Paul W. Mielke

Multi-response permutation procedures for a priori classifications

An exact permutation test for analyzing and/or dredging multi-response data at the ordinal or higher levels is presented. The associated test statistic is based on the average distance (or any specified norm) between points within a priori disjoint subgroups of a finite population of points in an r-dimensional space (corresponding to r measured responses from each object in a finite population of objects). Alternative approximate tests based on the beta and normal distributions are provided. Two detailed examples utilizing actual social science data are considered, including comparisons of the approximate tests. An additional example describes the behavior of these tests under a variety of conditions, including extreme data configurations

Lead Concentrations in Inner-City Soils as a Factor in the Child Lead Problem.

Soil samples were randomly collected from 422 vegetable gardens in a study area centered in downtown Baltimore, Maryland, and having a radius of 48.28 km (30 miles). The levels of lead, four other metals (cadmium, copper, nickel, and zinc), and pH were measured for each location. The application of multi-response permutation procedures, which are compatible with mapping techniques, reveals that lead (as well as cadmium, copper, nickel, and zinc) is concentrated and ubiquitous within the soils of the inner-city area of Metropolitan Baltimore. The probability values that the concentration of metals occurred by chance alone vary from about 10(-15) to 10(-23) depending on the metal considered. Our findings pose environmental and public health issues, especially to children living within the inner-city.

Data-dependent permutation techniques for the analysis of ecological data

Two distribution-free permutation techniques are described for the analysis of ecological data. These methods are completely data dependent and provide analyses for the commonly-encountered completely-randomized and randomized-block designs in a multivariate framework. Euclidean distance forms the basis of both techniques, providing consistency with the observed distribution of data in many ecological studies.

PAH and metal mixtures in New Orleans soils and sediments

The purpose of this study is to determine the degree of PAH contamination and the association of PAHs with inorganic substances in soils and sediments of New Orleans. Bonnet Carré Spillway (BCS) (n = 5) provides modern baseline data, while urban soil samples (CTY) (n = 27) and sediment samples from Bayou St. John (BSJ) (n = 11) provide experimental data for New Orleans. Soil samples were collected from the top 2.5 cm of the surface, air-dried, and sieved (2 mm). Sediments samples were collected with a Wildco-Ekman bottom dredge, air-dried and finely ground. Accelerated solvent extraction (ASE) was used to release PAHs from the samples and analysis was conducted with gas chromatography-mass spectrometry (GC-MS). Metals were extracted using a 5:1 ratio of 1 mol/L nitric acid (room temperature) for soil and sediment samples, shaken for 2 h, centrifuged (1000 x g for 15 min) and filtered. Metal analysis was done by inductively coupled plasma-atomic emission spectrometry (ICP-AES). Mann-Whitney tests show PAH differences (P < 0.001). Ranking of total PAHs is, BSJ sediments (10.3 mg/kg) > CTY soils (3.7 mg/kg) > BCS alluvium (0.28 mg/kg). The sum of the metals are similar for BSJ sediments (698 mg/kg) and CTY soils (679 mg/kg) and significantly lower for BCS (189 mg/kg). Manganese of these samples is similar for each site. For paired samples, Pearson Product Moment Correlation tests reveal that many PAHs are strongly associated with each other at all locations. For BCS alluvium and BSJ sediments, total PAHs are not significantly associated with total metals. For CTY, most pairs of metals are significantly associated, and total soil PAHs are strongly associated with total soil metals (correlation 0.78, P = 4.9 x 10(-4)). The linear model, total soil PAH = 136.3 + 6.25 (total soil metals) forms the basis for a predicted PAH map of New Orleans. Previous empirical research demonstrates an association between soil lead and childrens lead exposure. This study indicates that PAHs are part of the soil mixture of accumulated substances and by-products of industrial society that presents exposure potential in cities.

A Generalization of Cohen's Kappa Agreement Measure to Interval Measurement and Multiple Raters:

Cohens kappa statistic is frequently used to measure agreement between two observers employing categorical polytomies. In this paper, Cohens statistic is shown to be inherently multivariate in nature; it is expanded to analyze ordinal and interval data; and it is extended to more than two observers. A nonasymptotic test of significance is provided for the generalized statistic.

