Preliminary Results on a Robust Test for Variances Prepared under Contract No. Da-36-034-ord-1l77 (rd) (experimental Designs Far Industrial Research) = Number of Observations in Samples 1 and 2 Respectively

In testing the equality of several variances, it has been shown that the probabilities given by standard tests, derived on the assumption that the samples are drawn from a normal parent population, are subject to large errors when the normality assumption is not satisfied. Therefore a modified form of the F test for testing equality of two variances, when the means are knoim has been developed. This modified test involves calculating the standard F, but looking it up with degrees of freedom 6!J.and 6~ ratherthan I1:l and n2, where 1 6 = ---::1:---1 + 2" C2 • I1:l'~ = number of observations in samples 1 and 2 respectively By means of a sampling experinent with 12,000 values of F calculated from samples drawn from three parent populatiors, rect-'lngular, normal, and double exponential, the errors in probability levels found in the standard test for the non normal cases are [,Jl'eatly reduced by the modified test. Furthermore, this empirical work indicates this gain in "robustress" of the test is accompanied by a loss of power of only about ten percent by the use of the modified rather than standard test, where the parent population is normal.