64. Recall from Section 11.2 that if c1, c2, . . . , cI are numbers satisfying then c1m1. . . cImI is called a contrast in the mi s. Notice that with c1  1, c2  1, c3  . . .  cI  0, m1m2, which implies that every pairwise difference between mi s is a contrast (so is, e.g., m1  .5m2  .5m3). A method attributed to Scheff gives simultaneous CIs with simultaneous con -

dence level 100(1a)%for all possible contrasts (an in nite number of them!). The interval for is Using the critical icker frequency data of Exercise 63, calculate the Scheff intervals for the contrasts m1  m2, m1  m3, m2  m3, and .5m1  .5m2  m3

(the last contrast compares blue to the average of brown and green). Which contrasts appear to differ signi cantly from 0, and why?