# ANOVA for 2x3 factorial experiments

The following data are from three investigators (Adam Site; Ima Dumme, and Izzy Mor-Ose) who ran identical learning experiments in their own labs (after carefully training to gather data identically) to determine if their results differed by geographic area (Adam is from the Northeast, Ima from the Southwest, and Izzy from the Midwest). The data are number of trials to learn to go left at the first turn in a maze for each of their 20 rats. Answer each of the four questions and don't forget to include a verbal statement of your interpretation of the outcomes.

Adam Ima Izzy

16 24 28

16 2 35

5 9 34

10 22 33

15 22 22

11 23 37

6 18 26

27 14 31

18 8 37

30 5 27

5 19 24

6 13 30

31 19 12

20 6 37

25 36 32

18 19 40

12 19 28

25 21 21

16 27 24

29 22 28

1. Describe the data as completely as possible (a stem and leaf graph would be acceptable in addition to any statistics if you can't manage anything more elegant).

2. Determine if the results differed by region. Hint: several t-tests)

3. In what way would your analysis procedure change if I told you that the animals in each experiment were litter mates (16, 24, and 28 were litter mates as were 16, 2 and 35[different litters] through the table). Re-analyze the data appropriate to that information.

4. Compute and interpret the bi-variate correlations among the results (litter mates are matched pairs) of the three investigators.

5. The first ten animals in each column were females and the second ten were males. Construct a table of the data and using ANOVA (analysis of variance 2 X 3 factorial), determine if there are any sex differences and/or any interaction between region of the country and sex.

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#### Solution Summary

ANOVA for 2x3 factorial experiments with Null Hypothesis, Alternative Hypothesis, Significance Level, Critical Value, P value and an interpretation of the results.