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A noisy duel is a zero-sum, two-person game with the following structure. Each player has bullets which he can fire at any time in [0, 1]. If Player i fires at time t, he hits with probability Pi(t). The functions Pi are continuous and nondecreasing with P[sub i](0) = 0 and P[sub i](l) = 1. The number of bullets each player possesses at any time and the functions Pi are known to both. The payoff is I to the sole survivor, otherwise 0. This article states the authors' earlier result on the existence of a value of a noisy duel and presents a detailed discussion of the structure of epsilon-good strategies and criteria for the existence of good first-shot times. We present tables of values and shooting times for noisy duels, which, in some cases, can be used to trace the play of the game. An additional table illustrates how large an arsenal is necessary to overcome the effects of an opponent's superior accuracy. [ABSTRACT FROM AUTHOR]

This article proposes a refinement of the usual approximation due to Satterthwaite for making a significance test when the test statistic involves a single mean square in the numerator and a linear combination of mean squares in the denominator, that linear combination involving known positive constants. The test procedure is outlined in detail, and its derivation given in a separate section. The development of the technique essentially involves determining, by successive approximations, a function which serves as the test criterion. This function is given through terms in the cubes of the reciprocals of the degrees of freedom involved in the problem, thereby giving a deviation from the advertised significance level which is smaller (in magnitude) than the deviation provided by the Satterthwaite procedure. An expression approximating the power of the test is also developed. [ABSTRACT FROM AUTHOR]

Cochran's Q test for differences between related-sample percentages or proportions has generally been incorrectly presented in secondary sources. The most common mistake results from failure to recognize that rows containing only 1's or only O's, i.e., only successes or only failures, do not affect the value of Q. The F test, however, is affected by such rows. The probabilities from the x[sup 2] and F approximations are compared with the exact probabilities in three sets of data. A rule of thumb, based on extensive study of the distribution of Q in small samples, is given as an aid in judging when the x[sup 2] approximation is satisfactory for practical purposes. [ABSTRACT FROM AUTHOR]

Where Youden's extreme rank sum test is used, an early decision is often possible by performing the trials in sequence with the following method. After each trial is completed, the greatest lower bound and least upper bound of both extreme rank sums are calculated for all remaining trials. If the critical regions cover either or both intervals of the statistics or the intervals lie completely outside the critical regions, the round-robin test is terminated with the acceptance of the proper hypothesis. [ABSTRACT FROM AUTHOR]