An Approximate Closed Form Solution for a Quadratic Dose–Response Model*

The quadratic dose–response model is often used in radiobiology studies. Since the model is nonlinear, the least squares estimators of the parameters of the model are determined by an iterative procedure. We give a simple closed form approximation for estimating the parameters of the model.     

Stochastic Orderings of Order Statistics of Independent Random Variables with Different Scale Parameters

This is an article on recent results on stochastic comparisons of order statistics of n independent random variables differing in their scale parameters. Most of the results obtained so far are for the Weibull and the Gamma distributions.     

Labor-use efficiency in Indian banking: A branch-level analysis

This paper uses data envelopment analysis to measure labor-use efficiency of individual branches of a large public sector bank with a sizable network of branches across India. We find considerable variation in the average levels of efficiency of bank branches across the four metropolitan regions considered in this study. In this context, we introduce the concept of area or spatial efficiency for each region relative to the nation as a whole. Our findings suggest that the policies, procedures, and incentives handed down from the corporate level cannot fully neutralize the detrimental influence of the local work culture across different regions. Most of the potential reduction in labor cost appears to be coming from possible downsizing in the clerical and subordinate staff. Our analysis identifies branches that operate at very low levels of labor-use efficiency and possible candidates for increased supervision and control.     

Computing Jacobians using exterior products

In this paper we describe an exterior product method for computing the Jacobian of a transformation. This alternative procedure is often simpler than the conventional determinant approach. We illustrate the proposed method via commonly used transformations in statistical distribution theory.     

Polytomous logistic model for matched pairs case-control design:studies with covariates

Pair-wise matched case-control design is commonly used in epidemiological analysis for estimating odds ratios. In the most simplest situation, each subject is classified according to a binary outcome and the factor of interest being a two-level factor. Binary logistic models have beenfound to be very useful for studying such relationship. In our earlier studies we have shown that polytomous logistic model can be used for estimating odds ratios when the exposure of prime interest assumes multiple levels. In this paper, using the above model, we estimate the odds ratios for the possible levels of risk factor of interest adjusting for covariates which were notincluded in the matching process. An illustrative example is presented and discussed.     

An empirical comparison of several methods for testing the equality of dependent proportions

Three methods for testing the equality of nonindependent proportions were compared with, the use of Monte Carlo techniques. The three methods included Cochran's test, an ANOVA F test, and Hotelling's T² test. With respect to empirical significance levels, the ANOVA F test is recommended as the preferred method of analysis.

Oftentimes an experimenter is interested in testing the equality of several proportions. When the proportions are independent Kemp and Butcher (1972) and Butcher and Kemp (1974) compared several methods for analysing large sample binomial data for the case of a 3 x 3 factorial design without replication. In addition, Levy and Narula (1977) compared many of the same methods for analyzing binomial data; however, Levy and Narula investigated the relative utility of the methods for small sample sizes.     

The Detrimental Side Effects of Minimum Wage Laws

The adverse effects of minimum wage legislation demonstrate how a government policy presumably intended to help people worst off in society can actually end up causing far more harm than good. In this case, the victims are unskilled laborers. By making it illegal for employers to pay unskilled workers wages equal to their marginal revenue productivity, it causes unemployment for all workers whose productivity happens to be below the minimum wage. It also widens the wage gap between whites and minorities because there are disproportionate numbers of unskilled and uneducated minorities compared with whites.     

Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix

In this article we consider a set of t repeated measurements on p variables (or characteristics) on each of the n individuals. Thus, data on each individual is a p ×t matrix. The n individuals themselves may be divided and randomly assigned to g groups. Analysis of these data using a MANOVA model, assuming that the data on an individual has a covariance matrix which is a Kronecker product of two positive definite matrices, is considered. The well-known Satterthwaite type approximation to the distribution of a quadratic form in normal variables is extended to the distribution of a multivariate quadratic form in multivariate normal variables. The multivariate tests using this approximation are developed for testing the usual hypotheses. Results are illustrated on a data set. A method for analysing unbalanced data is also discussed.     

Andrews plots for multivariate data: some new suggestions and applications

Andrews plots (Biometrics 28 (1972) 125-136), as a tool to graphically interpret multivariate data, have recently gained considerable recognition. In this article, we first review the previous literature and then suggest a modification to the traditional Andrews plots. Finally, we illustrate a few new applications of these plots in robust design studies and in correspondence analysis, using real data.