Development of character strengths across the deployment cycle among U.S. Army soldiers.

OBJECTIVE: Despite a narrative of post-traumatic growth and resilience, research reliably demonstrating positive character development following adversity has proved elusive. In the current study, we examined changes in character strengths in Army soldiers deploying for the first time. METHOD: The sample was comprised of 212,386 Army soldiers (Mage  = 26.5 years old, SD = 7.13; 70.8% White) who were deploying for the first time. Character strengths were assessed once before and up to three times following soldiers' return from deployment. RESULTS: We found evidence for two classes of change-a resilient class ("stable high") and a declining class ("persistent low"). Most soldiers were resilient-they had high levels of character strengths prior to deployment and changed very little across the deployment cycle. Approximately 40% of soldiers started with lower character and experienced initial declines post-deployment, from which they experienced no more than small gains over time. CONCLUSIONS: Character strengths were highly stable across the deployment transition but some soldiers experienced initial declines from which they never fully rebounded. The findings are discussed in the context of the mechanisms that drive character development.

Interval estimation for linear functions of medians in within-subjects and mixed designs.

The currently available distribution-free confidence interval for a difference of medians in a within-subjects design requires an unrealistic assumption of identical distribution shapes. A confidence interval for a general linear function of medians is proposed for within-subjects designs that do not assume identical distribution shapes. The proposed method can be combined with a method for linear functions of independent medians to provide a confidence interval for a linear function of medians in mixed designs. Simulation results show that the proposed methods have good small-sample properties under a wide range of conditions. The proposed methods are illustrated with examples, and R functions that implement the new methods are provided.

Point-biserial correlation: Interval estimation, hypothesis testing, meta-analysis, and sample size determination.

The point-biserial correlation is a commonly used measure of effect size in two-group designs. New estimators of point-biserial correlation are derived from different forms of a standardized mean difference. Point-biserial correlations are defined for designs with either fixed or random group sample sizes and can accommodate unequal variances. Confidence intervals and standard errors for the point-biserial correlation estimators are derived from the sampling distributions for pooled-variance and separate-variance versions of a standardized mean difference. The proposed point-biserial confidence intervals can be used to conduct directional two-sided tests, equivalence tests, directional non-equivalence tests, and non-inferiority tests. A confidence interval for an average point-biserial correlation in meta-analysis applications performs substantially better than the currently used methods. Sample size formulas for estimating a point-biserial correlation with desired precision and testing a point-biserial correlation with desired power are proposed. R functions are provided that can be used to compute the proposed confidence intervals and sample size formulas.

Varying coefficient meta-analysis methods for odds ratios and risk ratios.

Odds ratios and risk ratios are useful measures of effect size in 2-group studies in which the response variable is dichotomous. Confidence interval methods are proposed for combining and comparing odds ratios and risk ratios in multistudy designs. Unlike the traditional fixed-effect meta-analysis methods, the proposed varying coefficient methods do not require effect-size homogeneity, and unlike the random-effects meta-analysis methods, the proposed varying coefficient methods do not assume that the effect sizes from the selected studies represent a random sample from a normally distributed superpopulation of effect sizes. The results of extensive simulation studies suggest that the proposed varying coefficient methods have excellent performance characteristics under realistic conditions and should provide useful alternatives to the currently used meta-analysis methods. (PsycINFO Database Record

CFA with binary variables in small samples: a comparison of two methods.

Asymptotically optimal correlation structure methods with binary data can break down in small samples. A new correlation structure methodology based on a recently developed odds-ratio (OR) approximation to the tetrachoric correlation coefficient is proposed as an alternative to the LPB approach proposed by Lee et al. (1995). Unweighted least squares (ULS) estimation with robust standard errors and generalized least squares (GLS) estimation methods were compared. Confidence intervals and tests for individual model parameters exhibited the best performance using the OR approach with ULS estimation. The goodness-of-fit chi-square test exhibited the best Type I error control using the LPB approach with ULS estimation.

Meta-analysis methods for risk differences.

The difference between two proportions, referred to as a risk difference, is a useful measure of effect size in studies where the response variable is dichotomous. Confidence interval methods based on a varying coefficient model are proposed for combining and comparing risk differences from multi-study between-subjects or within-subjects designs. The proposed methods are new alternatives to the popular constant coefficient and random coefficient methods. The proposed varying coefficient methods do not require the constant coefficient assumption of effect size homogeneity, nor do they require the random coefficient assumption that the risk differences from the selected studies represent a random sample from a normally distributed superpopulation of risk differences. The proposed varying coefficient methods are shown to have excellent finite-sample performance characteristics under realistic conditions.

