package for R (R Development Core Team, 2007b), an open source statistical programming language and environment. MBESS implements methods that are not widely available elsewhere, yet are especially helpful for the idiosyncratic techniques used within the behavioral, educational, and social sciences. The major categories of functions are those that relate to confidence interval formation for noncentral t, F, and � 2 parameters, confidence intervals for standardized effect sizes (which require noncentral distributions), and sample size planning issues from the power analytic and accuracy in parameter estimation perspectives. In addition, MBESS contains collections of other functions that should be helpful to substantive researchers and methodologists. MBESS is a long-term project that will continue to be updated and expanded so that important methods can continue to be made available to researchers in the behavioral, educational, and social sciences. R is an open source statistical programming language and environment for (essentially) all operating systems that has gained a widespread following in quantitative disciplines (R Development Core Team, 2007b). This following is perhaps most prevalent in the statistical sciences, where many published works now provide R routines

The root mean square error of approximation (RMSEA) is one of the most widely reported measures of misfit/fit in applications of structural equation modeling. When the RMSEA is of interest, so too should the accompanying confidence interval. A narrow confidence interval reveals that the plausible parameter values are confined to a relatively small range, at the specified level of confidence. The accuracy in parameter estimation approach to sample size planning is developed for the RMSEA so that the confidence interval for the population RMSEA will have a width whose expectation is sufficiently narrow. Analytic developments are shown to work well with a Monte Carlo simulation study. Freely available computer software is developed so that the methods discussed can be implemented. The methods are demonstrated for a repeated measures design, where the way in which social relationships and initial depression influence coping strategies and later depression are examined.

In addition to evaluating a structural equation model (SEM) as a whole, often the model parameters are of interest and confidence intervals for those parameters are formed. Given a model with a good overall fit, it is entirely possible for the targeted effects of interest to have very wide confidence intervals, thus giving little information about the magnitude of the population targeted effects. With the goal of obtaining sufficiently narrow confidence intervals for the model parameters of interest, sample size planning methods for SEM are developed from the accuracy in parameter estimation approach. One method plans for the sample size so that the expected confidence interval width is sufficiently narrow. An extended procedure ensures that the obtained confidence interval will be no wider than desired, with some specified degree of assurance. A Monte Carlo simulation study was conducted that verified the effectiveness of the procedures in realistic situations. The methods developed have been implemented in the MBESS package in R so that they can be easily applied by researchers.

Longitudinal studies are necessary to examine individual change over time, with group status often being an important variable in explaining some individual differences in change. Although sample size planning for longitudinal studies has focused on statistical power, recent calls for effect sizes and their corresponding confidence intervals underscore the importance of obtaining sufficiently accurate estimates of group differences in change. We derived expressions that allow researchers to plan sample size to achieve the desired confidence interval width for group differences in change for orthogonal polynomial change parameters. The approaches developed provide the expected confidence interval width to be sufficiently narrow, with an extension that allows some specified degree of assurance (e.g., 99%) that the confidence interval will be sufficiently narrow. We make computer routines freely available, so that the methods developed can be used by researchers immediately.