ABSTRACT
In Chapter 3, you learned how to test a null hypothesis that all a groups have the same mean. A global test such as this one that is sensitive to any differences among the levels of the factor is often referred to as testing an omnibus null hypothesis. Although the importance of this methodology cannot be overemphasized, it must also be recognized that it has certain limitations. Specifically, anytime a is three or greater and the null hypothesis is rejected, the precise inference to be made is unclear. For example, if a = 3, all that the statistical test has infonned us at this point is that the statement tt1 = tt2 = ft3 is false. However, it is not necessarily true that all three means are different from each other. For example, one possible inference is that tt 1 = tt2. but both ttl and J.t2 differ from f.t3· However, perhaps ttz = ft3, but both differ from 11 1. Obviously, we need a way to decide which individual means do indeed differ from each other. The name given to this topic is individual comparisons.
