Consider the following three contrasts: (1) difference between the sum of the reduction in blood sugar levels using diet types 1 and 3 from that using diet types 2 and 4; (2) difference between the sum of the reduction in blood sugar level using diet types 1 and 2 from that using diet types 3 and 4; (3) difference in the sum of the reduction in blood sugar level using diet types 2 and 3 from that using diet types 1 and 4.
(a) Find the sum of squares due to each of the contrasts, and discuss their contribution to the treatment sum of squares.
(b) What null hypothesis is indicated by contrast (1)? Test the hypothesis at a 5% level of significance.
(c) What type of hypothesis is indicated by contrast (2)? Test the hypothesis at the 10% level of significance.