Biomedical subjects
Publications and source records attributed to Kenneth J Berry.
In many studies, respondents may mark all answers that apply when responding to a multiple-choice question, i.e., a cafeteria or multiple-response question. One exact and two approximate permutation methods are described to analyze multiple-response questions. The methods provide the probability, under the null hypothesis, that the multiple binary responses do not differ among specified groups.
An extension of a multiple regression prediction model to multiple response variables is presented. An algorithm using least sum of Euclidean distances between the multivariate observed and model-predicted response values provides regression coefficients, a measure of effect size, and inferential procedures for evaluating the extended multivariate multiple regression prediction model.
The Fisher-Pitman and powers of ranks permutation tests are shown to provide substantial resistance to extreme values when compared with the conventional t test for analyzing matched-pairs experimental designs.
A nonasymptotic chi-squared technique is shown to have very useful properties for the analysis of large sparse r-way contingency tables. Examples of analyses of 4 x 5, 5 x 6, 6 x 7, and two 2 x 2 x 2 sparse contingency tables provide comparisons of the nonasymptotic chi-squared technique with asymptotic chi-squared and exact chi-squared techniques. The asymptotic chi-squared analyses yield inflated probability values for the five tables. The nonasymptotic chi-squared technique yields probability values much closer to the exact probability values than the asymptotic chi-squared technique for the five tables.
The Fisher-Pitman permutation test is shown to possess significant advantages over conventional alternatives when analyzing differences among independent samples with unequal variances.
A multivariate extension of a univariate procedure for the analysis of experimental designs is presented. A Euclidean-distance permutation procedure is used to evaluate multivariate residuals obtained from a regression algorithm, also based on Euclidean distances. Applications include various completely randomized and randomized block experimental designs such as one-way, Latin square, factorial, nested, and split-plot designs, with and without covariates. Unlike parametric procedures, the only required assumption is the randomization of subjects to treatments.
A universal measure of the magnitude of effect size is introduced for Euclidean-based regression analyses of experimental designs. The measure is based on the ratio of the sums of Euclidean residuals obtained under the alternative and null hypotheses.
A data-dependent analysis assumes that all the information available to a researcher is contained within the observed data. Data-dependent methods for the analysis of experimental designs are shown to provide significant advantages over conventional techniques such as an F test. Two versions of three data-dependent methods based on permutations of the data are described and compared. One version utilizes ordinary least squares regression, and the other version utilizes least absolute deviations regression to analyze experimental designs. Analyses of an unbalanced two-way experimental design illustrate the differences among the six data-dependent approaches and the classical ordinary least squares F test, which depends on the assumptions of normality, homogeneity, and independence.