摘要:

The earlier literature on three-factor interactions in a three-way contingency table was concerned mainly with the null hypothesisH0that these interactions are all nil. In the present article, we present methods for testingH0which are easier to apply than those suggested by earlier writers on this subject, and in addition we develop methods for obtaining simultaneous confidence intervals for estimating the magnitudes of the three-factor interactions in the three-way contingency table, i.e., in theI×J×Kcontingency table. We also show how to partition a chi-square statistic for testingH0in a 2 × 2 ×Ktable intoK− 1 asymptotically independent components that can be used to testK− 1 different sub-hypotheses into which the hypothesisH0can be partitioned, and we introduce a rough and ready approximate method for testingH0in a 2 ×J×Ktable which is much simpler than any other valid method presented heretofore for testingH0.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10482163

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

Bayesian rules for decision under uncertainty are derived constructively from two principles of consistent behavior and two principles asserting that the decision maker can scale his preferences for consequences and judgments concerning unpredictable events by reference to simple lotteries involving only two consequences and based on an imaginary experiment with subjectively equally likely outcomes. It is shown that the two principles of consistent behavior require the decision maker's scaled judgments to obey the axioms of probability, and by use of one further principle of consistent behavior it is shown that they should also agree with the usual definition of conditional probability and hence with Bayes' rule.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10482164

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

Many existing continuous sampling plans are designed to provide a desired AOQL by requiring 100% inspection whenever incoming quality is found to be sufficiently poor. However, such extensive inspection is not practical for those cases where destructive testing is required, The continuous sampling procedure developed here is especially designed for these situations where the amount of inspection must be stringently limited. It uses certain a priori information about the quality behavior of the production process. It then improves upon this information by a limited amount of sampling inspection in order to determine when a process adjustment is needed.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10482165

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

When economists apply regression to monthly or quarterly data to estimate structural parameters, they generally either (a) use seasonally adjusted data or (b) use unadjusted data and allow for seasonal shifts in the intercept term. Starting from a more general model than either of these procedures, this paper spells out their implicit assumptions and derives expressions for the specification bias arising from incorrect assumptions. The expected values of the estimates in (a) and (b) are weighted averages of the coefficients in the more general model. The weights are regression coefficients. If parameters do not vary seasonally, procedure (b) yields unbiased estimates. Expected values of estimates from procedure (a) are random variables. If we apply covariance analysis to test for seasonal variation in coefficients, seasonally unadjusted data will yield unbiased estimates; seasonally adjusted data will not. Empirical results obtained from seasonally adjusted data differ substantially from those obtained from unadjusted data.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10482166

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

This paper identifies a type of highly correlated noise—systematic noise—that often arises in applications of linear regression to observations of spacecraft. An explicit formula is given for the inverse of the covariance matrix. The inverse matrix has a simple series expansion in ε2, where 1/ε is the amplitude of the systematic noise. When the leading term, the so-called filter matrix, is used in place of the exact inverse to estimate the regression parameters, the systematic noise is eliminated. The filter matrix is shown to be optimum among all matrices that eliminate systematic noise from the estimates. An example is discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10482167

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

The data arenunivariate observations that are not necessarily from the same population, from continuous populations, or independent. The problem is to develop an approximate expression for a specified one of the upper (or lower) extremes of this set of observations when a type ofm-dependence occurs. General expressions are developed that depend onn, the extreme considered, and the arithmetic average of the cumulative distribution functions (cdf's) for the individual observations. These results seem to be in a form that is satisfactory for practical applications, and a rule is given for deciding whennis large enough for their use. Also, a basis is furnished for deciding on the suitability of the model from the characteristics of the experimental situation, and consistent estimation of the average of the cdf's is considered. In practice, the asymptotic distributions that occur for the case of samples from continuous populations also seem to frequently occur for nonsample cases involving data that are not necessarily continuous. Some reasons are given which tend to explain the frequent occurrence of these types of asymptotic distributions.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10482168

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

Analysis of the 1960 census figures for native whites indicates reductions over the 1950 census in certain kinds of errors: 1) a decline in age heaping at almost every year of age, the major exception being age 59; 2) a decline in the absolute level of undercount; and 3) smaller net enumeration error rates for almost all five-year age groups.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10482169

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

A class of estimators is proposed for the estimation of the center of the Cauchy distribution. Each estimator in the class is the arithmetic average of a central subset of the sample order statistics. Although the sample median is a member of the proposed class, it is not the most efficient. The average of roughly the middle quarter of the ordered sample has the lowest asymptotic variance.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10482170

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

This paper examines “conjugate pairs” of points on the OC curve of a Wald Sequential Probability Ratio Test (SPRT). Such pairs are shown to exist for certain classes of SPRT's. For these classes, every point on the OC curve is a member of exactly one such pair. The well-known optimality property of a SPRT, which states that no other test of equal size and power (at the defining values of the parameter) can have a smaller expected sample size for either of the defining values, is extended to each conjugate pair. The OC curve is shown to be obtainable in a simple way, without the necessity of a parametric representation, by use of this notion of conjugate pairs.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10482171

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

Price indexes for nonhomogeneous products based upon input prices of labor and materials are inadequate because they take no account of productivity changes. Under the assumption that real output is proportional to real input of materials, it can be demonstrated that both price and productivity are functions of labor and materials costs and input of labor time. Price and productivity measures emerge from a simultaneous solution. Some very simple computational equations are derived. The method developed in this paper is tested in an empirical case. Highway prices for a fifteen-year period are calculated and compared with the Bureau of Public Roads index. The test is satisfactory.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10482172

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor