_ 'On the Problem of the Most Efficient Tests of Statistical Hypotheses'. Pp. 289-337 in: Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character. Vol. 231.

First Edition of the 'Neyman-Pearson lemma.' Entire volume offered. Buckram, large 4to. Ex-Carnegie Institution of Washington. Very Good. The paper in this volume is reprinted in Chapter 6 of Joint Statistical Papers of J. Neyman and E. S. Pearson (Berkeley & Los Angeles, 1967). 'The Neyman-Pearson theory of testing statistical hypotheses has become an integral part of every statistician's education and vocabulary. In 1928 the likelihood ratio criterion was put forward. No optimality was claimed, but the criterion was shown able to reproduce many existing tests and to provide appealing new ones. A major breakthrough occurred in 1933 with the optimality result that has become known as the Neyman-Pearson fundamental lemma. This settled the testing of a simple (i.e., fully specified) hypothesis against a simple alternative' (Herbert A. David, 'Egon S. Pearson', in The American Statistician, May 1981, Vol. 35, No. 2). 'Neyman's most influential relationship in London was with Karl Pearson's son, Egon Pearson, with whom he would collaborate in the study of hypothesis testing, leading to significant advancements in modern statistical methodology. The two decided to continue their investigation via letters and occasional meetings. What resulted from their combined work between 1928 and 1933 became known as the Neyman-Pearson theory, or the Neyman-Pearson fundamental lemma. Their first joint paper was published in 1928. It was followed by a series of ten published papers that culminated in 1933 with the publication of 'On the Problem of the Most Efficient Tests of Statistical Hypotheses' ' (Answers Web site).…