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作者：David, FN
摘要：The distribution of the criterion [psi]2 is discussed for the case when the hypothesis tested is true. The conclusion is reached that Neyman''s assumption that [psi]2 is distributed as x2 is valid for samples of 20 and over.
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作者：Gordon, RD
作者单位：University of California System; University of California San Diego; Scripps Institution of Oceanography
摘要：In estimating bacterial densities in solutions, direct microscopic counting and preparation of plates for plate-counting are often impractical or impossible. In such cases resort is often had to the method of successive dilutions, which is described. Several ways of interpreting data so obtained have previously come into some use, notably tables of modes by Halvorson and Ziegler. Their mode estimate is subject to theoretical objections, and has been found experimentally to disagree with direct...
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作者：Johnson, NL; Welch, BL
摘要：Formulae are given for calculating the cumulants of the x-distribution, as far as the 6th, with considerable accuracy.
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作者：Haldane, JBS
摘要：In this note the author shows how a rather fuller x2 analysis of the mendelian data of the preceding paper results in the extraction of some further information of interest.
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作者：Roberts, E; Dawson, WM; Madden, M
摘要：Observed Mendelian ratios obtained in rats, mice and rabbits are compared to the theoretical expectations. From 1 to 5 allelic pairs are involved, giving 2 to 32 classes. For obtaining probabilities with 2 classes the formula [image] were used. Among 65 ratios, 5 depart significantly from the theoretical.
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作者：Morgan, WA
摘要：The Neyman and Pearson likelihood ratio method is applied to derive a criterion for testing whether the variances in a sample from a normal bivariate population are equal. The test obtained depends only on the sample values of the variances and correlation coefficients but its power increases with the numerical value of the population correlation p. Being independent of p it appears to be the appropriate test criterion to use when p is unknown.
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作者：Newman, D
摘要：The object of the paper is to consider the ratio q[long dash]w/s, where w is the range of a sample of n individuals from a normal population, and s is an independent estimate of the population standard deviation with f/ degrees of freedom. The expectation of q is first considered and a short table given, by use of which, in conjunction with existing tables, this expectation can be calculated. The methods of calculating the upper 5% and 1% levels of the distribution of q (exact for n=2, 3, appr...
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作者：Welch, BL
摘要：A method of approximating the probability integral of the distribution of a maximum likelihood estimate is given.
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作者：Pitman, EJG
摘要：Suppose that X and Y are normally correlated variables and that we have a sample of n pairs of observed values (x r, y r) and wish to determine whether the sample values indicate that the variances of X and Y are unequal. A simple and exact significance test is developed, which may be used when the exact value of the correlation coefficient of X and Y is unknown. It is also shown how fiducial limits for the ratio of the variances of X and Y may be determined. A similar method gives very easily...
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作者：Pitman, EJG
摘要：Tests of certain hypotheses concerning location and scale parameters of chance variables are developed. These tests are unbiased and are applicable to chance variables with any continuous distributions. An application to the comparison of variances of normal variables yields Bartlett''s test, which is thus shown to be unbiased. This test is discussed in detail. The Neyman-Pearson variances test is shown to be biased except when the samples are all of the same size.
