Showing papers in "Biometrical Journal in 1985"
TL;DR: In this article, the dependence of chronic obstructive respiratory disease prevalence on smoking and age was investigated using the binary logistic model and a linear model of the log odds of response.
Abstract: Logistic probability models—models linear in the log odds of the outcome event—have found extensive application in modelling of unordered categorical responses. This paper illustrates some extensions of logistic models to the modelling of probabilities of ordinal responses. The extensions arise naturally from discrete probability models for the conditional distribution of the ordinal response, as well as from linear modelling of the log odds of response. Methods of estimation and examination of fit developed for the binary logistic model extend in a straightforward manner to the ordinal models. The models and methods are illustrated in an analysis of the dependence of chronic obstructive respiratory disease prevalence on smoking and age.
44 citations
30 citations
TL;DR: In this article, the decomposition of the complete point symmetry model in a rectangular contingency table is shown, and the respective decompositions for the local and reverse local point symmetry models in a square contingency table are given.
Abstract: The decomposition for the complete point symmetry model in a rectangular contingency table is shown. Also the respective decompositions for the local point symmetry model and the reverse local point symmetry model in a square contingency table are given. Moreover test procedures for the decomposed models and an example are given.
24 citations
24 citations
TL;DR: In this article, the authors propose a test procedure based on the principle described by MARCUS, PERITZ and GABRIEL (1976) for multiple testing of multinomial models in the case of one or two samples.
Abstract: For multiple testing of multinomial models in the case of one or two samples we propose using test procedures based on the principle described by MARCUS, PERITZ and GABRIEL (1976). These methods are based in each step of the sequentially rejective strategy on tests which exhaust the full α level (i.e. which are not conservative). The tests can be performed in a finite or asymptotic version.
21 citations
TL;DR: In this article, a chi-square test for significance of treatments and interactions is proposed. But the test is based on the standard analysis of variance of a two-way classification.
Abstract: This paper considers a common problem in analysis of variance where the responses to a set of treatments are nominal (i.e. are recorded in frequencies) with no underlying metric. Reasoning by analogy from standard analysis of variance of a two-way classification we develop chi-square tests for significance of treatments and interactions. Two tests are proposed for interaction and their asymptotic properties are studied.
18 citations
TL;DR: Two approaches to multivariate linear calibration in linear models are compared based on knowledge of the distribution of the variable to be predicted and the other one uses only information about the measurement instrument.
Abstract: In this paper two approaches to multivariate linear calibration in linear models are compared One of these approaches is based on knowledge of the distribution of the variable to be predicted The other one uses only information about the measurement instrument The methods are compared with respect to risk function and their functional relationship is analysed When concerns risk functions we concentrate on asymptotic results
16 citations
TL;DR: In this article, a simulation study was performed to compare three statistical tests with respect to their performances in the two-sample location problem for contaminated normal distributions, and the results showed the t-test to be inferior to the other two tests.
Abstract: A simulation study was performed to compare three statistical tests with respect to their performances in the two-sample location problem for contaminated normal distributions. The three tests were: the t-test, the rank-transformed t-test, and the Wilcoxon rank-sum test. The results showed the t-test to be inferior to the other two tests.
15 citations
14 citations
TL;DR: In this paper, the performance of the standard confidence limits for a proportion is studied over the entire range of proportions, and for various prescribed values of the nominal confidence coefficient, and modifications are suggested resulting in limits with average confidence coefficients close to the 95% nominal value.
Abstract: The performance of the standard confidence limits for a proportion is studied over the entire range of proportions, and for various prescribed values of the nominal confidence coefficient. In the light of the conservative nature of these limits, modifications are suggested resulting in limits with average confidence coefficients close to the 95% nominal value. A comparison is made with a solution obtained from the application of Bayes's theorem to the problem.
12 citations
TL;DR: In this article, the conditional distribution of a random variable independent of a given random variable is shown to be a generalized distribution of the random variable, and the proof does not depent on the specific form of the regression function, and it is also indicated how these results can be used for good-ness of fit purposes.
Abstract: The bivariate distribution of (X, Y), whereX andY are non-negative integer-valued random variables, is characterized by the conditional distribution ofY givenX=x and a consistent regression function ofX onY. This is achieved when the conditional distribution is one of the distributions: a) binomial, Poisson, Pascal or b) a right translation of these. In a) the conditional distribution ofY is anx-fold convolution of another random variable independent ofX so thatY is a generalized distribution. A main feature of these characterizations is that their proof does not depent on the specific form of the regression function. It is also indicated how these results can be used for good-ness-of-fit purposes.
TL;DR: In this article, a simple Fortran Subroutine is given for the exact calculation of permutational distributions for two independent samples for special cases such as the Fisher-Pitman randomization test, the Mann-Whitney U-test, the Mantel-Haenszel test and the exact test for 2×k contingency tables.
