Parametric Probability Densities and Distribution Functions for Tukey \u3ci\u3eg\u3c/i\u3e-and-\u3ci\u3eh\u3c/i\u3e Transformations and their Use for Fitting Data

The family of g-and-h transformations are popular algorithms used for simulating non-normal distributions because of their simplicity and ease of execution. In general, two limitations associated with g-and-h transformations are that their probability density functions (pdfs) and cumulative distribution functions (cdfs) are unknown. In view of this, the g-and-h transformations’ pdfs and cdfs are derived in general parametric form. Moments are also derived and it is subsequently shown how the g and h parameters can be determined for prespecified values of skew and kurtosis. Numerical examples and parametric plots of g-and-h pdfs and cdfs are provided to confirm and demonstrate the methodology. It is also shown how g-and-h distributions can be used in the context of distribution fitting using real data sets

Multiple Comparison Procedures, Trimmed Means And Transformed Statistics

A modification to testing pairwise comparisons that may provide better control of Type I errors in the presence of non-normality is to use a preliminary test for symmetry which determines whether data should be trimmed symmetrically or asymmetrically. Several pairwise MCPs were investigated, employing a test of symmetry with a number of heteroscedastic test statistics that used trimmed means and Winsorized variances. Results showed improved Type I error control than competing robust statistics

Statistical practices of educational researchers: An analysis of their ANOVA, MANOVA, and ANCOVA analyses

Articles published in several prominent educational journals were examined to investigate the use of data-analysis tools by researchers in four research paradigms: between-subjects univariate designs, between-subjects multivariate designs, repeated measures designs, and covariance designs. In addition to examining specific details pertaining to the research design (e.g., sample size, group size equality/inequality) and methods employed for data analysis, we also catalogued whether: (a) validity assumptions were examined, (b) effect size indices were reported, (c) sample sizes were selected based on power considerations, and (d) appropriate textbooks and/or articles were cited to communicate the nature of the analyses that were performed. Our analyses imply that researchers rarely verify that validity assumptions are satisfied and accordingly typically use analyses that are nonrobust to assumption violations. In addition, researchers rarely report effect size statistics, nor do they routinely perform power analyses to determine sample size requirements. We offer many recommendations to rectify these shortcomings.Social Sciences and Humanities Research Counci

Parametric probability densities and distribution functions for Tukey g-and-h transformations and their use for fitting data

Abstract The family of g-and-h transformations are popular algorithms used for simulating non-normal distributions because of their simplicity and ease of execution. In general, two limitations associated with g-andh transformations are that their probability density functions (pdfs) and cumulative distribution functions (cdfs) are unknown. In view of this, the g-and-h transformations' pdfs and cdfs are derived in general parametric form. Moments are also derived and it is subsequently shown how the g and h parameters can be determined for prespecified values of skew and kurtosis. Numerical examples and parametric plots of g-and-h pdfs and cdfs are provided to confirm and demonstrate the methodology. It is also shown how g-and-h distributions can be used in the context of distribution fitting using real data sets. Mathematics Subject Classification: 65C05, 65C10, 65C6

Applying Clinical Significance Methodology to Alcoholism Treatment Trials: Determining Recovery Outcome Status with Individual- and Population-Based Measures

Background: The current analysis applies clinical significance methodology to alcoholism treatment outcome research using data available from Project MATCH. Because of its high internal validity and its inclusion of multiple measures assessing multiple outcome dimensions, MATCH was considered an ideal study to explore the utility of this methodology Methods: Data reported here are from a total of 1,726 participants enrolled in either aftercare (n= 774) or outpatient (n= 952) arms of the study. First, a cutoff score was determined differentiating functional versus dysfunctional status on three outcome measures: percent days abstinent (PDA), mean drinks per drinking day (DDD) and negative consequences of alcohol use. Second, the reliable change in pre‐ to post‐treatment scores on these three measures was calculated Results: The results reported herein support the importance of distinguishing between statistical and clinical significance of outcomes. During three months post‐treatment, approximately one‐half of the treated patients were “recovered” (i.e., both functional and reliably changed) with respect to both PDA (i.e., 51%) and negative consequences of drinking (i.e., 47%); however, only about one‐third of individuals remained recovered throughout the full one‐year follow‐up period (i.e., 33% on PDA and 35% on negative consequences). These individual‐based change outcomes compared similarly to a population‐based indicator of heavy drinking. Alternatively, only about one‐quarter of participants were recovered using two distinct criteria for mean DDD (i.e., 23–29%), and even fewer participants remained recovered on mean DDD over the full one‐year follow‐up period (i.e., about 14–18%) Conclusions: Based on study limitations, more work is required to make clinical significance methodology practically useful to alcoholism treatment trials including more precise definitions of functional status and relative change as well as better interpretation of the inter‐relationship between multiple measures assessing multiple outcome domains