In many applications available data from several independent studies address the same question, and it is essential to have statistical methods for combining the results from the different studies. This article addresses this issue in two setups: (1) a testing hypothesis concerning the common mean vector of two independent linear models having different variances, and (2) a testing hypothesis concerning a common variance component in linear models involving two variance components. The interblock analysis of a balanced incomplete block design (BIBD) is a special case of (1) when we are interested in testing the equality of the treatment effects. Testing the significance of the treatment variance component in a BIBD with random effects is a special case of (2). We suggest some new test procedures for the testing problems in (1) and (2) and also give a review of the various existing tests. We numerically compare the powers of the various tests and make specific recommendations regarding the choice of the test to be used in practical applications.