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作者：WISHART, J
摘要：Explicit expressions for the exact cumulants of Fisher''s z-distribution are given. Cumulants for the logarithmic x 2-distribution are first found (the same result was published by Bartlett and Kendall in 1946) and the cumulants of 2 obtained by considering the z-distribution as the difference between two logarithmic x 2-distributions. Cumulants of the logarithmic t-distribution are obtained by specializing the z-distribution.
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作者：WELCH, BL
摘要：A population parameter [eta] is estimated by a statistic [gamma], normally distributed about [eta] with variance [image], where the [sigma]i are positive numbers and the [sigma]2 are unknown variances. If independent estimates of these variances are provided by the observed data, it is possible to make probability statements about [gamma] similar to those Student gave for the mean of a single sample. The form of the exact solution is given and a series solution is developed. The series converg...
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作者：BARNARD, GA
摘要：In considering a significance level as a probability, it is necessary to isolate a class of events having the given probability. Some of the difficulties in this isolation and identification are pointed out in connection with a particular problem.
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作者：CARTER, AH
摘要：Tables of the percentage points of z are available for a range of values of [image] 1 and [image] 2. Outside the range tabulated 2 approx. formulae have been suggested. One, depending on an expansion of z in an Edgeworth series, involves laborious calculations. The 2d, due to Fisher and Cochran, is given in Fisher and Yates'' Tables and is widely used. Wishart has recently pointed out that an approximation to any cumulant, obtained by considering its leading term only, is improved by writing l...
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作者：FINNEY, DJ
摘要：In certain expts. it is not possible to administer doses at fixed levels to the subjects, although it is possible later to measure the dose each actually receives. Probit methods are given to make possible the regression analysis of the relationship between dose and response. An example is given in which dose is expressed in terms of 2 measurements and a probit plane is estimated. The validity of x 2 in testing goodness of fit is doubted, since the dose groups are necessarily small. Various ad...
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作者：SILLITTO, GP
摘要：The distribution of [tau] previously given by Kendall covers the situation in which neither ranking contains ties. This paper supplements Kendall''s work for the case in which one (only) of the rankings contains ties. Formulae are given for the maximum score S (in Kendall''s sense) and for the variance of the distribution of scores. A table is given of the probability distribution of S for up to 10 ranked pairs and all numbers of paired and triplet rankings.
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作者：PLACKETT, RL
摘要：Upper limits for the ratio of mean range to standard deviation in samples of n from any population are given by [image]. For large n, the upper limit is approx. [image].
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作者：HARTLEY, HO; KHAMIS, SH
摘要：Many statistics have sampling distributions which are not easily evaluated numerically. If it is possible to find simple formulae for the moments, the distributions may be approx. evaluated in a simple way. When R moments are known, the effective range is subdivided into (R + 1) intervals and the moments (plus Sheppard''s corrections) expressed as linear combinations of the frequencies. Since the matrix of the system of equations is non-zero, the unknown frequencies are then obtained from the ...
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作者：DAVID, FN
摘要：Two shortcomings of the ordinary X2 test for goodness of fit are that it disregards the signs of deviations between observed and expected values and takes no account of the order of those signs. Neyman''s [PSI]2 criterion involves a priori specification of the parameters of the hypothesis to be tested. A test criterion is given which takes into account only the signs of deviations and the order of signs. Tables of the frequency distribution of the criterion are given for 2 to 14 signs. It is s...
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作者：PLACKETT, RL
摘要：In the situation in which samples of [image] observations are drawn from each of [kappa] [rho]-variate normal distributions and the covariance matrices determined, it is required to test the hypothesis that variances and covariances of the [kappa] distributions are all equal. Exact tests are given for any number of 1- or 2-variate normal populations and for two 3- or 4-variate populations, where [image] > [rho][kappa]. The moments of the test criterion are given for the general case. The power...