Abstract: A simple Fortran Subroutine is given for the exact calculation of permutational distributions for two independent samples. Important special cases are the Fisher-Pitman randomization test, the Mann-Whitney U-test, the Mantel-Haenszel-test and the exact test for 2×k contingency tables. The algorithm needs polynomial time and is of use even for personal- or microcomputers.
TL;DR: The best α-designs have higher efficiencies than the Khare and Federer designs, and can be constructed straightforwardly using the concise table of generating arrays in PATTERSON, WILLIAMS and HUNTER as discussed by the authors.
Abstract: KHARE and FEDERER (1981) have proposed a method for constructing resolvable incomplete-block designs with, they claim, higher efficiencies than those of the α-designs described by PATTERSON and WILLIAMS (1976a). This claim is shown here to be unfounded. The best α-designs have higher efficiencies than the Khare and Federer designs, and can be constructed straightforwardly using the concise table of generating arrays in PATTERSON, WILLIAMS and HUNTER (1978).
TL;DR: In this paper, an efficient regression-type estimator is proposed which is more efficient than the conventional regression estimator and hence than mean per unit estimator, ratio and product estimators.
Abstract: For the estimation of population mean in simple random sampling, an efficient regression-type estimator is proposed which is more efficient than the conventional regression estimator and hence than mean per unit estimator, ratio and product estimators and many other estimators proposed by various authors. Some numerical examples are included for illustration.
TL;DR: The method of moments estimator, discussed in this paperISHER and YATES (1970), for the density of bacteria is compared with the maximum likelihood or MPN estimator: For sample sizes used in practice the estimators are found to be very similar.
Abstract: The method of moments estimator, discussed in FISHER and YATES (1970), for the density of bacteria is compared with the maximum likelihood or MPN estimator: For sample sizes used in practice the estimators are found to be very similar. Estimators which reduce bias are discussed and their use recommended.
TL;DR: The authors showed that categorical data can be analyzed by analysis of variance methods; applying least squares, linear additive models, F-teste for significance, and so forth, which enriches an alternative analysis which leads to chi-square tests, c.f.
Abstract: This paper shows that categorical data can be analysed by analysis of variance methods; applying least squares, linear additive models, F-teste for significance and so forth. It enriches an alternative analysis which leads to chi-square tests, c.f. author (1982), LIGHT and MARGOLIN (1971).
TL;DR: The use of the score statistic to test whether a generalised distribution gives an improved fit over a non-generalised distribution is recommended in this article, where several specific examples are given.
Abstract: The use of the score statistic to test whether a generalised distribution gives an improved fit over a non-generalised distribution is recommended. The score statistic for a generalised exponential family is derived. Several specific examples are given.
TL;DR: In this paper, the problem of determining the optimum sample size in each stratum in stratified sampling for several variables is expressed and solved as a multistage decision process through dynamic programming.
Abstract: The procedure of determining the optimum sample size in each stratum in stratified sampling for several variables is expressed and solved as a multistage decision process through dynamic programming Using data published elsewhere, the dynamic programming approach was shown to give results identical to those obtained by some other already suggested approaches The advantage is that dynamic programming can more easily handle problems involving several strata and/or variables
TL;DR: In this paper, the authors set up a model for contingency tables of any dimension, and used three-dimensional contingency tables as an example to discuss first and second order interaction effects, and the conventional independence are expressed by hypotheses concerning interaction effects.
Abstract: Proceeding from Lancaster's definition of interactions between random variables, the authors set up a model for contingency tables of any dimension. Three-dimensional contingency tables are used as an example to discuss first and second order interaction effects, and the conventional independence are expressed by hypotheses concerning interaction effects. The opinions of other authors regarding second order interaction effects are discussed.
TL;DR: In this paper, a model was developed for forecasting of crop yields in which growth indices of biometrical characters based on two or more periods simultaneously have been used for predicting crop yields.
Abstract: A model has been developed for forecasting of crop yields in which growth indices of biometrical characters based on two or more periods simultaneously have been utilised. The growth indices are obtained as weighted accumulations of observations on biometrical characters in different periods, weights being respective correlation coefficients between yield and biometrical characters. This model has been found better than the models in use.
TL;DR: In this article, a new model for summarizing data on survival distribution is proposed and a simple graphical method (or equivalently a linear-regression-based method) for estimation of parameters is given.
Abstract: This note proposes a new model for summarising data on survival distribution. A simple graphical method (or equivalently a linear-regression-based method) for estimation of parameters is given. The model is shown to describe adequately data on Survivorship of Starling Birds reported by LACK (1943) and data on power generators reported by DHILLON (1981). A comment is added to illustrate how one can obtain a goodness of fit statistic which has a chi-squared distributions.
