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作者：HOFFDING, W
摘要：Kendall in 1938 obtained the sampling distribution of [tau] from a universe in which all possible rankings are equally likely and showed that the distribution is asymptotically normal. In terms of the probabilities [rho], that 2 members (x 1, y 1) and (x 2, y 2) of the universe are concordant (they are concordant when (x 1[long dash]x 2) (y 1[long dash]y 2) > 0) and [kappa], that of 3 members one is concordant with the other 2, it is shown that the distribution of [tau] is asymptotically norma...
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作者：GEARY, RC
摘要：Universal normality may be tested by a field of tests for kurtosis given by [alpha](c) = 1/[image] [SIGMA]
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作者：WHITFIELD, JW
摘要：The use of [tau] for tied rankings (Kendall; Biometrika, 1946) is extended to the case where one variable is ranked and the other expressed as a dichotomy, the dichotomy being viewed as a ranking in which all data are tied at two values only. In applying the method to the case of the 2X2 table, a slight discrepancy is noted with the usual x 1 calculation.
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作者：DAVID, FN
摘要：The hypothesis that there is randomness within a sequence of alternatives is to be tested against the field of alternate hypotheses that the dependence is of the type in simple Markoff chains. A conditional power function formula is obtained for sequences of [gamma]1 E''s and [gamma]2''Es arranged in k sets. The function is plotted for a few typical sequences.
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作者：MORAN, PAP
摘要：It is shown that the covariance of 2 time series, each generated by weighted sums of sequences of independent random variables having the same distribution (for each series), is asymptotically normally distributed. The variance of the distribution is calculated in terms of the weights. It is pointed out that the wts. may not be detd. from the sample and used to determine the variance. It is instead necessary to decide first the orders and coeffs. of the stochastic difference equations which ge...
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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：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...
