Errata

My article entitled "Replications, Significance Tests, and Confidencein Findings in Survey Research" (POQ 47:261–69) is marredby a serious error which has implications for most of the contentsof the article. Table 1, which is adapted from a table published by Rosenthaland Hall,¹ gives the critical values of required for significance at several levels; itdoes not give the critical values of Trans , or () (). Rather, the latter should be referreddirectly to a table giving the areas under the normal curve,or, in other words, it should be treated as though it were aZ from a single-sample test. This means that the comparisons of significance test resultsfrom pooled data and from series of replications in Tables 2and 3 do not support the conclusion that using a replicate designrather than pooled data lessens the probability of Type II errors.In the case of Table 2, the probability from the pooled sampleis lower than the correct one from the series of replications,and in the case of Table 3, the probabilities are about thesame. The data in Table 4 illustrate a kind of situation in whicha replicate design may be the preferred one for another reason.The replicate design allows an estimate of sampling variabilityfrom the actual variability among a small number of samples,whereas the single-sample and pooled-sample significance testresults may be substantially in error due to the unstable meaningof the "zero" assigned to the reference category for the dummyvariables. However, the estimated probability for the arrayof replications should be .05 rather than the probability reported. Another error with less serious implications for the paper asa whole is that the third "alternative formula" for Trans is incorrect as printed. One of thefirst two formulas, or () (), should be used instead. The major error resulted from a misreading of the paper by Rosenthaland Hall. I apologize to Rosenthal and Hall and to any readersof my paper who have used the table of critical values incorrectlyin their research.     

AN ANALYSIS OF THE DYNAMIC THEORY OF THE MULTI—PRODUCT FIRM USING THE CALCULUS OF VARIATIONS

The purpose of this paper is to present the theory of the multi-product firm in situations where the revenue function depends not only on the rate of output but also on changes in the rate of output, and, similarly, where the cost function depends on changes in the rate of factor utilization as well as the rate of their utilization. Since the analysis will utilize the calculus of variations, a general introduction to this technique is also presented. The model analyzed assumes perfect foresight and knowledge concerning the revenue, cost, and production functions, and the calculus of variations is used to derive the conditions for an extremum. The first section presents the mathematical model and the model of the firm, and the optimality conditions are discussed in the second section.     

An integrated production and inventory model for a whole manufacturing supply chain involving reverse logistics with finite horizon period

This paper proposes a model and solution method for coordinating integrated production and inventory cycles in a whole manufacturing supply chain involving reverse logistics for multiple items with finite horizon period. A whole manufacturing supply chain involving reverse logistic consists of tier-2 suppliers supplying raw materials to tier-1 suppliers, tier-1 suppliers producing parts, a manufacturer which manufactures and assembles parts from tier-1 suppliers into finished products, distributors distributing finished products to retailers, retailers selling products to end customers and a third party which collects the used finished products from end customers, dissembles collected products into parts, and feed the parts back to the supply chain. In this system, we consider a finite horizon period. A mathematical model for representing the behaviors of the system is developed. Solution methods based on decentralized and a combination of decentralized and centralized decision making process, referred to as the semi-centralized decision making process, are proposed to solve the model while the centralized decision making process is solved by a mixed integer nonlinear programming method. A numerical example is used to demonstrate the model and the solutions based on the three types of the coordination.     

Examining Localized Patterns of Air Quality Perception in Texas: A Spatial and Statistical Analysis

Environmental and human health issues associated with outdoor air pollution, such as ozone, sulfur dioxide, and other pollutants in metropolitan regions, are an area of growing concern for both policy officials and the general public. Increasing attention from the news media, new health data, and public debate over the effectiveness of clean air regulations have raised the importance of air quality in the public consciousness. While public perceptions of air quality have been studied thoroughly dating back to the 1960s, little empirical research has been conducted to explain the spatial aspects of these perceptions, particularly at the local level. Although recent studies suggest characteristics of local setting are important in shaping perceptions of air quality, the roles of proximity, neighborhood characteristics, and location have not been clarified. This study seeks to improve understanding of the major factors shaping public perceptions of air quality by examining the spatial pattern of local risk perception, the role of socioeconomic characteristics in forming these perceptions, and the relationship between perceived and scientifically measured air pollution. First, we map the spatial pattern of local air quality perceptions using Geographic Information Systems (GIS) across the Dallas and Houston metropolitan areas. Next, we explain these perceptions through local contextual factors using both bivariate correlations and multivariate regression analysis. Results indicate that perceptions of air quality in the study areas are not significantly correlated with air quality based on readings of air monitoring stations. Instead, perceptions appear to be influenced by setting (urban vs. rural), state identification, access to information, and socioeconomic characteristics such as age, race, and political identification. We discuss the implications of the findings and provide direction on how further research can provide a deeper understanding of the local contextual factors influencing public perceptions.     

MATERIAL REQUIREMENTS PLANNING UNDER UNCERTAINTY

This paper presents a framework for characterizing and studying the uncertainty which can affect inventory investment and service level performance in a material requirements planning (MRP) system. It also presents the results of a simulation experiment which compared two techniques (safety stock and safety lead time) for building inventory to protect against uncertainty. The simulation results disclose consistent differences between the techniques in protecting a representative part against timing and quantity uncertainty in both demand and supply for the part. The paper not only provides some initial insights into the behavior of MRP systems under uncertainty, but also establishes some guidelines for choosing between safety stock and safety lead time.     

Extension of the Application of Conway‐Maxwell‐Poisson Models: Analyzing Traffic Crash Data Exhibiting Underdispersion

The objective of this article is to evaluate the performance of the COM‐Poisson GLM for analyzing crash data exhibiting underdispersion (when conditional on the mean). The COM‐Poisson distribution, originally developed in 1962, has recently been reintroduced by statisticians for analyzing count data subjected to either over‐ or underdispersion. Over the last year, the COM‐Poisson GLM has been evaluated in the context of crash data analysis and it has been shown that the model performs as well as the Poisson‐gamma model for crash data exhibiting overdispersion. To accomplish the objective of this study, several COM‐Poisson models were estimated using crash data collected at 162 railway‐highway crossings in South Korea between 1998 and 2002. This data set has been shown to exhibit underdispersion when models linking crash data to various explanatory variables are estimated. The modeling results were compared to those produced from the Poisson and gamma probability models documented in a previous published study. The results of this research show that the COM‐Poisson GLM can handle crash data when the modeling output shows signs of underdispersion. Finally, they also show that the model proposed in this study provides better statistical performance than the gamma probability and the traditional Poisson models, at least for this data set.     

Symbols Build Communication and Thought: The Role of Gestures and Words in the Development of Engagement Skills and Social‐emotional Concepts during Toddlerhood

Social skills and symbol skills are positively associated in middle childhood, but the relation between these domains is less clear in newly verbal toddlers. Vygotsky proposed that symbols are both tools for interaction and mental tools for thought. Do symbols help even very young children build skills for interacting with and conceptualizing the social world? Longitudinal data from 108 children and mothers were collected when children were 14, 24, and 36 months. Children's gestures and words during mother–child interactions were used as symbol skill indicators to predict children's abilities to engage others and the number of social‐emotional concepts children portray during play. In a series of growth models, words had a stronger effect on engagement skills whereas early gesture use predicted later development of social‐emotional concepts. Therefore, even in early development, symbols serve as both communication tools and mental tools to construct understanding of the social‐emotional world.