Using effect coding, analyze the following 2 x 3 factorial experiment:
What is(are) the following?
(a) Proportion of variance accounted for by each factor and by their interaction.
(b) Regression sum of squares due to each factor and the interaction.
(c) Mean square residuals.
(d) Regression equation.
(e) F ratio for each factor and for the interaction.
(f) Construct a 2 x 3 table. In the marginals of the table show the main effects of A and B. In each cel show the interaction term (for an example of such a table, see Table 12.11).
(g) Using relevant values from the table under (f) and the relevant n's, show how the regression sums of squares for A, B, and A x B may be obtained.
(h) Since the F ratio for the interaction is statistically significant [see (e)], what type of tests are indicated?
(i) Using values from the table under (0 and relevant n's, calculate sums of squares for simple effects for A and for B. Calculate the F ratios for the simple effects and display the results in a table, using a format as in Table 12.7.
(j) What should the sum of the sums of squares for the simple effects for A be equal to?
(k) What should the sum of the sums of squares for the simple effects for B be equal to?
(l) Show how by using relevant values from the table under (f) and the intercept (a) from the regression equation obtained under (d) one can calculate the mean of each cell.
(m) Test interaction contrasts for the following: