Gregory A. Mack

K-Sample Rank Tests for Umbrella Alternatives

Abstract Distribution-free test procedures are proposed for the k-sample problem, where the alternatives of interest are of the form F 1 (x) ≥ ··· ≥ Fl(x) ≤ ··· ≤ Fk (x) for all x, with at least one strict inequality. These are referred to as umbrella alternatives, and both the l (point of umbrella) known and l unknown settings are considered. Small sample null distributions are discussed, and the results of a Monte Carlo power study are presented. A detailed example illustrating the use of the unknown umbrella point procedure is also given.

On the Use of a Friedman-Type Statistic in Balanced and Unbalanced Block Designs

Distribution-free tests and multiple comparison procedures are considered for randomized block designs. A general Friedman-type statistic is defined that is usable in almost any block design with arbitrary missing data structure. For balanced incomplete block designs a multiple comparison procedure and exact tables are given for a statistic equivalent to one proposed by Durbin (1951). Finally, for designs with missing observations on only one treatment, we present exact tables for the test statistic, and we consider a multiple comparison procedure.

A Friedman-Type Rank Test for Main Effects in a Two-Factor ANOVA

Abstract A distribution-free test is considered for testing main effects in a two-factor ANOVA. Large-sample properties (cell sizes tending to infinity) including efficiencies and the limiting distribution of the test statistic are obtained. For proportional frequencies a simple sum of squares formula is obtained for the test statistic and multiple comparison procedures are given. For general designs the statistic is expressed using generalized inverses. Some tables for the null distribution of the statistic are also given.

Polycyclic aromatic hydrocarbons and their derivatives in indoor and outdoor air in an eight-home study

Abstract A pilot field study was performed in Columbus, OH, during the winter of 1986/1987. The objectives were to determine the feasibility of the use of a newly developed quiet sampler in indoor air sampling for particles and semivolatile organic compounds (SVOC) and to measure the concentrations of polycyclic aromatic hydrocarbons (PAH), PAH derivatives, and nicotine in air in selected residences. Eight homes were chosen for sampling on the basis of these characteristics: electric/gas heating system, electric/gas cooking appliances, and the absence/presence of environmental tobacco smoke (ETS). The indoor sampler was equipped with a quartz-fiber filter to collect particles followed by XAD-4 resin to trap SVOC. A PS-1 sampler with a similar sampling module was used outdoors. The indoor air was sampled in the kitchen and living room areas over two consecutive 8-h periods. The outdoor air was sampled concurrently with the indoor samples over a 16-h period. Fifteen PAH, five nitro-PAH, five oxygenated PAH, and three nitrogen heterocyclic compounds were determined in these samples. The most abundant PAH found indoors was naphthalene. The indoor concentrations of PAH derivatives were lower than those of their parent compounds. Average concentrations of all but three target compounds (naphthalene dicarboxylic acid anhydride, pyrene dicarboxylic acid anhydride, and 2-nitrofluoranthene) were higher indoors than outdoors. Environmental tobacco smoke was the most significant influence on indoor pollutant levels. Homes with gas heating systems had higher indoor pollutant levels than homes with electric heating systems. However, the true effects of heating and cooking systems were not characterized as accurately as the effects of ETS because of the small sample sizes and the lack of statistical significance for most pollutant differences in the absence of ETS. The concentrations of PAH marker compounds (phenanthrene, fluoranthene, and pyrene) correlated well with the concentrations of other target compounds. Quinoline and isoquinoline can be used to indicate indoor levels of ETS.

PCDDs and PCDFs in human adipose tissue from the EPA FY82 NHATS repository

Abstract Analysis for tetra- through octachloro-PCDDs and PCDFs was completed for 46 tissue samples prepared from the U.S. Environmental Protection Agency (EPA) National Human Adipose Tissue Survey (NHATS). The samples were prepared as composites from over 900 specimens to represent the nine U.S. census divisions and three age groups (0–14, 15–44, and 45 plus years). The data demonstrate that PCDDs and PCDFs are prevalent in the general U.S. population and that differences exist with age.

Trends of PCB, hexachlorobenzene, and β-benzene hexachloride levels in the adipose tissue of the U.S. population

Results are presented on the levels of selected toxic chemicals in the adipose tissue of the U.S. population. Estimates of baseline levels and time trends are presented for the chemicals beta-benzene hexachloride (beta-BHC), hexachlorobenzene, and polychlorinated biphenyls (PCBs). The statistical analyses are based on chemical data obtained from analysis of tissue specimens collected from a nationally representative sample of autopsied cadavers and surgical patients by EPAs National Human Adipose Tissue Survey during the period 1970 through 1983. The results show that while nearly the entire U.S. population has detectable levels of these chemicals, the actual concentration levels of beta-BHC and PCBs are steadily decreasing and the levels of HCB are remaining fairly constant. Comparisons of levels across demographic subpopulations show that there are some differences in concentration levels across geographic regions, age groups, and race groups.

A quick and easy distribution-free test for main effxcts in a two-factor ANOVA

A distribution-free test for main-effects in a two-factor ANOVA is studied and an extensive set of tables for its exact null distributions is presented. Two different large sample approximations for its null distributions are discussed and the adequacy of each approximation is studied. Recommendations are made concerning the sample sizes required for the use of each of these approximations.