Question

In: Statistics and Probability

A team of comparative psychologists are interested in the maternal behavior or rats. In an experiment,...

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

Solutions

Expert Solution

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


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