How Accurate Is the Pearson r-from-Z Approximation? A Monte Carlo Simulation Study

The Pearson r-from-Z approximation estimates the sample correlation (as an effect size measure) from the ratio of two quantities: the standard normal deviate equivalent (Z-score) corresponding to a one-tailed p-value divided by the square root of the total (pooled) sample size. The formula has utility in meta-analytic work when reports of research contain minimal statistical information. Although simple to implement, the accuracy of the Pearson r-from-Z approximation has not been empirically evaluated. To address this omission, we performed a series of Monte Carlo simulations. Results indicated that in some cases the formula did accurately estimate the sample correlation. However, when sample size was very small (N = 10) and effect sizes were small to small-moderate (ds of 0.1 and 0.3), the Pearson r-from-Z approximation was very inaccurate. Detailed figures that provide guidance as to when the Pearson r-from-Z formula will likely yield valid inferences are presented.     

Case study: The combined use of imipramine and behavior modification to reduce aggression in an adult male diagnosed as having autistic disorder

The present study examined the behavior decelerative effects of combined imipramine (tofranil) and behavior modification in a severely retarded, depressed autistic man. A simple interrupted time-series design was conducted and the primary data analytic techniques consisted of modified trend analyses and dependent samples t-tests. Consistent with previous theory and scant empirical research, results indicated that combined imipramine and behavior modification significantly reduced daily episodes of self-directed and other-directed aggression. Specifically, controlling for the effects of time, the combined treatment regimen led to significant reductions in both level and slope across three topographies of aggressive behavior. Limitations of the present study and recommendations for future research were discussed. It was concluded that combined imipramine and behavior modification may be an effective strategy for reducing aggression in the developmentally disabled.     

Disaster Preparedness: Relationships Among Prior Experience,Personal Characteristics,and Distress1

At the peak of a hurricane watch and warning, participants completed a questionnaire asking about their prior experience with a hurricane (property loss and distress), and their degree of preparation, perceived threat, and distress when threatened by Hurricane Emily (Study 1) or Hurricane Fran (Study 2). In Study 1, age, income, internal locus of control, perceived threat, and current distress predicted preparation. Among participants with hurricane experience, age and distress as a result of the hurricane accounted for a significant portion of preparation variance. In Study 2, age, perceived threat, and hurricane experience predicted preparation. The findings support both the conservation of resources stress model (Hobfoll, 1989) and the warning and response model (Lindell & Perry, 1992). Implications of the findings and future research directions are discussed.     

Testing the significance of a correlation with nonnormal data: Comparison of Pearson, Spearman, transformation, and resampling approaches

It is well known that when data are nonnormally distributed, a test of the significance of Pearson's r may inflate Type I error rates and reduce power. Statistics textbooks and the simulation literature provide several alternatives to Pearson's correlation. However, the relative performance of these alternatives has been unclear. Two simulation studies were conducted to compare 12 methods, including Pearson, Spearman's rank-order, transformation, and resampling approaches. With most sample sizes (n ≥ 20), Type I and Type II error rates were minimized by transforming the data to a normal shape prior to assessing the Pearson correlation. Among transformation approaches, a general purpose rank-based inverse normal transformation (i.e., transformation to rankit scores) was most beneficial. However, when samples were both small (n ≤ 10) and extremely nonnormal, the permutation test often outperformed other alternatives, including various bootstrap tests. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Alcohol use among american college students in relation to need for cognition and expectations of alcohol's effects on cognition

This article describes the development of a new self-report measure for assessing expectations for alcohol's cognitive effects and presents an empirical investigation of the association between cognitive alcohol expectancies and alcohol use. The present study also examined the potential moderating effects of need for cognition on the association between cognitive expectancies and drinking. Participants consisted of 179 college undergraduates from a midsized public university in the southeastern United States. Results of hierarchical multiple regression analyses, conducted separately for males and females, indicated several main effects for both cognitive alcohol expectancies and need for cognition on alcohol use. In contrast to these main effects, there were no significant multiplicative interaction effects, suggesting that need for cognition did not moderate the direction of association between cognitive expectancies and drinking. The results of homologizer/moderator analyses, however, did indicate a number of significant interaction effects for both males and females. These significant homologizer findings indicated that thestrength of association between cognitive alcohol expectancies and drinking increased as need for cognition increased. Implications of the present findings for future research are discussed. This research was supported, in part, by a sabbatical award granted by the College of Charleston. The author thanks Michael Tavernetti for his assistance with this project and Dr. Rhonda Swickert for her helpful feedback on an earlier version of this article.     

Ezekiel’s classic estimator of the population squared multiple correlation coefficient: Monte Carlo-based extensions and refinements

Abstract

Ezekiel’s adjusted R² is widely used in linear regression analysis. The present study examined the statistical properties of Ezekiel’s measure through a series of Monte Carlo simulations. Specifically, we examined the bias and root mean squared error (RMSE) of Ezekiel’s adjusted R² relative to (a) the sample R² statistic, and (b) the sample R² minus the expected value of R². Simulation design factors consisted of sample sizes (N?=?50, 100, 200, 400), number of predictors (2, 3, 4, 5, 6), and population squared multiple correlations (ρ² = 0, .10, .25, .40, .60). Factorially crossing these design factors resulted in 100 simulation conditions. All populations were normal/Gaussian, and for each condition, we drew 10,000 Monte Carlo samples. Regarding systematic variation (bias), results indicated that with few exceptions, Ezekiel’s adjusted R² demonstrated the lowest bias. Regarding unsystematic variation (RMSE), the performance of Ezekiel’s measure was comparable to the other statistics, suggesting that the bias-variance tradeoff is minimal for Ezekiel’s adjusted R². Additional findings indicated that sample size-to-predictor ratios of 66.67 and greater were associated with low bias and that ratios of this magnitude were accompanied by large sample sizes (N?=?200 and 400), thus suggesting that researchers using Ezekiel’s adjusted R² should aim for sample sizes of 200 or greater in order to minimize bias when estimating the population squared multiple correlation coefficient. Overall, these findings indicate that Ezekiel’s adjusted R² has desirable properties and, in addition, these findings bring needed clarity to the statistical literature on Ezekiel’s classic estimator.