Biomedical subjects
Publications and source records attributed to Janis E Johnston.
A fundamental shift in editorial policy for psychological journals was initiated when the fourth edition of the Publication Manual of the American Psychological Association (1994) placed emphasis on reporting measures of effect size. This paper presents measures of effect size for the chi-squared and the likelihood-ratio goodness-of-fit statistic tests.
A permutation method is presented to calculate resampling probability values for differences between two independent indices of ordinal variation and consensus.
Permutation procedures to compute exact and resampling probability values associated with measures of association for ordered r x c contingency tables are described. Comparisons with asymptotic probability values demonstrated that exact and resampling permutation procedures were preferred for sparse contingency tables.
Goodman and Kruskal's tau measure of categorical association is advanced as a replacement for conventional measures of effect size for r x c contingency tables. Goodman and Kruskal's tau is an asymmetric measure of categorical association which is based entirely on the observed data and possesses a clear interpretation in terms of proportional reduction in error. Comparisons with conventional measures of effect size based on chi-squared such as Pearson's phi2, Tschuprow's T2, and Cramer's V2 demonstrate the advantages of employing tau as a measure of effect size.
Fisher's well-known continuous method for combining independent probability values from continuous distributions is compared with an exact discrete analog of Fisher's continuous method for combining independent probability values from discrete distributions using matched-pairs t-test data. Fisher's continuous method is shown to be inadequate for combining probability values from many discrete distributions, given the continuity assumption when discrete distributions are considered. Although Fisher's continuous method does not detect a well-documented effect among distributions, the exact discrete analog method clearly detects the effect.
When analyzing categorical data, it is often important to assess the magnitude of variation, or consensus, among observations in unordered categories. Utilizing the theory of partitions, exact solutions for five commonly used measures of categorical variation are presented. When the number of partitions is very large, resampling methods provide close approximations to exact probability values.
An algorithm and associated FORTRAN program are provided for the exact variance of weighted kappa. Program VARKAP provides the weighted kappa test statistic, the exact variance of weighted kappa, a Z score, one-sided lower- and upper-tail N(0,1) probability values, and the two-tail N(0,1) probability value.
Permutation procedures to compute exact and resampling probability values for weighted kappa are described. Comparisons with asymptotic probability values demonstrate that exact permutation procedures are advantageous for sparse data sets, whereas resampling permutation procedures are appropriate for both sparse and nonsparse data sets.
Resampling permutation procedures provide good approximations to exact permutation procedures and are therefore the preferred alternative when large samples render exact tests intractable. Resampling permutation procedures are described for three measures of variation and the three corresponding measures of consensus among ordered categories.
An algorithm and computer program to calculate exact goodness-of-fit tests for unordered categories with equal probabilities under the null hypothesis are presented. FORTRAN program EBGF utilizes partitions and multinomial weights to reduce computation times for Fisher's exact, exact chi-square, exact likelihood-ratio, exact Freeman-Tukey, and exact Cressie-Read goodness-of-fit tests.
Traditional asymptotic probability values resulting from log-linear analyses of sparse frequency tables are often much too large. Asymptotic probability values for chi-squared and likelihood-ratio statistics are compared to nonasymptotic and exact probability values for selected log-linear models. The asymptotic probability values are all too often substantially larger than the exact probability values for the analysis of sparse frequency tables. An exact nondirectional permutation method is presented to analyze combined independent multinomial distributions. Exact nondirectional permutation methods to analyze hypergeometric distributions associated with r-way frequency tables are confined to r = 2.
Permutation tests are based on all possible arrangements of observed data sets. Consequently, such tests yield exact probability values obtained from discrete probability distributions. An exact nondirectional method to combine independent probability values that obey discrete probability distributions is introduced. The exact method is the discrete analog to Fisher's classical method for combining probability values from independent continuous probability distributions. If the combination of probability values includes even one probability value that obeys a sparse discrete probability distribution, then Fisher's classical method may be grossly inadequate.
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.