TL;DR: In this article, the authors used a mathematical framework to develop an estimator of population size and density using weighted least squares, which is a two-stage method, based on the BURNHAM and ANDERSON estimator.
Abstract: ANDERSON and POSPAHALA (1970) investigated the estimation of wildlife population size using the belt or line transect sampling method and devised a correction for bias, thus leading to a class of estimators with desirable characteristics. This work was given a basic and rigorous mathematica framework by BURNHAM and ANDERSON (1976). In the present article we use this mathematical framework to develop an estimator of population size and density using weighted least squares. The approach is a two-stage Method.
TL;DR: In this article, the authors illustrate two advantages of using canonical correlation as a tool in the discriminant problem, with more than two populations, rather than the more familiar Anderson discriminant function.
Abstract: This paper illustrates two advantages of using canonical correlation as a tool in the discriminant problem, with more than two populations, rather than the more familiar Anderson discriminant function. These advantages are: i) simultaneous test of significance as to whether the means of the populations differ and ii) given that the means differ, a graphic tool to illustrate the nature of the difference between the populations. If there are natural groupings of the populations, an analytic technique is also available to augment i). This latter property is also demonstrated in the accompanying application.
TL;DR: In this article, improved estimators for population mean are proposed which are better than the combined ratio estimator and some other well known existing estimators, from the point of view of bias and mean square error.
Abstract: When stratified random sampling is used for the estimation of population mean, use of ‘Combined ratio estimator’ is well known. Some improved estimators for population mean are proposed which are better than ‘Combined ratio estimator’ and some other well known existing ones, from the point of view of bias and mean square error. An empirical illustration is given.
TL;DR: Several asymptotic tests were proposed for testing the null hypothesis of marginal homogeneity in square contingency tables with r categories as discussed by the authors, and a simulation study was performed for comparing the power of four finite conservative conditional test procedures and of two asymPTotic tests for twelve different contingency schemes for small sample sizes.
Abstract: Several asymptotic tests were proposed for testing the null hypothesis of marginal homogeneity in square contingency tables with r categories. A simulation study was performed for comparing the power of four finite conservative conditional test procedures and of two asymptotic tests for twelve different contingency schemes for small sample sizes. While an asymptotic test proposed by STUART (1955) showed a rather satisfactory behaviour for moderate sample sizes, an asymptotic test proposed by BHAPKAR (1966) was quite anticonservative. With no a priori information the performance of (r - 1) simultaneous conditional binomial tests with a Bonferroni adjustment proved to be a quite efficient procedure. With assumptions about where to expect the deviations from the null hypothesis, other procedures favouring the larger or smaller conditional sample sizes, respectively, can have a great efficiency. The procedures are illustrated by means of a numerical example from clinical psychology.
TL;DR: In this paper, the statistical theory for fitting various selection models, and the known asymptotic results by simulation are evaluated by simulation, and it is shown that there is further information in data from these experiments besides the estimates of the selection parameters, namely the bounds for the effective population sizes.
Abstract: Data from gene frequency perturbation experiments are being used to resolve the selectionistneutralist debate over the evolutionary significance of electrophoretic enzyme variation. Previous statistical analyses of such data have encountered the major difficulty that the effective population size is not known. In this article, we give the statistical theory for fitting various selection models, and we evaluate the known asymptotic results by simulation. We also show that there is further information in data from these experiments besides the estimates of the selection parameters, namely estimates of the bounds for the effective population sizes.
TL;DR: Empirical regression is defined as conditional expected value based on an estimation of a twodimensional density as discussed by the authors, which is a model-free mathematical means for a first evaluation of measured data of an unknown stochastical relation between two quantities.
Abstract: Empirical regression is defined as conditional expected value based on an estimation of a twodimensional density. It is a modelfree mathematical means for a first evaluation of measured data of an unknown stochastical relation between two quantities. The numerical procedures may be applied for calculation of the mean course of an unknown relation hidden in the measured data. Disregarding the statistical background an other aspect of application is the analyzing of time series, especially smoothing of time series and modelfree recording of the trend component in non-stationary time series. The calculated regression curve provides an objective basis for comparing of different measured courses as well as for a further evaluation, e. g. in respect of a suitable choice of an analytical expression. The possibility of interpolation and the smoothing properties of empirical regression give essential advantages for internal regression as one step in the process of model construction.
TL;DR: This paper developed a robust classification procedure based on modified maximum likelihood estimators for classifying an observation in one of the two populations π1 and π2 and showed that this procedure is superior to the classical and nonparametric procedures.
Abstract: We develop a robust classification procedure, based on TIKU'S (1967, 1980, 1982) MML (modified maximum likelihood) estimators, for classifying an observation in one of the two populations π1 and π2 and show that this procedure is superior to the classical and nonparametric procedures.