As described in the Chapter 2 exercises, an important series of studies by Bennett et al. (1964) attempted to find evidence for changes in the brain as a result of experience. Posttreatment weights of the cortex of animals reared in an enriched environment or in a deprived environment are shown below for three replications of the study done at different times of year. Cortex weights (in milligrams) for experimental and control animals are as follows: (Raw data are adapted from those reported in Freedman, Pisani, & Purves, 1978, p. 452.) Twelve pairs of rats served as subjects in each study, with one member of each pair assigned randomly to the enriched environment and the other to the deprived environment. The two scores on the same row above for a given experiment came from two male rats taken from the same litter. The experimental hypothesis was that, even though both groups were permitted to feed freely, animals reared in the more stimulating environment would develop heavier cortexes. In Chapter 2, you were asked to test this hypothesis using a randomization test. Now, a series of parametric analyses are requested. First Analysis, Experiment 2 Data Only a. How many independent observations are there in Experiment 2? b. What full model should be used to describe these independent observations? c. What constraint on this model is of interest to test? What restricted model incorporates this constraint? d. What is the sum of squared errors associated with the full model? With the restricted model? e. Carry out the statistical test comparing these two models. f. What is your conclusion? Second Analysis, Data from Experiments 1,2, and 3 g. Now use the data from all three experiments. Assume that you are interested in whether the three experiments revealed the same advantage for the experimental animals within sampling error regardless of the time of year when the experiment was run. State the models appropriate for testing this hypothesis and carry out the analysis, again providing parameter estimates and sums of squared errors for your models as well as stating your conclusion.
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