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# Assignment 9

Multivariate Data Analysis
Psychology 6140

## MANOVA Problem

These problems deal with the Reading rate & comprehension data in the file readcomp sas, which gives results for 30 children in a two-way multivariate design, where 3 teachers each taught two classes; one used a 'contract' method, the other using a 'non-contract' method. The response variables are the reading rate (rate) and comprehension (comp) subtests on the Iowa Test of Basic Skills. The factor variables are teacher and class.

1. Make plots of the cell means for Teacher and Class type factors for both the reading rate and comprehension. Interpret the pattern of results, ignoring for the moment whether apparent differences are significant.

[SAS hint] Use PROC SUMMARY to get the means, followed by PROC PLOT, e.g.,

```proc summary data=readcomp nway;
class teacher class;
var rate comp;
output out=means mean=rate comp;
proc plot data=means;
plot (rate comp) * class = teacher;
```
2. Make a bivariate plot of the cell means on rate vs. means on comprehension; use some code or symbol to distinguish the various groups. Use PROC CORR to find the var-cov matrix for each group, and plot (by hand and guestimation) an ellipse around each cell mean. Find and plot the centroid (grand mean) location, and an ellipse to represent the withincells (error) var-covariance (from /PRINTE).
3. Carry out a two-way factorial MANOVA of the Reading Rate and Comprehension data, testing all effects at the .05 level. Present the reulsts in the form of a MANOVA table containing sums of squares and cross products matrices for each of the effects in the model, plus error and total. Write a two paragraph or so description of the results, such as might appear within the results section of a journal article.
4. Summarize the overall findings in this experiment concerning the effects of contract vs. non-contract teaching including both the reading rate and comprehension data.