The test of homogeneity of variances arises in various statistical problems. In this paper, we compared five Levene-type tests including Levene’s test, Welch’s test, James’s test, Brown and Forsythe’s test and Alexander–Govern’s test in terms of power and size. The simulation results show that the bootstrapping after applying Noguchi and Gel (J Nonparametr Stat 22:897–913, 2010) correction and removing structural zeros significantly improve the performance of Type I error rates. We identify the best in terms of controlling the Type I error rate and power for each number of groups.