The problem of testing homogeneity of many within-subject variances us
ing small samples is addressed. The asymptotic null distribution of mi
nus twice the likelihood ratio statistic, as the number of subjects te
nds to infinity, is derived. By inverting the characteristic function
of this statistic numerically, the performance of the corresponding cr
itical values may be assessed, and compared with competing approximati
ons. A real data example and a theoretical comparison demonstrate the
accuracy of the critical values derived.