Aggregated statistical rankings are arbitrary

In many areas of mathematics, statistics, and the social sciences, the intriguing, and somewhat unsettling, paradox occurs where the “parts” may give rise to a common decision, but the aggregate of those parts, the “whole”, gives rise to a different decision. The Kruskal-Wallis nonparametric statistical test on n samples which can be used to rank-order a list of alternatives is subject to such a Simpson-like paradox of aggregation. That is, two or more data sets each may individually support a certain ordering of the samples under Kruskal-Wallis, yet their union, or aggregate, yields a different outcome. An analysis of this phenomenon yields a computable criterion which characterizes which matrices of ranked data, when aggregated, can give rise to such a paradox. Received: 6 November 2001/Accepted: 7 March 2002     

A mixture model for random graphs

The Erdös–Rényi model of a network is simple and possesses many explicit expressions for average and asymptotic properties, but it does not fit well to real-world networks. The vertices of those networks are often structured in unknown classes (functionally related proteins or social communities) with different connectivity properties. The stochastic block structures model was proposed for this purpose in the context of social sciences, using a Bayesian approach. We consider the same model in a frequentest statistical framework. We give the degree distribution and the clustering coefficient associated with this model, a variational method to estimate its parameters and a model selection criterion to select the number of classes. This estimation procedure allows us to deal with large networks containing thousands of vertices. The method is used to uncover the modular structure of a network of enzymatic reactions.     

Field Measurement of Dermal Soil Loading Attributable to Various Activities: Implications for Exposure Assessment

Estimates of soil adherence to skin are required for assessment of dermal exposures to contaminants in soils. Previously available estimates depend heavily on indirect measurements and/or artificial activities and reflect sampling of hands only. Results are presented here from direct measurement of soil loading on skin surfaces of volunteers before and after normal occupational and recreational activities that might reasonably be expected to lead to soil contact. Skin surfaces assayed included hands, forearms, lower legs, faces and/or feet. Observed hand loadings vary over five orders of magnitude (roughly from 10^–3 to 10² mg/cm²) and are dependent upon type of activity. Hand loadings within the current default range of 0.2 to 1.0 mg/cm² were produced by activities providing opportunity for relatively vigorous soil contact (rugby, farming). Loadings less than 0.2 mg/cm² were found on hands following activities presenting less opportunity for direct soil contact (soccer, professional grounds maintenance) and on other body parts under many conditions. The default range does not, however, represent a worst case. Children playing in mud on the shore of a lake generated geometric mean loadings well in excess of 1 mg/cm² on hands, arms, legs, and feet. Post-activity average loadings on hands were typically higher than average loadings on other body parts resulting from the same activity. Hand data from limited activities cannot, however, be used to conservatively predict loadings that might occur on other body surfaces without regard to activity since non-hand loadings attributable to higher contact activities exceeded hand loadings resulting from lower contact activities. Differences between pre- and post-activity loadings also demonstrate that dermal contact with soil is episodic. Typical background (pre-activity) geometric mean loadings appear to be on the order of 10^-2 mg/cm² or less. Because exposures are activity dependent, quantification of dermal exposure to soil will remain inadequate until data describing relevant human behavior (type of activity, frequency, duration including interval before bathing, clothing worn, etc.) are generated.     

Tests for the multivariate two-sample problem based on empirical probability measures

Nonparametric tests are proposed for the equality of two unknown p-variate distributions. Empirical probability measures are defined from samples from the two distributions and used to construct test statistics as the supremum of the absolute differences between empirical probabilities, the supremum being taken over all possible events. The test statistics are truly multivariate in not requiring the artificial ranking of multivariate observations, and they are distribution-free in the general p-variate case. Asymptotic null distributions are obtained. Powers of the proposed tests and a competitor are examined by Monte Carlo techniques.     

The family system,temporary or permanent auxiliary ego: The differential fate of self-objects

This paper addresses the integration of developmental theory and family system theory. It is based on the assumption that the combination and integration of these two sets of theory gives the social work clinician the richest possible base for diagnostic assessment and intervention. Two points of intersection of these theories, birth and mate selection, are utilized to highlight the natural linkages between the theories and to demonstrate the combined power to more fully inform clinical practice.The human being like any other organism can be understood only in relation to its ecological niche, to which it is fitted by evolution and with which it is in balance or is striving for balance at every point of its life.     

Self Actualization in Marital Enrichment

The study attempted to evaluate the effectiveness of the Pairing Enrichment Program (PEP), a marriage enrichment program, in enhancing self-actualization. Shostrom's Personal Orientation Inventory (POI) was administered to an experimental group of married couples immediately prior to participating in PEP. A waiting list control group completed the POI at the same time. Three weeks later, following the completion of PEP for the experimental group, the POI was again administered to both groups. An analysis of co-variance was performed to test the effects of gender, group, and the interaction of these two factors on change in self-actualization (Post-POI minus Pre-POI), adjusting for six co-variables: Education of each, age of each, number of years married, and number of children. The results indicated that 1) being husband or wife had no significant effect on one's level of self-actualization, and that 2) the change in level of self-actualization was significantly greater (Positive Direction) for PEP participants than for non-PEP participants on the "I" and "C" scales of the POI     

Assessing Lund's critical values for testing for outliers in linear regression models

This note assesses Lund's critical bounds as approximations to the critical values of a size-a test for detecting single outlier in a multiple linear regression model. A Monte Carlo experiment shows that the empirical sizes are very close to the nominal sizes, and the regressors have little effect on the empirical sizes. Lund's tables are revised to higher accuracy.     

On the distribution of quadratic forms in normal random variables

This paper provides necessary and sufficient conditions for a quadratic form in singular normal random variables to be distributed as a given linear combination of independent noncentral chi-square variables. Using this result, an extension of Cochran's theorem to quadratic forms of noncentral chi-square variables is derived.