## Practice Problems: ANOVA

Neuroscience researchers examined the impact of environment on rat development. Rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), standard (cage with other rats), enriched (cage with other rats and toys), super enriched (cage with rats and toys changes on a periodic basis). After two months, the rats were tested on a variety of learning measures (including the number of trials to learn a maze to a three perfect trial criteria), and several neurological measure (overall cortical weight, degree of dendritic branching, etc.). The data for the maze task is below. Compute the appropriate test for the data provided below.

 Impoverished Standard Enriched Super Enriched 22 17 12 8 19 21 14 7 15 15 11 10 24 12 9 9 18 19 15 12

 Source SS df MS F Between 323.35 3 107.7833 12.71 Within 135.6 16 8.475 Total 458.95 19

1. What is your computed answer? F = 12.71 (3,16) p < .01

2. What would be the null hypothesis in this study? Environment will have no impact on learning ability as operationalized by maze performance in rats.

3. What would be the alternate hypothesis? Environment will have an impact on learning ability as operationalized by maze performance in rats.

4. What is your Fcrit? Fcrit = 5.29

5. Are there any significant differences between the four testing conditions? Yes - There is no significant difference between the impoverished group and the standard group (Fcomp = 2.32 and qobs= 2.15, n.s.). There is a significant difference between the impoverished group and both the enriched and supenriched group (Fcomp = 16.15 and qobs= 5.68, p < .01) and Fcomp = 31.90 and qobs= 7.98, p < .01), respectively). There is no significant difference between the standard group and the enriched group (Fcomp = 6.24 and qobs= 3.53, n.s.). There is a significant difference between the standard group and the supenriched group (Fcomp = 17.03 and qobs= 5.83, p < .05). There is no significant difference between the enriched group and the superenriched group (Fcomp = 2.65 and qobs= 2.30, p < .05)).

6. Interpret your answer. Environment may have an impact on ability to learn. Differences were found between groups when each group is compared to a group at least two levels above the one under study. Thus for example, there is a difference between the impoverished and the enriched and superenriched but not between the impoverished and the standard groups.

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