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Two measures of effect size are described for the Mantel--Haenszel test. Both measures belong to the r-family of effect size measures. One measure is based on a maximum-corrected model, and the second measure is based on a chance-corrected model. DOI: 10.2466/03.PR0.107.5.393-401

Lead (Pb) is extremely toxic and a major cause of chronic diseases worldwide. Pb is associated with health disparities, particularly within low-income populations. In biological systems, Pb mimics calcium and, among other effects, interrupts cell signaling. Furthermore, Pb exposure results in epigenetic changes that affect multigenerational gene expression. Exposure to Pb has decreased through primary prevention, including removal of Pb solder from canned food, regulating lead-based paint, and especially eliminating Pb additives in gasoline. While researchers observe a continuous decline in children's blood lead (BPb), reservoirs of exposure persist in topsoil, which stores the legacy dust from leaded gasoline and other sources. Our surveys of metropolitan New Orleans reveal that median topsoil Pb in communities (n = 274) decreased 44% from 99 mg/kg to 54 mg/kg (P value of 2.09 x 10-08), with a median depletion rate of ~2.4 mg⋅kg⋅y-1 over 15 y. From 2000 through 2005 to 2011 through 2016, children's BPb declined from 3.6 µg/dL to 1.2 µg/dL or 64% (P value of 2.02 x 10-85), a decrease of ~0.2 µg⋅dL⋅y-1 during a median of 12 y. Here, we explore the decline of children's BPb by examining a metabolism of cities framework of inputs, transformations, storages, and outputs. Our findings indicate that decreasing Pb in topsoil is an important factor in the continuous decline of children's BPb. Similar reductions are expected in other major US cities. The most contaminated urban communities, usually inhabited by vulnerable populations, require further reductions of topsoil Pb to fulfill primary prevention for the nation's children. [ABSTRACT FROM AUTHOR]

Permutation statistical methods possess a number of advantages compared with conventional statistical methods, making permutation statistical methods the preferred statistical approach for many research situations. Permutation statistical methods are data‐dependent, do not rely on distribution assumptions such as normality, provide either exact or highly‐accurate approximate probability values, do not require knowledge of theoretical standard errors, and are ideal methods for small data sets where theoretical mathematical functions are often poor fits to discrete sampling distributions. On the other hand, permutation statistical methods are computationally intensive. Computational efficiencies for permutation statistical methods are described and permutation statistical methods are illustrated with a variety of common statistical tests and measures. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bootstrap and Resampling Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods [ABSTRACT FROM AUTHOR]

When the categories of the independent variable in an analysis of variance are quantitative, it is more informative to evaluate the trends in the treatment means than to simply compare differences among the treatment means. A permutation alternative to the conventional F test is shown to possess significant advantages when analyzing trend among quantitative treatments in a one-way analysis of variance. An example with and without an extreme data point illustrates the effectiveness of the permutation alternative for the analysis of trend when homogeneity of variance is compromised. [ABSTRACT FROM AUTHOR]

Monte Carlo resampling methods to obtain probability values for chi-squared and likelihood-ratio test statistics for multiway contingency tables are presented. A resampling algorithm provides random arrangements of cell frequencies in a multiway contingency table, given fixed marginal frequency totals. Probability values are obtained from the proportion of resampled test statistic values equal to or greater than the observed test statistic value. [ABSTRACT FROM AUTHOR]

The reporting of measures of effect size has become increasingly important in psychology. A Monte Carlo resampling permutation procedure is introduced to find near-optimum maximum values for Smart's τc measure for two-way ordinal contingency tables, also termed Kendall's τc since Kendall introduced τa and τb. Comparisons between resampling and exact procedures demonstrate the accuracy and utility of resampling measures of effect size for two-way ordinal contingency tables. The resampling procedure is shown to be more precise than the traditional method of standardizing τ,c. [ABSTRACT FROM AUTHOR]

The measurement of the magnitude of association between a nominal independent variable and an ordinal dependent variable is an important, but neglected, component in psychological research. Two measures of nominal-ordinal association are described and compared. Resampling permutation methods are utilized to compute probability values for both measures. [ABSTRACT FROM AUTHOR]