Let be numbers satisfying . Then is called a contrast in the mi’s. Notice that with ,...

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., is

Using the critical flicker frequency data of Exercise 42, calculate the Scheffé intervals for the contrasts (this last contrast compares blue to the average of brown and green). Which contrasts appear to differ significantly from 0, and why?

Reference exercise 42

The critical flicker frequency (cff) is the highest frequency (in cycles/sec) at which a person can detect the flicker in a flickering light source. At frequencies above the cff, the light source appears to be continuous even though it is actually flickering. An investigation carried out to see whether true average cff depends on iris color yielded the following data (based on the article “The Effects of Iris Color on Critical Flicker Frequency,” J. of General Psych., 1973: 91–95):

a. State and test the relevant hypotheses at significance level .05 by using the F table to obtain an upper and/or lower bound on the P-value. [Hint: and CF = 13,598.36.]

b. Investigate differences between iris colors with respect to mean cff.