Comparing the Variances of Two Dependent Groups

Let X and Y be dependent random variables with variances σ 2 x and σ 2 y . Recently, McCulloch (1987) suggested a modification of the Morgan-Pitman test of H o : σ 2 x =σ 2 y But, as this paper describes, there are situations where McCulloch’s procedure is not robust. A subsample approach, similar to the Box-Scheffe test, is also considered and found to give conservative results, in terms of Type I errors, for all situations considered, but it yields relatively low power. New results on the Sandvik-Olsson procedure are also described, but the procedure is found to be nonrobust in situations not previously considered, and its power can be low relative to the two other techniques considered here. A modification of the Morgan-Pitman test based on the modified maximum likelihood estimate of a correlation is also considered. This last procedure appears to be robust in situations where the Sandvik-Olsson (1982) and McCulloch procedures are robust, and it can have more power than the Sandvik-Olsson. But it too gives unsatisfactory results in certain situations. Thus, in terms of power, McCulloch’s procedure is found to be best, with the advantage of being simple to use. But, it is concluded that, in terms of controlling both Type I and Type II errors, a satisfactory solution does not yet exist.