We use the concepts of stochastic complexity, description length, model selection and nonparametric histogram density to develop a new method for testing homogeneity of several populations. The test ...procedure depends only on the data and the smoothing parameters, which are shown to be readily chosen according to the criterion of minimum stochastic complexity. The procedure is shown to have asymptotic power 1. Two examples are given to illustrate its practical use. Justifications of the test procedure and comparison with related methods are also presented through a simulation study.
For testing the equality of variances for correlated variables, Harris (1985) suggested Wald type test statistics. In this note we show that this test coincides with the generalized least squares ...statistic employed in the analysis of covariance structures. We derive the generalized least squares estimator of the common variance. This estimator is compared with the average sample variances which is the ordinary least squares estimator for this problem.
Cressie and Read(1984) introduced multino~riial goodness-of-fit statistics
based on a, class of divergence measures I
a
between discrete distributions.
It was also introduced that a class of ...statistics R
a
for the test of homogeneity
for multino~riial populations based on I
a
(Read and Cressie(1988)). This class includes Pearson's X
2
statistic (when a = 1) and the log-likelihood ratio statistic (when a = 0). All R
a
have the same chi-squared limiting null distribution. The power of the class is ordinary approximated from a noncentral chi-squared distribution that is also the same for all a. Applying the power approximation theories for the multinomial goodness-of-fit test developed by Broffitt and Randles(1977) and Drost et al.(l989), Taneichi and Sekiya(1995)
proposed three approximations to the power of R
a
that vary with the statistic
chosen. In this paper we propose a. new approximation to the power of R
a
The new approximation is a normal approximation based on a normalizing transformation of the statistics. Moreover, the proposed approximation and the other approximations are numerically compared with the power directly calculated from the product multinomial model. As a result of comparison, the new approximation is found to be effective for the statistics when a a≤0.
We test the hypothesis of homogeneity over time in the rate of an event with a modification of Page's cumulative sum (cusum) procedure. The modification draws on an indifference zone approach to ...testing that is well suited to the epidemiologic study of retrospective data. We provide procedures for evaluating the significance level of the largest observed cusum value occurring in a sequence of fixed length. We draw inferences unconditionally with a known baseline rate of the event, and conditionally on observed margins with unknown baseline rate. Data collected over a five year period from one New York City hospital serve to illustrate the modified cusum test in a study of fluctuations in the proportions of chromosomally normal, trisomic, X-monosomic and triploid spontaneous abortions.
For the current manufacturing processes, there are many systems in which automatic and manual processes coexist. Compatibility of a model is a very important factor to perform correct analysis ...through simulation. In particular, unit utilization is also a very important factor. Analysis values vary according to how to examine and enter input data necessary for modeling. This study divides processes into automatic and manual ones to suggest how to perform different types of data collection. Automatic process implements data processing based on cycle time per unit while manual one measures cycle time per operator to process data in consideration of shifts per workplace. On completing input data, test for appropriateness is performed, followed by analysis of throughput and the operation rate per unit through a simulation model. Techniques in this study are applicable to general system simulations and will become inevitable for more thorough and accurate analysis.
It is shown that the "usual" nonrandomized, conditional test for comparing proportions using independent binomial samples, is very conservative in the sense that the actual significance level ...attributable to an outcome is often one-fourth to one-half of the anticipated value. A nonrandomized unconditional test is proposed, and for sample sizes up to 15, tables are given in an appendix which specify one-sided critical regions of size less than or equal to the nominal values 0.05, and 0.01 (two-sided critical regions are also given). Numerical examples illustrating the use of the tables and a brief description of the algorithm used to generate the tables are included.
