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The article discusses moments of the distribution of sample size, N in a sequential probability ratio test (SPRT). The present paper provides variance, the third and the fourth moments of N. The details are worked out in five common applications of the SPRIT. The relation of the variance of N to the truncation of a SPRT is discussed is also discussed in the paper. Scholar A. Wald indicated in passing how one can obtain the moments of N, but the only published literature where the author encountered a general expression for the variance of N. However, their expression is incorrect. Using scholar J. Wolfowitz's results, which they do, or differentiating Wald's, fundamental identity twice one gets provided. In many practical applications of the SPRT, μ and moments in an equation derived are differentiable functions of a real-valued parameter. The limiting expressions for the moments can then be determined by standard methods of mathematical analysis. However, for the third and fourth moments the actual technique may involve an excessive amount of arithmetic.

In this paper we examine how well the asymptotic null distribution of a two sample test due to Lehmann approximates the small sample distribution of the test, compare the validity of this Lehman test with the validity of the two sample t test under the null hypothesis of equal means, and compare the power of this Lehmannn test with the power of the t test. Our general conclusion is that experimenters will prefer to use the t test when the underlying distribution is the scale contaminated compound normal distribution and the sample sizes are less than thirty. [ABSTRACT FROM AUTHOR]

In this paper the first two moments of the ratio (treatment sum of squares)/(treatment sum of squares + error sum of squares)over all possible random assignment of treatments to the experimental plots, for a class of 2 associate PBIBD has been obtained. These two moments are compared with the corresponding moments of a continuous beta distribution to settle the question of approximating the randomization test by the usual F-test. It has been shown that a reasonable approximation to the randomization test based on the statistic F is equivalent to modifying the normal theory test by multiplying the numbers of d.f. of the F-distribution by a factor depending on the heterogeneity of the blocks. [ABSTRACT FROM AUTHOR]