Recently, D’Agostino and Cureton {1972] discussed a test of normality against skewed alternatives; the test was based upon g1, the third standardized sample moment. In an earlier paper, D’Agostino [1970] suggested that an experimenter might be interested in testing the underlying assumption of normality associated with an analysis of variance. For such a test, one would be required to decide if k independent random samples were drawn from k normal populations. The purpose of this note is to suggest a simple extension of the test based upon g1, to the case of k independent random samples.