43. Let c1, c2, . . . , cI be numbers satisfying
ci
0. Then

ci i
c11 cII is called a contrast in the is.

Notice that with c1
1, c2
1, c3

cI
0,

ci i
1  2, which implies that every pairwise difference between is is a contrast (so is, e.g., 1  .52  .53). A method attributed to Scheffé gives simultaneous CIs with simultaneous confidence level 100(1  )% for all possible contrasts (an infinite number of them!). The interval for

ci i is

cix i
 (
c2 i /Ji

)1/2
[(I  1)
MSE
F,I1,nI]1/2 Using the critical flicker frequency data of Exercise 42, calculate the Scheffé intervals for the contrasts 1  2, 1 

3, 2  3, and .51 .52  3 (this last contrast compares blue to the average of brown and green). Which contrasts appear to differ significantly from 0, and why?