摘要:

Sample sizes are given such that the ratio of variances from two independent normal populations can be estimated within 100pper cent of the true ratio, with confidence 1 − α, forp= .2, .25, .33, .4, .5, .6, .75, 1.0, 1.5, 2.0; 1 − α = .90, .95, .99.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480685

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

Computer generated pseudo random numbers were used to simulate drawing 1000 pairs of samples ofN1,N2= 5, 10, 20 from bivariate populations normal (O, σi2I) having σ2/σ1= 1, 1.6 or 3.2, and from circular bivariate symmetrical leptokurtic populations with zero means, equal variances and β2− 3 = 3.2 or 6.2. Results suggest that the null distribution ofT2for pairs of bivariate normal samples withN1=N2≥ 10 is rather robust against variance inequality but that this robustness does not extend to disparate sample sizes, and that upper tail frequencies of the distribution of bivariateT2forN1,N2≥ 10 are not substantially affected by moderate degrees of symmetrical leptokurtosis. In simulations of sampling from circular normal populations with scale parameters in the ratio of 1.6:1 and 3.2:1 respectively, the proportion ofMexceeding the null 5% point ranged from 9% and 49% forN1=N2= 5 to 60% and 100% forN1=N2= 20. In simulations of homoscedastic leptokurtic sampling, the proportions ofMexceeding the null normal 5% point forN1=N2= 5 and forN1=N2= 20 were 8% and 17% for β2− 3 = 3.2, and 22% and 42% for β2− 3 = 6.2.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480686

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

The most frequently used practical regression model is that in which it is supposed that the dependent variate is normal for given values of the independent variate. In this paper it is pointed out that another regression model of wide applicability may be furnished by the contrary assumption—that the independent variate is normal for given values of the dependent variate. The particular case where the dependent variate is a vector of dummy variables is explored in detail.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480687

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

Paired comparisons among competing items are analogous to games between contestants and the process of determining the winning item amongtcontestants is analogous to a tournament. In this paper four different types of tournaments are investigated for the eight-player case. Expressions are developed for (1) the probability that each player wins and (2) the expected number of games required. Examples are presented for comparison of tournament types and to study the effects of (a) the initial draw, (b) mis-classification when usinga prioriinformation in initial pairing, and (c) “byes.” Some generalizations in terms of number of players and replication are developed.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480688

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

The purpose of this paper is to present tables for the construction of confidence limits on the multiple correlation coefficient when sampling from ak-variate normal population. Ezekiel and Fox [3, pp. 296–8] prepared charts which serve this purpose whenkis eight or less. The tables in this paper are for cases involving values ofkthat are larger than eight. Some brief historical comment is also given, and (in the next to the last paragraph) an illustration of the use of the tables.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480689

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

Tables for the Wilcoxon two-sample statistic are presented. The normal approximation to the distribution of the statistic and the use of continuity corrections are considered. A compilation of existing tables of the exact distribution of the Wilcoxon statistic and some additional exact percentage points computed for the same statistic are given. Moreover, a reasonably complete bibliography is included.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480690

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

Sets bounded by random variables that are functions of the firstk, k<n, members of a random sample ofnmembers from a normal distribution are studied. These sets have the property that, before the random sample is drawn, the probability is 1 − α, 0 <a< 1, that they contain a point whose coordinates are specified functions of all of thenmembers of the random sample. Usually, these specified functions will be estimates of the distribution parameters. After numerical values are obtained for thekmembers of the subsample, the set is fixed and affords a regional forecast along with an index of the reliance to be placed on the forecast for the eventual parameter estimate which will be based on allnmembers of the random sample. Such sets and indices are called “forecast sets” and “forecast coefficients,” respectively.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480691

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

This paper illustrates the application of life table techniques to data on school enrollments as a means of estimating school life expectancy. The school life tables which are derived are double decrement tables which show the joint effects of death and school dropouts on school attendance patterns. Such tables drawn up for 1950–52 and 1957–59 show the improvements in school retention by age during the last decade. Modifications of this type of analysis which would incorporate the probability of other phenomena occurring and extend the applications to other population groups are suggested.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480692

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

In this note some aspects of residual analysis are considered critically. The relation between residual analysis in the sense of Freund, Vail, and Clunies-Ross and the analysis of covariance is clearly exhibited. The note establishes exact expressions for the difference between the “true” additional regression sum of squares obtained by simultaneous regression analysis and the regression sum of squares due to additional variables by residual analysis. The difference is given some simple interpretations. It is shown that a residual analysis test statistic considered by Freund,et al. is subject to certain serious defects.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480693

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

For dichotomous data based on unequal frequencies, the formulae for analysis of variance, estimates and confidence bounds are presented in detail, along with the corresponding χ2and χ12test statistics. A theorem is given which relates the formulae for analysis of heteroscedastic observations to those of homoscedastic observations. The formulae presented in this paper may be justified by this theorem.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480694

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor