A multiple comparison procedure called the Protected LSD (Protected Least Significant Difference) is performed as follows. If the ANOVA F test rejects H0 at level α, then for each pair of means θi and θi€², declare the means different if

Note that each t test is done at the same α level as the ANOVA F test. Here we are using an experimentwise α level, where

(a) Prove that no matter how many means are in the experiment, simultaneous inference from the Protected LSD is made at level α.
(b) The ordinary (or unprotected) LSD simply does the individual t tests, at level α, no matter what the outcome of the ANOVA F test. Show that the ordinary LSD can have an experiment wise error rate greater than α. (The unprotected LSD does maintain a comparisonwise error rate of α.)
(c) Perform the LSD procedure on the fish toxin data of Example 11.2.1. What are the conclusions?

Transcribed Image Text:

at least one false llthe means experimentwise α-Pl assertion of difference are equal