摘要:

A generalization is given to the multivariate case of the linear model usually employed in the determination of accuracy of observations. Likelihood ratio tests are derived for testing hypotheses concerning systematic differences among observers, and a criterion is suggested for evaluating the magnitude of errors of measurement.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480876

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

This paper shows that the least-squares estimate of the matrix of coefficients in a multivariate linear regression model maximizes the squared vector correlation coefficient between the dependent variables and a linear transformation of the explanatory variables.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480877

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

The expected significance level (ESL) of a test, proposed by Dempster and Schatzoff (4) as a criterion for comparing sensitivities of competing test statistics, is defined as the expected value of the observed significance level under a simple alternative hypothesis. For example, the ESL of a lower tailed test of the hypothesisH0:X∼F(x) againstH1:X∼G(x) is given by ñF(x)dG(x). In this paper, the sensitivities of several proposed tests of the general linear hypothesis are compared by simulating their ESL's under a wide variety of parameterizations. The results indicate that Wilks's likelihood ratio criterion A and Hotelling'sT02provide about the same levels of protection over a wide spectrum of alternatives, whereas Roy's largest characteristic root is shown to be rather insensitive to alternatives involving more than one non-zero root. Other proposed test statistics are shown to be less sensitive as judged by the ESL criterion.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480878

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

Adapting the usual manual methods of computing Kendall'stauto automatic computation result in a running time of orderN2. A method is described with running time of orderNlogN.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480879

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

Random sampling experiments were performed to determine whether Goodman and Kruskal's asymptotic theory (2) for the sample version (G) of the measure of association Gamma (γ) is applicable to small samples.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480880

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

The procedures of Scheffé [4] and Welch [5] for testing equality of means of two normal populations are compared according to the expected lengths of the confidence intervals they yield, and a criterion is developed for deciding which of the two methods is better in any given situation. An expression for the expected length of the confidence interval for the Scheffé procedure was developed by Scheffé. Because of the asymptotic series nature of the Welch procedure, in this case, the analogous expression is more involved. It is developed below. A numerical computation was carried out for the case of a two-sided 90 per cent confidence interval. The results are presented in graphical form. Finally, it is shown that in large samples, the two procedures are equivalent.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480881

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480882

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A relatively complete discussion is provided for the limiting distributions of certain sample correlation coefficients and sample correlation ratios. It is assumed for the random variablesXandYthat the conditional distribution ofY, givenX=x, is multivariate normal with a constant, but unknown, covariance matrix and that the distribution ofXhas finite fourth moments. The sample coefficients are then based on a random sample from the (X, Y)-distribution. For the case of a univariate random variableXthe limit laws are shown to depend on theX-distribution only through its coefficient of excess. In other cases they are determined from the coefficients of excess of univariate distributions closely related to the distribution ofX.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480883

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

In the application of Bross' covast test [1] for detecting differences between two treatments with dichotomous response variable in the presence of a covariable, pairwise comparisons are made between subjects receiving different treatments. In the process, the set of all such comparisons is partitioned into two subsets potentially favoring one or the other treatment. Under random allocation of the treatments (with respect to the covariable), the expected proportion of each of these subsets,E(r) andE(1 —r), will be 0.5; in actual experimental situations, however,rwill not usually be equal to 0.5. Approximations are given for the expected value of the test statistic conditional on the ordering with respect to the covariable, both under the “Grand Null Hypothesis” of [1] and under the hypothesis of no treatment differences. Some procedures are suggested for dealing with the caser≠ 0.5.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480884

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

A common problem in sample estimation is the one of producing estimates for parts of the original universe (these parts are variously referred to in the literature as domains, subuniverses or subpopulations and may be defined in terms of areas or other characteristics). A technique is presented for producing these part-estimates when ratio or regression estimates are involved. This technique is used to produce estimates of retail trade for areas such as States, geographic divisions, Federal Reserve Districts, etc. from the national sample used for the Monthly Retail Trade program. The technique used provides a quick computation of the estimate and its variance for any specified combination of counties. The estimates produced are always consistent with each other and with the national estimates.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10480885

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor