Editor's Notes

Two examples are given that illustrate the Gauss–Markov theorem. The examples will help students appreciate the use of the word best in connection with the term BLUE (best linear unbiased estimator). The examples will also provide several instructive exercises.     

Editor's Notes

Proceedings of the Third International Conference on Teaching Statistics Editor David Vere-Jones; assistants: Shelley Carlyle and Brian P. Dawkins. Published by the International Statistical Institute. Available from ISI Permanent Office, 428 Prinses Beatrixlaan, P.O. Box 950, 2270 AZ Voor-burg, The Netherlands. $38 (U.S.), including postage and handling. Reviewed by Elliot A. Tanis     

Editor's Report

There are two common methods for statistical inference on 2 × 2 contingency tables. One is the widely taught Pearson chi-square test, which uses the well-known χ²statistic. The chi-square test is appropriate for large sample inference, and it is equivalent to the Z-test that uses the difference between the two sample proportions for the 2 × 2 case. Another method is Fisher’s exact test, which evaluates the likelihood of each table with the same marginal totals. This article mathematically justifies that these two methods for determining extreme do not completely agree with each other. Our analysis obtains one-sided and two-sided conditions under which a disagreement in determining extreme between the two tests could occur. We also address the question whether or not their discrepancy in determining extreme would make them draw different conclusions when testing homogeneity or independence. Our examination of the two tests casts light on which test should be trusted when the two tests draw different conclusions.