Confidence intervals for the MMPI-2

The confidence intervals for the Minnesota Multiphasic Personality Inventory (MMPI-2) clinical scales were investigated. Based on the clinical scale reliabilities published in the MMPI-2 manual, estimated true scores, standard errors of measurement for estimated true scores, and 95% confidence intervals centered around estimated true scores were calculated at 5-point MMPI-2 T-score intervals. The relationships between obtained T-scores, estimated true T-scores, scale reliabilities, and confidence intervals are discussed. The possible role of error measurement in defining scale high point and code types is noted.     

Confidence intervals for standardized linear contrasts of means

Most psychology journals now require authors to report a sample value of effect size along with hypothesis testing results. The sample effect size value can be misleading because it contains sampling error. Authors often incorrectly interpret the sample effect size as if it were the population effect size. A simple solution to this problem is to report a confidence interval for the population value of the effect size. Standardized linear contrasts of means are useful measures of effect size in a wide variety of research applications. New confidence intervals for standardized linear contrasts of means are developed and may be applied to between-subjects designs, within-subjects designs, or mixed designs. The proposed confidence interval methods are easy to compute, do not require equal population variances, and perform better than the currently available methods when the population variances are not equal.     

Confidence intervals for the parameters of psychometric functions

A Monte Carlo method for computing the bias and standard deviation of estimates of the parameters of a psychometric function such as the Weibull/Quick is described. The method, based on Efron's parametric bootstrap, can also be used to estimate confidence intervals for these parameters. The method's ability to predict bias, standard deviation, and confidence intervals is evaluated in two ways. First, its predictions are compared to the outcomes of Monte Carlo simulations of psychophysical experiments. Second, its predicted confidence intervals were compared with the actual variability of human observers in a psychophysical task. Computer programs implementing the method are available from the author.     

Confidence intervals for the overall effect size in random-effects meta-analysis

One of the main objectives in meta-analysis is to estimate the overall effect size by calculating a confidence interval (CI). The usual procedure consists of assuming a standard normal distribution and a sampling variance defined as the inverse of the sum of the estimated weights of the effect sizes. But this procedure does not take into account the uncertainty due to the fact that the heterogeneity variance (tau2) and the within-study variances have to be estimated, leading to CIs that are too narrow with the consequence that the actual coverage probability is smaller than the nominal confidence level. In this article, the performances of 3 alternatives to the standard CI procedure are examined under a random-effects model and 8 different tau2 estimators to estimate the weights: the t distribution CI, the weighted variance CI (with an improved variance), and the quantile approximation method (recently proposed). The results of a Monte Carlo simulation showed that the weighted variance CI outperformed the other methods regardless of the tau2 estimator, the value of tau2, the number of studies, and the sample size.     

Revisiting confidence intervals for repeated measures designs

Loftus and Masson (1994) proposed a method for computing confidence intervals (CIs) in repeated measures (RM) designs and later proposed that RM CIs for factorial designs should be based on number of observations rather than number of participants (Masson & Loftus, 2003). However, determining the correct number of observations for a particular effect can be complicated, given that its value depends on the relation between the effect and the overall design. To address this, we recently defined a general number-of-observations principle, explained why it obtains, and provided step-by-step instructions for constructing CIs for various effect types (Jarmasz & Hollands, 2009). In this note, we provide a brief summary of our approach.     

On approximate confidence intervals for measures of concordance

The use ofU-statistics based on rank correlation coefficients in estimating the strength of concordance among a group of rankers is examined for cases where the null hypothesis of random rankings is not tenable. The studentizedU-statistics is asymptotically distribution-free, and the Student-t approximation is used for small and moderate sized samples. An approximate confidence interval is constructed for the strength of concordance. Monte Carlo results indicate that the Student-t approximation can be improved by estimating the degrees of freedom.Research partially supported on ONR Contract N00014-82-K-0207.     

Relationships of ordinal position and family size to psychosocial measures of delinquents

First-born, middle-born, and last-born white male delinquents in small and large families (N=72) were compared on 21 variables. Seven of the 21 variables showed some effect of either ordinal position, family size, or their interaction: reading achievement, Quay's unsocialized-psychopathic behavior classification, staff predictions of institutional adjustment, family intactness, Gough's socialization scale, future-events test never responses, and Rosenberg's self esteem scale. The pattern of results suggested that firstborns and delinquents from smaller families were better socialized or had better socialization resources than lastborns and those from larger families.This study was part of a larger research project performed under personal-service contracts CT 24867 and CT 46381 with the Department of Child Welfare, Commonwealth of Kentucky, through Grant No. 73A804 from the Kentucky State Crime Commission with funds made available by the State of Kentucky and the Law Enforcement Assistance Administration, U.S. Department of Justice, under the authority of the Omnibus Crime Control and Safe Streets Act of 1968, as amended. Points of view or opinions stated in this document are those of the author and do not necessarily represent the official position or policies of the U.S. Department of Justice or the Kentucky State Crime Commission. Appreciation is extended to Lewis Davidson and Michael McColloch for their data collection efforts.     

Confidence intervals and sample size calculations for the weighted eta-squared effect sizes in one-way heteroscedastic ANOVA

Effect size reporting and interpreting practices have been extensively recommended in academic journals when primary outcomes of all empirical studies have been analyzed. This article presents an alternative approach to constructing confidence intervals of the weighted eta-squared effect size within the context of one-way heteroscedastic ANOVA models. It is shown that the proposed interval procedure has advantages over an existing method in its theoretical justification, computational simplicity, and numerical performance. For design planning, the corresponding sample size procedures for precise interval estimation of the weighted eta-squared association measure are also delineated. Specifically, the developed formulas compute the necessary sample sizes with respect to the considerations of expected confidence interval width and tolerance probability of interval width within a designated value. Supplementary computer programs are provided to aid the implementation of the suggested techniques in practical applications of ANOVA designs when the assumption of homogeneous variances is not tenable.     