Determining vehicle operating speed and lateral position along horizontal curves using linear mixed-effects models.

OBJECTIVE: Despite recent improvements in highway safety in the United States, serious crashes on curves remain a significant problem. To assist in better understanding causal factors leading to this problem, this article presents and demonstrates a methodology for collection and analysis of vehicle trajectory and speed data for rural and urban curves using Z-configured road tubes. METHODS: For a large number of vehicle observations at 2 horizontal curves located in Dexter and Ames, Iowa, the article develops vehicle speed and lateral position prediction models for multiple points along these curves. Linear mixed-effects models were used to predict vehicle lateral position and speed along the curves as explained by operational, vehicle, and environmental variables. Behavior was visually represented for an identified subset of "risky" drivers. RESULTS: Linear mixed-effect regression models provided the means to predict vehicle speed and lateral position while taking into account repeated observations of the same vehicle along horizontal curves. CONCLUSIONS: Speed and lateral position at point of entry were observed to influence trajectory and speed profiles. Rural horizontal curve site models are presented that indicate that the following variables were significant and influenced both vehicle speed and lateral position: time of day, direction of travel (inside or outside lane), and type of vehicle.

Development and validation of a Coping with Discrimination Scale: factor structure, reliability, and validity.

Four studies were conducted to develop and validate the Coping With Discrimination Scale (CDS). In Study 1, an exploratory factor analysis (N = 328) identified 5 factors: Education/Advocacy, Internalization, Drug and Alcohol Use, Resistance, and Detachment, with internal consistency reliability estimates ranging from .72 to .90. In Study 2, a confirmatory factor analysis (N = 328) provided cross-validation of the 5-factor model as well as evidence for validity of the scale. The validity evidence was similar across racial groups and for males and females. In Study 3, the estimated 2-week test-retest reliabilities (N = 53) were between .48 and .85 for the 5 factors. Education/Advocacy, Internalization, Drug and Alcohol Use, and Detachment were positively associated with active coping, self-blame, substance use, and behavioral disengagement, respectively, providing further support for validity of the CDS. Finally, incremental validity evidence was obtained in Study 4 (N = 220), where it was shown that the CDS explained variance in outcome variables (i.e., depression, life satisfaction, self-esteem, and ethnic identity) that could not be explained by general coping strategies.

Varying coefficient meta-analytic methods for alpha reliability.

The conventional fixed-effects (FE) and random-effects (RE) confidence intervals that are used to assess the average alpha reliability across multiple studies have serious limitations. The FE method, which is based on a constant coefficient model, assumes equal reliability coefficients across studies and breaks down under minor violations of this assumption. The RE method, which is based on a random coefficient model, assumes that the selected studies are a random sample from a normally distributed superpopulation. The RE method performs poorly in typical meta-analytic applications where the studies have not been randomly sampled from a normally distributed superpopulation or have been randomly sampled from a nonnormal superpopulation. A new confidence interval for the average reliability coefficient of a specific measurement scale is based on a varying coefficient statistical model and is shown to perform well under realistic conditions of reliability heterogeneity and nonrandom sampling of studies. New methods are proposed for assessing reliability moderator effects. The proposed methods are especially useful in meta-analyses that involve a small number of carefully selected studies for the purpose of obtaining a more accurate reliability estimate or to detect factors that moderate the reliability of a scale.

Meta-analytic interval estimation for standardized and unstandardized mean differences.

The fixed-effects (FE) meta-analytic confidence intervals for unstandardized and standardized mean differences are based on an unrealistic assumption of effect-size homogeneity and perform poorly when this assumption is violated. The random-effects (RE) meta-analytic confidence intervals are based on an unrealistic assumption that the selected studies represent a random sample from a large superpopulation of studies. The RE approach cannot be justified in typical meta-analysis applications in which studies are nonrandomly selected. New FE meta-analytic confidence intervals for unstandardized and standardized mean differences are proposed that are easy to compute and perform properly under effect-size heterogeneity and nonrandomly selected studies. The proposed meta-analytic confidence intervals may be used to combine unstandardized or standardized mean differences from studies having either independent samples or dependent samples and may also be used to integrate results from previous studies into a new study. An alternative approach to assessing effect-size heterogeneity is presented.

