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, some, 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 an α of 0.01?

great	some	no
0 0 2 3 1 2 0 1	6 2 3 1 5 4 3 5	9 4 3 2 9 7 5 4

a) Obtain/compute the appropriate values to make a decision about H₀.
critical value ______________ =  ; test statistic =__________________
Decision: Reject H0 or Fail to reject H0

b) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = ___________ ;  ---Select--- 1) na 2) trivial effect 3) small effect 4)medium effect 5) large effect


c) Regardless of the H₀ decision , conduct Tukey's post hoc test for the following comparisons:
2 vs. 3: difference = ___________
1 vs. 3: difference = ___________

d) Regardless of the H₀ decision, conduct Scheffe's post hoc test for the following comparisons:
1 vs. 2: test statistic = ___________ ; significant
2 vs. 3: test statistic = ___________ ; significant

Answer 1

	SS	df	MS	F	p-value	F-critical
Between:	73.0000	2	36.5000	9.7488	0.0010	5.780
Within:	78.6250	21	3.7440
Total:	151.6250	23
					α =	0.01

a) critical value = 5.780 , test stat = 9.7488

decision: reject Ho

b) eta square ,effect size = SSbet/SST=   0.4815 (medium)

c)

Level of significance	0.05
no. of treatments,k	3
DF error =N-k=	21
MSE =	3.7440
q-statistic value(α,k,N-k)	4.6119

test stat = mean difference/√(MSE/n)

2 vs. 3: difference = not significant (test stat = 2.558 , difference=1.75)
1 vs. 3: difference =significant (test stat = 6.212 , difference=4.25 )

d)

Test statistic, F'=   (X̅I - X̅j)²/(MSE*√(1ni+1/nj))

1 vs. 2: test statistic = 6.677   ; significant: yes
2 vs. 3: test statistic = 3.272 ; significant: NO