We investigate the asymptotic properties of some statistics based on quadratic entropy (QE), a notion introduced by Rao (Sankrya A 44 (1992) 1-21) as a general measure of variability in a population. Sample QE based on i.i.d. observations from a distribution function is defined and its asymptotic distribution is derived. The use of QE in the place of variance in analysis of diversity of cross classified data provides a generalization of ANOVA. We call this method ANOQE (analysis of quadratic entropy). The ANOQE statistic for testing equality of populations based on one-way classified data is constructed and its asymptotic and bootstrap distributions are derived.