If disturbance correlation arising from two-stage cluster sampling is ignored, it can lead to inefficient regression estimates and predictions as well as misleading inferences. This paper addresses the problem of testing for the intra-class correlation (block effects) in a two-stage clustered regression model. A point optimal invariant test is constructed to compute the power and the critical values at a 5% level of significance for various data sets. The comparative study demonstrates that the new test is uniformly most powerful invariant for a special case, when block size is half of the sample size.