Question

In a 4 x 3 x 3 fixed effects (between groups) design experiment, with 5 observations per cell, determine the degrees of freedom associated with each of the sums of squares components for this design and the total number of participants in this design. (10 marks)

Answer 1

degrees of freedom for group 1 = 4 - 1 = 3

degrees of freedom for group 2 = 3 - 1 = 2

degrees of freedom for group 3 = 3 - 1 = 2

degrees of freedom for group 1 * group 2 = (4 - 1) * (3 - 1) = 6

degrees of freedom for group 1 * group 3 = (4 - 1) * (3 - 1) = 6

degrees of freedom for group 2 * group 3 = (3 - 1) * (3 - 1) = 4

degrees of freedom for group 1 * group 2 * group 3 = (4-1) * (3 - 1) * (3 - 1) = 12

degrees of freedom for total = Number of observations - 1 = 4 * 3 * 3 * 5 - 1 = 179

degrees of freedom for error = 179 - (3 + 2 + 2 + 6 + 6 + 4 + 12) = 144