A researcher studied the regression of attitudes toward school busing on political party affiliation. She administered an attitude scale to samples of Conservatives, Republicans, Liberals, and Democrats, and obtained the following scores. The higher the score, the more favorable the attitude. (The scores are illustrative.)
(a) Using dummy coding, do a regression analysis of these data. Calculate (1) R2; (2) SSreg; (3) SSres; (4) the regression equation; (5) the overall F ratio.
(b) Using effect coding, do a regression analysis of these data. Calculate the same statistics as in (a).
(c) Using the regression equations obtained under (a) and (b), calculate the means of the four groups. (d) Calculate F ratios for the following comparisons: (1) between Conservatives and Republicans; (2) between Liberals and Democrats; (3) between the mean of Conservatives and Republicans, and that of Liberals and Democrats; (4) between the mean of Conservatives, Republicans, and Democrats, and the mean of Liberals.
(e) Taken together, what type of comparisons are 1, 2, and 3 in (d)?
(f) Assuming that the researcher wished to use the Scheffe test at a = .05 for the comparisons under (d), what F ratio must be exceeded so that a comparison would be declared statistically significant?
(g) Using the regression coefficients obtained from the analysis with effect coding under (d), and C* [if you don't have access to a computer program that reports C, use C* given in the answers, under (g)] calculate F ratios for the same comparisons as those done under (d). In addition, calculate F ratios for the following comparisons: (1) between Republicans and Democrats; (2) between Liberals and Democrats, against the Conservatives.
(h) Assume that the researcher advanced the following a priori hypotheses: that Republicans have more favorable attitudes toward school busing than do Conservatives; that Liberals are more favorable than Democrats; that Liberals and Democrats are more favorable toward school busing than Conservatives and Republicans. Use orthogonal coding to express these hypotheses and do a regression analysis. Calculate the following: (1) R2
; (2) the regression equation; (3) the overall F ratio; (4) t ratios for each of the b's; (5) regression sum of squares due to each hypothesis; (6) residual sum of squares; (7) F ratios for each hypothesis; (8) What should each of these F ratios be equal to? (9) What should the average of these F ratios be equal to? Interpret the results obtained under (a)-(h).