Question

A team of comparative psychologists are interested in the maternal behavior or rats. In an experiment, 10, 20, and 25 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	25 days old
16 11 26 16 21 19	31 16 21 26 24 23	56 26 41 34 36 31

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. 3: difference =  ; significant:  ---Select--- Yes No
1 vs. 2: difference =  ; significant:  ---Select--- Yes No

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

Answer 1

Groups	Count	Sum	Average	Variance
10 days old	6	109	18.16667	26.16667
20 days old	6	141	23.5	25.1
25 days old	6	224	37.33333	108.6667

Hypothesis:

H₀ : All means are equal

H₁: Atleast one mean is not equal

alpha = 0.05

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1174.333	2	587.1667	11.01396	0.001139	3.68232
Within Groups	799.6667	15	53.31111
Total	1974	17

Since the test statistic F (11.01) is greater than critical value 3.68, hence we reject null hypothesis and there is a significant evidence to conclude that At least one of the rat pup ages differed on the mother retrieval time.

e) Conduct Tukey's Post Hoc Test

treatments pair	Tukey HSD Q statistic	Tukey HSD p-value	Tukey HSD inferfence
1 vs 2	1.7892	0.436811	insignificant
1 vs 3	6.43	0.001051	** p<0.01
2 vs 3	4.6408	0.013136	* p<0.05

1 vs. 3: difference = 6.43 ; significant: Yes
1 vs. 2: difference = 1.7892 ; significant: No

f) Conduct Scheffe's Post Hoc Test

treatments pair	Scheffé test statistic	Scheffé p-value	Scheffé inferfence
1 vs 2	1.2652	0.467458	insignificant
1 vs 3	4.5467	0.001507	** p<0.01
2 vs 3	3.2815	0.017279	* p<0.05

1 vs. 2: test statistic = 1.2652 ; significant: No
1 vs. 3: test statistic = 4.5467 ; significant: Yes