The authors propose a new test of goodness of fit for the simple null hypothesis that the actual distribution is equal to a given, everywhere continuous distribution function. Under theNeyman-Pearson setup they obtain a test which (a) is meaningful without reference to any specific set of alternatives, and (b) is based on the fact we tend to dis-believe tall scores for improbable events. They also show that their test is connected with a pseudo distance between two distribution functions defined in terms of theKullback-Leiber mean information index. Finally, they compare their test with the standard procedures, viz. chi-square test,Kolmogorov’s test and two modifications of the latter, applying all of them to data published byDurbin.