On a Test of Significance in Pearson’s <i>Biometrika Tables</i> (No. 11)

Abstract

Summary The publication by Pearson and Hartley of numerical values for the proposed solution of Behrens' problem developed by Welch, affords an opportunity of clarifying in concrete terms, ideas which have in the past been disputed in perhaps a too abstract an atmosphere. Behrens' problem was to find a test of significance suitable for testing the hypothesis that two normal populations with unknown variances had a common mean. The fact that an unknown variance-ratio entered into the test was a comparatively novel feature, and has led to the problem being described as a test-case for examining different views of the process of testing hypotheses.