Two-sample test for dispersion differences based on a quadratic form statistics T, using placement statistics, is proposed. The null mean and variance of the test statistics are derived and asymptotic normality is established. The proposed test �and Mood�s test are seen to have same efficacy expressions under contiguous dispersion alternatives. We carryout simulation power study for small samples under dispersion alternatives. The study shows that for normal, Cauchy and exponential distributions the power of the proposed test is greater than or equal to the maximum of powers of the tests �and �derived by Gillespie and Wolfe [3].