Exploring multivariate data graphically:a brief review with examples

Many methods for obtaining graphical representations of multivariate data have been suggested over the last decade, but it is only relatively recently that software has become available which makes use of these procedures routine. In this paper, a number of examples are used to illustrate the application of graphical methods for the exploration of multivariate data. The diagrams produced may prove useful in consultations with clients and in examining the results from more formal methods.     

Sources of drug information among adolescent students

A sample of 1023 eighth and tenth grade students in small to medium-sized central Texas school districts was assessed to determine the amount of information they receive from ten sources about six categories of drugs. The amount of information males reported receiving about each drug category was significantly greater than what females reported, and the amount of information that eighth graders reported receiving about each drug category was significantly greater than what tenth graders reported. Television was the primary source of drug information for all categories of drugs except inhalants, for which friends and television were equally important sources. Parents and printed media (magazines or newspapers) were of secondary importance, followed by friends and teachers. Adolescents were less likely to receive drug-related information from experience, siblings, church, doctors, and police. The reliance on the mass media for drug information in smaller school districts is a pattern which has been previously observed in larger urban districts. This consistency suggests that mass media approaches to drug education are likely to be as effective in rural areas and smaller towns as they are among urban adolescents. Implications for television programming are discussed.     

Increasing contraceptive use in Bangladesh: The role of demand and supply factors

This article analyzes the determinants of contraceptive use in Bangladesh, focusing on the roles of demand for additional children and of family planning service supply. Data from the Matlab Family Planning Health Services Project are used to examine the contributions of these factors to the difference in prevalence of modern contraceptive use between the project area and a control area served by the government family planning and health programs. Results of multivariate analysis deriving from the Easterlin synthesis framework show the importance of family planning supply factors in reducing psychic and resource costs of fertility regulation and in activating latent demand for contraception. Demand for birth limiting and for birth spacing emerge as important explanatory factors; demand for birth spacing is greater in the project area, and both demand measures exert a stronger effect on contraceptive behavior in that area.     

Arrow's paradox and mathematical theory of democracy

Two measures, the weight of coalitions and the probability of situations in decision making, are used to characterize the representativeness, i.e. the capability of individuals to represent the social preference. It is proved that there always exists an individual who represents a majority on average, and an individual who represents a majority in most cases. This result is applied to Arrow's social choice model. It follows that there always exists a dictator who is a representative of the society rather than a dictator in a proper sense. After the concept of dictator has been refined to a dictator in a proper sense, Arrow's axioms become consistent. The idea of optimal representation is extended to limited groups of representatives which make decisions on behalf of the whole society. We consider the cabinet (named by analogy with the cabinet of ministers) which consists of a few representatives with delimited domains of competence, and the council which makes decisions by means of voting. It is shown that the representativeness of optimal cabinets and councils tends to 100% of maximally possible values as the number of their members increases, independently of the size of the society. We suggest a geometric interpretation of optimal representatives, cabinets, and councils, based on approximation formulas for the indicators of representativeness derived for the model with a large number of independent individuals. Finally, for cabinets and councils we establish the consistency of different concepts of optimality with respect to different indicators of representativeness. Our consideration is applicable to multicriteria decision making. An appointment of a cabinet or a council corresponds to selecting a few partial criteria. Therefore, the obtained results can be used for reducing the set of partial criteria to a certain sufficient minimum. The concepts of dictator, cabinet, and council can be understood as models of president, government, and parliament, respectively. Thus our results justify reducing social choice to individual choice or small group choice. Although it is in use in all democratic systems, its acceptability is not evident at all. In other words, we justify the demoncraticity of such forms of political power as the president, the parliament, and the government.     

Sampling Strategies for Toxic Air Contaminants

Annual concentrations of toxic air contaminants are of primary concern from the perspective of chronic human exposure assessment and risk analysis. Despite recent advances in air quality monitoring technology, resource and technical constraints often impose limitations on the availability of a sufficient number of ambient concentration measurements for performing environmental risk analysis. Therefore, sample size limitations, representativeness of data, and uncertainties in the estimated annual mean concentration must be examined before performing quantitative risk analysis. In this paper, we discuss several factors that need to be considered in designing field-sampling programs for toxic air contaminants and in verifying compliance with environmental regulations. Specifically, we examine the behavior of SO2, TSP, and CO data as surrogates for toxic air contaminants and as examples of point source, area source, and line source-dominated pollutants, respectively, from the standpoint of sampling design. We demonstrate the use of bootstrap resampling method and normal theory in estimating the annual mean concentration and its 95% confidence bounds from limited sampling data, and illustrate the application of operating characteristic (OC) curves to determine optimum sample size and other sampling strategies. We also outline a statistical procedure, based on a one-sided t-test, that utilizes the sampled concentration data for evaluating whether a sampling site is compliance with relevant ambient guideline concentrations for toxic air contaminants.     

Grounded Neural Networking: Modeling Complex Quantitative Data

The latest advances in artificial intelligence software (neural networking) have finally made it possible for qualitative researchers to apply the grounded theory method to the study of complex quantitative databases in a manner consistent with the postpositivistic, neopragmatic assumptions of most symbolic interactionists. The strength of neural networking for the study of quantitative data is twofold: it blurs the boundaries between qualitative and quantitative analysis, and it allows grounded theorists to embrace the complexity of quantitative data. The specific technique most useful to grounded theory is the Self‐Organizing Map (SOM). To demonstrate the utility of the SOM we (1) provide a brief review of grounded theory, focusing on how it was originally intended as a comparative method applicable to both quantitative and qualitative data; (2) examine how the SOM is compatible with the traditional techniques of grounded theory; and (3) demonstrate how the SOM assists grounded theory by applying it to an example based on our research.     

The validity of survey responses on abortion: Evidence from Estonia

This paper presents results of a validation survey of abortion conducted in Tallinn, Estonia in April and May 1992. The sample was drawn from patient records in a maternity hospital. Women who had an abortion in that hospital in 1991 were asked about recent abortions as part of a survey about women’s health. More than 80% of the respondents reported having a recent abortion. Some respondents misreported their abortion as a miscarriage. Moreover, some variation in reporting was associated with respondents’ characteristics. Ethnic Estonians were less likely to report their abortion than were Russians, women over age 40 were less likely to report the abortion than younger women, and women who had the abortion late in the first trimester were less likely to report that abortion. There was some evidence that unmarried women were less likely than married women to report their abortion, and that women who had borne three or more children were less likely to report their abortion than women who had borne fewer children. These differences probably stem from the extent to which pregnancy or abortion is considered stigmatizing for women in different situations.