The significance of difference between means without reference to the frequency distribution function

Most existing tests for significance of difference between means require specific assumptions concerning the distribution function in the parent population. The need for a test which can be applied without making any such assumption is stressed. Such a statistical test is derived. The application of the test involves converting scores to rank orders. The exact probabilities may then be calculated for specified differences between samples by means of which the null hypothesis may be tested. The application of the test is simple and requires a minimum of calculation. The test loses in precision because of the conversion to rank orders but gains in generality since it may be safely used with any kind of distribution.This study was started at the Iowa Child Welfare Research Station of the State University of Iowa. I should like to express my gratitude for the help I received there.