.4407
		2	1.8750	.97437	.182	-.6907	4.4407

1 vs. 2: difference = -2.0000  ; significant: No  
2 vs. 3: difference = -1.8750  ; significant: No  

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 3: test statistic = 3.8750  ; significant: Yes
1 vs. 2: test statistic = -2.0000 ; significant:  No