Quantities and associations of lead, zinc, cadmium, manganese, chromium, nickel, vanadium, and copper in fresh Mississippi delta alluvium and New Orleans alluvial soils

The topic of this study is the effect of anthropogenic metals on the geochemical quality of urban soils. This is accomplished by comparing the metal contents and associations between two alluvial soils of the lower Mississippi River Delta, freshly deposited alluvial parent materials and alluvial soils collected from a nearby urban environment. Fresh alluvium samples (n = 97) were collected from the Bonnet Carré Spillway. The urban alluvial soil samples (n = 4026) were collected from New Orleans and stratified by census tracts (n = 286). The Spillway samples tend to have less Pb and Zn than generally noted for the baseline of natural soils. Except for Mn and V, Spillway alluvium contains significantly less metal than urban soils. For Spillway samples, the median metal content (in microg g(-1)) is 4.7 Pb, 11.1 Zn, 0.7 Cd, 164 Mn, 0.8 Cr, 3.9 Ni, 3.2 V, and 3.9 Cu. For urban soils, the median metal content (in microg g(-1)) is 120 Pb, 130 Zn, 3.2 Cd, 138 Mn, 2.1 Cr, 9.8 Ni, 3.8 V, and 12.7 Cu. Metal associations also differ between Spillway alluvium and urban alluvial soils. Fresh alluvium correlation coefficients between individual metals vary from 0.87 to 0.99 (P < 10(-13)) except for Cr which ranges from 0.57 to 0.68 (P < 10(-7)). The urban soil correlation coefficients for metals and the index value are 0.40-0.98. In urban soils, Pb, Zn, Cr, and Cu are dominant metals and highly associated, with a correlation coefficient ranging from 0.83 to 0.98 (P < 10(-25)). Their strong association justifies the use of GIS to map the integrated soil metal index (sum of the medians of metals by census tract) of New Orleans. Although also positively correlated (0.40-0.68, P < 10(-10)), Cd, Mn, Ni and V differ in their distribution in the city compared to Pb, Zn, Cr and Cu. Overall, significantly higher metal values occur in the inner city and lower values occur in outlying areas. The human health impact of the mixture of metals is not well understood. This study provides empirical data about the mixture and distribution of metals in New Orleans alluvial soils. Given common technical development, especially of traffic flows in cities, similar patterns of soil metals are expected for all US cities and probably international cities as well. Primary prevention of urban metal accumulations is necessary to enhance and sustain the development of urban culture.

On asymptotic non-normality of null distributions of mrpp statistics

Severe departures from normality occur frequently for null distributions of statistics associated with applications of mulLi-response permutation procedures (MRPP) for either small or large finite populations. This paper describes the commonly encountered situation associated with asymptotic non-normality for null distributions of MRPP statistics which does not depend on the underlying multivariate distribution. In addition, this paper establishes the existence of a non-degenerate underlying distribution for which the null distributions of MRPP statistics are asymptotically non-normal for essentially all size structure configurations. It is known that MRPP statistics are symmetric versions of a broader class of statistics, most of which are asymmetric. Because of the non-normality associated with null distributions of MRPP statistics, this paper includes necessary results for inferences based on the exact first three moments of anv statistic in this broader class (analogous to existing results for MRPP st...

Permutation Techniques Based on Euclidean Analysis Spaces: A New and Powerful Statistical Method for Ecological Research

The statistical procedures that are most widely used in ecological population and community research belong to the family of parametric methods. Embedded in these procedures are assumptions about the normal distribution of the underlying population, homogeneity of variances and linear response patterns. One of the problems encountered in ecological and vegetation studies, however, is that these assumptions are very difficult, if not impossible, to meet. In addition, a very serious shortcoming of the most widely used statistical methods is the lack of congruence between the geometry of the data space, which is for the most part Euclidean, and the analysis space, which in the standard parametric tests and most of the nonparametric tests, is not Euclidean. In ecological and vegetation studies, the combination of a failure to meet model assumptions and a lack of congruence between the geometries of the data space and the analysis space can lead, as shown in this paper, to gross errors in data interpretation and hypothesis testing.

Improvements in the Permutation Test for the Spatial Analysis of the Distribution of Artifacts into Classes

Refinements and extensions to the permutation test for assessing the intrasite patterning of artifact distributions in an archaeological space are presented. Specifically, a Pearson type III distribution is employed to approximate the sampling distribution of the test statistic, an improved weighting is introduced to increase the efficiency of the test, and a method is presented to permit the inclusion of unclassified artifacts in the spatial analysis.

A MONTE CARLO INVESTIGATION OF THE FISHER Z TRANSFORMATION FOR NORMAL AND NONNORMAL DISTRIBUTIONS

The Fisher transformation of the sample correlation coefficient r (1915, 1921) and two related techniques by Gayen (1951) and Jeyaratnam (1992) are examined for robustness to nonnormality. Monte Carlo analyses compare combinations of sample sizes and population parameters for seven bivariate distributions. The Fisher, Gayen, and Jeyaratnam approaches are shown to provide useful results for a bivariate normal distribution with any population correlation coefficient ρ and for nonnormal bivariate distributions when ρ = 0. In contrast, the techniques are virtually useless for nonnormal bivariate distributions when ρ#0.0. Surprisingly, small samples are found to provide better estimates than large samples for skewed and symmetric heavy-tailed bivariate distributions.