A simple statistic is proposed to test the hypothesis that a sample comes from a distribution in the domain of attraction of the Gumbel distribution. It is based on the topkorder statistics and is a generalization of the Shapiro–Wilk goodness-of-fit statistic. The critical region of the test and its power against the alternative that the sample comes from a distribution in another domain of attraction are studied theoretically and by simulation. The power turns out to be superior to that of other tests previously proposed.