Question

A team of comparative psychologists are interested in the maternal behavior or rats. In an experiment, 10, 20, and 30 day-old rat pups were separated from their mothers. They then recorded the time (in seconds) required for the mother rats to retrieve the pups. The psychologists were interest in whether retrieval time varies with age. The data are given below. What can be concluded with an α of 0.05?

10 days old	20 days old	30 days old
16 11 26 16 48 19	31 16 21 26 24 23	31 26 41 34 36 31

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 rat pup ages differed on the mother retrieval time.None of the rat pup ages differed on the mother retrieval time.   

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

Tests of Between-Subjects Effects
Dependent Variable:Time
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	408.778a	2	204.389	2.671	.102
Intercept	12587.556	1	12587.556	164.519	.000
Day	408.778	2	204.389	2.671	.102
Error	1147.667	15	76.511
Total	14144.000	18
Corrected Total	1556.444	17

critical value =F(0.05, 2, 15)=3.3823 ; test statistic = 2.671
Decision: Fail to reject H0  

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = 408.778/1556.444=0.2626 ; small effect

d) Make an interpretation based on the results.

None of the rat pup ages differed on the mother retrieval time.   

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

Multiple Comparisons
Dependent Variable:Time
	(I) Day	(J) Day	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
						Lower Bound	Upper Bound
Tukey HSD	1	2	-.8333	5.05012	.985	-13.9509	12.2842
		3	-10.5000	5.05012	.128	-23.6175	2.6175
	2	1	.8333	5.05012	.985	-12.2842	13.9509
		3	-9.6667	5.05012	.169	-22.7842	3.4509
	3	1	10.5000	5.05012	.128	-2.6175	23.6175
		2	9.6667	5.05012	.169	-3.4509	22.7842
Scheffe	1	2	-.8333	5.05012	.986	-14.5383	12.8716
		3	-10.5000	5.05012	.150	-24.2049	3.2049
	2	1	.8333	5.05012	.986	-12.8716	14.5383
		3	-9.6667	5.05012	.194	-23.3716	4.0383
	3	1	10.5000	5.05012	.150	-3.2049	24.2049
		2	9.6667	5.05012	.194	-4.0383	23.3716

1 vs. 2: difference = -.8333  ; significant: No  
1 vs. 3: difference = -10.5000  ; significant: No  

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 3: test statistic = -.8333 ; significant: No  
2 vs. 3: test statistic = -9.6667  ; significant: No