ABSTRACT
Birch, Burdick, and Ting (1990) conducted a simulation study to compare several tests for H0 : cr~ = 0. In particular, they studied the tests based on F 2 using a modified Satterthwaite approximation, the Jeyaratnam-Graybill lower bound on crt and the lower bound in (6.4.2). Their results suggest that both the Satterthwaite and Jeyaratnam-GraybiJI tests can have levels of significance greater than the stated level. The test based on (6.4.2), on the other hand, is generally conservative, but does not suffer an undue loss of power. To summarize, we recommend the lower bound on cr~ in (6.4.2) for testing the hypothesis H0 : cr~ = 0. If the lower bound is positive, the null hypothesis is rejected . The lower bounds on cr~ and crl; formed from (3.3.3) can likewise be used for testing H0 : cr~ = 0 and H0 : crl; = 0.