Estimating standardized linear contrasts of means with desired precision.

L. Wilkinson and the Task Force on Statistical Inference (1999) recommended reporting confidence intervals for measures of effect sizes. If the sample size is too small, the confidence interval may be too wide to provide meaningful information. Recently, K. Kelley and J. R. Rausch (2006) used an iterative approach to computer-generate tables of sample size requirements for a standardized difference between 2 means in between-subjects designs. Sample size formulas are derived here for general standardized linear contrasts of k > or = 2 means for both between-subjects designs and within-subjects designs. Special sample size formulas also are derived for the standardizer proposed by G. V. Glass (1976).

Confidence intervals for a ratio of two independent binomial proportions.

Several large-sample confidence intervals for the ratio of independent binomial proportions are compared in terms of exact coverage probability and width. A non-iterative approximate Bayesian interval is derived and its frequency properties are superior to all of the non-iterative confidence intervals considered. The approximate Bayesian interval, which is very easy to compute, has performance characteristics that are very similar to the computationally intensive score method. Two sample size determination formulas are presented, one for desired absolute precision and the other for desired relative precision.

Meta-analytic interval estimation for bivariate correlations.

The currently available meta-analytic methods for correlations have restrictive assumptions. The fixed-effects methods assume equal population correlations and exhibit poor performance under correlation heterogeneity. The random-effects methods do not assume correlation homogeneity but are based on an equally unrealistic assumption that the selected studies are a random sample from a well-defined superpopulation of study populations. The random-effects methods can accommodate correlation heterogeneity, but these methods do not perform properly in typical applications where the studies are nonrandomly selected. A new fixed-effects meta-analytic confidence interval for bivariate correlations is proposed that is easy to compute and performs well under correlation heterogeneity and nonrandomly selected studies.

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.

The moderating role of employee positive well being on the relation between job satisfaction and job performance.

This research provides further clarification to the age-old quest to better understand the happy/productive worker thesis. Using data from 109 managers employed by a large (over 5000 employees) customer services organization on the West Coast of the United States, both job satisfaction (r=.36, p<.01, 95% CI=.18 to .52) and psychological well-being (PWB; r=.43, p<.01, 95% CI=.26 to .58) were associated with supervisory performance ratings. Using Fredrickson's (2001) broaden-and-build model as the theoretical base, the authors found that PWB moderates the relation between job satisfaction and job performance. Consistent with Fredrickson's model, performance was highest when employees reported high scores on both PWB and job satisfaction. This moderating effect of PWB may account for some of the inconsistent results of previous studies.

Confidence interval for a coefficient of dispersion in nonnormal distributions.

A new confidence interval for the coefficient of dispersion (mean absolute deviation from the median divided by median) is proposed and is shown to perform better than the BCa bootstrap confidence interval.

Confidence intervals for a ratio of binomial proportions based on paired data.

Four interval estimation methods for the ratio of marginal binomial proportions are compared in terms of expected interval width and exact coverage probability. Two new methods are proposed that are based on combining two Wilson score intervals. The new methods are easy to compute and perform as well or better than the method recently proposed by Nam and Blackwelder. Two sample size formulas are proposed to approximate the sample size required to achieve an interval estimate with desired confidence level and width.

Statistical inference for a linear function of medians: confidence intervals, hypothesis testing, and sample size requirements.

When the distribution of the response variable is skewed, the population median may be a more meaningful measure of centrality than the population mean, and when the population distribution of the response variable has heavy tails, the sample median may be a more efficient estimator of centrality than the sample mean. The authors propose a confidence interval for a general linear function of population medians. Linear functions have many important special cases including pairwise comparisons, main effects, interaction effects, simple main effects, curvature, and slope. The confidence interval can be used to test 2-sided directional hypotheses and finite interval hypotheses. Sample size formulas are given for both interval estimation and hypothesis testing problems.

Sample size requirements for estimating intraclass correlations with desired precision.

A method is developed to calculate the approximate number of subjects required to obtain an exact confidence interval of desired width for certain types of intraclass correlations in one-way and two-way ANOVA models. The sample size approximation is shown to be very accurate.