A comparative study of association measures

This paper discusses the general problem of measuring the association between an independent nominal-scaled variableX and a dependent variableY whose scale of measurement may be interval, ordinal or nominal. The theoretical foundations of a wide range of asymmetric association measures are discussed. Some new measures are also suggested. Fifteen of these association measures, some previously suggested, some new, are singled out for a computer-assisted numerical study in which we compute the value actually taken by each measure under a wide variety of conditions. This comparative study provides important insights into the behavior of the measures.     

Implicit measures of association in psychopathology research

Studies obtaining implicit measures of associations in Diagnostic and Statistical Manual of Mental Disorders (4th ed., Text Revision; American Psychiatric Association, 2000) Axis I psychopathology are organized into three categories: (a) studies comparing groups having a disorder with controls, (b) experimental validity studies, and (c) incremental and predictive validity studies. In the first category, implicit measures of disorder-relevant associations were consistent with explicit beliefs for some disorders (e.g., specific phobia), but for other disorders evidence was either mixed (e.g., panic disorder) or inconsistent with explicit beliefs (e.g., pain disorder). For substance use disorders and overeating, expected positive and unexpected negative associations with craved substances were found consistently. Contrary to expectation, implicit measures of self-esteem were consistently positive for patients with depressive disorder, social phobia, and body dysmorphic disorder. In the second category, short-term manipulations of disorder-relevant states generally affected implicit measures as expected. Therapeutic interventions affected implicit measures for one type of specific phobia, social phobia, and panic disorder, but not for alcohol use disorders or obesity. In the third category, implicit measures had predictive value for certain psychopathological behaviors, sometimes moderated by the availability of cognitive resources (e.g., for alcohol and food, only when cognitive resources were limited). The strengths of implicit measures include (a) converging evidence for dysfunctional beliefs regarding certain disorders and consistent new insights for other disorders and (b) prediction of some psychopathological behaviors that explicit measures cannot explain. Weaknesses include (a) that findings were inconsistent for some disorders, raising doubts about the validity of the measures, and (b) that understanding of the concept "implicit" is incomplete.     

Confidence intervals and sample size calculations for the standardized mean difference effect size between two normal populations under heteroscedasticity

The use of effect sizes and associated confidence intervals in all empirical research has been strongly emphasized by journal publication guidelines. To help advance theory and practice in the social sciences, this article describes an improved procedure for constructing confidence intervals of the standardized mean difference effect size between two independent normal populations with unknown and possibly unequal variances. The presented approach has advantages over the existing formula in both theoretical justification and computational simplicity. In addition, simulation results show that the suggested one- and two-sided confidence intervals are more accurate in achieving the nominal coverage probability. The proposed estimation method provides a feasible alternative to the most commonly used measure of Cohen’s d and the corresponding interval procedure when the assumption of homogeneous variances is not tenable. To further improve the potential applicability of the suggested methodology, the sample size procedures for precise interval estimation of the standardized mean difference are also delineated. The desired precision of a confidence interval is assessed with respect to the control of expected width and to the assurance probability of interval width within a designated value. Supplementary computer programs are developed to aid in the usefulness and implementation of the introduced techniques.     

One-sided nonparametric tests for ordinal data

Baumgartner, Weiss, and Schindler (1998) introduced a novel non-parametric test for the two-sample comparison that is superior to commonly used tests such as the Wilcoxon rank-sum test. A modification of the novel test statistic can be used for one-sided comparisons based on ordinal data. Such comparisons frequently occur in psychological research, and the Wilcoxon test is often recommended for their analysis. Here, the two tests were compared in a simulation study. According to this study the tests have a similar type I error rate, but the modified Baumgartner-Weiss-Schindler test is more powerful than the Wilcoxon test.     

Models for ordinal hierarchical classes analysis

This paper proposes an ordinal generalization of the hierarchical classes model originally proposed by De Boeck and Rosenberg (1998). Any hierarchical classes model implies a decomposition of a two-way two-mode binary arrayM into two component matrices, called bundle matrices, which represent the association relation and the set-theoretical relations among the elements of both modes inM. Whereas the original model restricts the bundle matrices to be binary, the ordinal hierarchical classes model assumes that the bundles are ordinal variables with a prespecified number of values. This generalization results in a classification model with classes ordered along ordinal dimensions. The ordinal hierarchical classes model is shown to subsume Coombs and Kao's (1955) model for nonmetric factor analysis. An algorithm is described to fit the model to a given data set and is subsequently evaluated in an extensive simulation study. An application of the model to student housing data is discussed.     

Some properties of two measures of multivariate association

Two kinds of measures of multivariate association, based on Wilks' and the Bartlett-Nanda-Pillai trace criterionV, respectively, are compared in terms of properties of the univariateR ² which they generalize. A unified set of derivations of the properties is provided which are self-contained and not restricted to decompositions in canonical variates. One conclusion is that asymmetric index based on allows generalization of the multiplicative decomposition ofR ² in terms of squared partial correlations, but not the additive decomposition in terms of squared semipartial correlations, while the reverse is true for anasymmetric index based onV.We are indebted to Jos M. F. ten Berge for some fruitful discussions.