Comment on J. Berkson's paper “in dispraise of the exact test”

This paper rejects the preference expressed by Berkson for the heuristic test statistic T_N with standard normal distribution testing equality of two binomial probabilities in favour of Fisher's conditional exact test statistic T_E. Conditioning upon k₁ + k₂ = k shows that T_N admits too large first kind error probabilities. But also unconditionally T_N is systematically too large compared to T_E, giving too small critical levels at given experimental outcomes and power which is misleadingly too large. This is mainly due to the fact that T_N is not suitably corrected for continuity (at small sample sizes).     

Discussion on the paper by Stone

Summary. The single-input case of the 'technical efficiency' theory of M. J. Farrell is reformulated geometrically and algebraically. Its linear programming developments as 'data envelopment analysis' are critically reviewed, as are the related techniques of 'stochastic frontier analysis'. The sense and realism of using data envelopment analysis or stochastic frontier analysis techniques, rather than some value-based method, for the assessment of police force efficiency are questioned with reference to the Spottiswoode report and related studies.     

Discussion on the paper by Friedman and Fisher

Statistics and Computing -