Question

Application Exercise:
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 α = 0.05?

Great	Some	No
0 0 2 3 1 2 0 1	5 2 3 1 5 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) Obtain/compute the appropriate values 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) Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:
2 vs. 3: difference = ____________; significant: ---Select---Yes or No
1 vs. 2: difference = ____________ ; significant: ---Select---Yes or No

f) Regardless of the H₀ decision in b), conduct Scheffe's post hoc test for the following comparisons:
2 vs. 3: test statistic = ____________ ; significant: ---Select---Yes or No
1 vs. 2: test statistic = ____________; significant: ---Select---Yes or No

Answer 1

a) What is the appropriate test statistic?
one-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.
critical value =3.467 ; test statistic = 8.801
Decision: Reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = 0.456; ---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.

e) Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:
2 vs. 3: difference = -1.5; significant: No
1 vs. 2: difference = -2.375 ; significant: Yes

f) Regardless of the H₀ decision in b), conduct Scheffe's post hoc test for the following comparisons:
2 vs. 3: test statistic = -1.610 ; significant: No
1 vs. 2: test statistic = -2.550; significant:No