A popular class of tests for simple autoregressive processes is considered in the context of the error components model previously discussed by Revanker (1980) and King (1982). We show that the expected value of all such test statistics is further from the rejection region in this model, relative to the classical model. More importantly, as the degree of positive autocorrelation becomes very strong, the power of each test must decline to its level of significance, irrespective of the data.