Let be numbers satisfying . Then is called a contrast in the mi

’s.

Notice that with , which implies that every pairwise difference between mi

’s is a contrast (so is, e.g., ).

A method attributed to Scheffé gives simultaneous CIs with simultaneous confidence level for all possible contrasts (an infinite number of them!). The interval for is Using the critical flicker frequency data of Exercise 42, calculate the Scheffé intervals for the contrasts

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