An educational researcher studied the effects of three methods of teaching on achievement in algebra. She randomly assigned 25 students to each method. At the end of the semester she measured achievement on a standardized algebra test. To increase the sensitivity of her analysis, the researcher decided to use the students' IQ scores, which were on file, as a covariate. The data (illustrative) for the three groups are as follows:
Analyze the data, using effect coding for the meth-ods, and assigning —l's to Method C What is (are) the following:
(a) Separate regression equations for the three methods.
(b) Common b.
(c) F ratio for the test of homogeneity of regression coefficients.
(d) F ratio for the test of the common b.
(e) Proportion of variance accounted for by the teaching methods, over and above the covariate.
(f) F ratio for the differences among the teaching methods after covarying IQ.
(g) F ratio for the differences among the teaching methods without covarying IQ.
(h) Regression equation in which the product vec-tors are not included.
(i) Adjusted means for the three methods.
(j) Test of differences among the b's for the coded vectors in the equation obtained under (h) equiv-alent to.
(k) Variance/covariance matrix of the b's in the equation obtained under (h).
(I) Augmented variance/covariance matrix of the b's (C*).
(m) Using relevant elements of C*, test the differences between (1) b for Method A and b for Method B; (2) b for Method B and b for Method C; (3) b's for Methods A and B versus b fa Method C.