Abstract We investigate the power properties of a new goodness-nf-fit test proposed by rontz (1980). This new test is compared with the (The squared test and the Kolmogoma Smirnov (K-S) test for normality when the samples come from (i) the family of asymmetric stable distributions, (ii) mixtures of normal distributions, and (iii) the Pearson family. The general conclusion is that the new test performs better than the Chi squared and the K-S test when the parent distribution is heavy-tailed. If the hypothesized distribution differs from the true distribution in location only, the new test does not do as well as the other two. Keywords: Chi squared testKolmogorov-Smirnov testFoutz fn testAsymmetric stable distributionsmixed normal distributionsPearson's distributions