# MBESS v4.4.3

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## The MBESS R Package

Implements methods that useful in designing research studies and analyzing data, with particular emphasis on methods that are developed for or used within the behavioral, educational, and social sciences (broadly defined). That being said, many of the methods implemented within MBESS are applicable to a wide variety of disciplines. MBESS has a suite of functions for a variety of related topics, such as effect sizes, confidence intervals for effect sizes (including standardized effect sizes and noncentral effect sizes), sample size planning (from the accuracy in parameter estimation [AIPE], power analytic, equivalence, and minimum-risk point estimation perspectives), mediation analysis, various properties of distributions, and a variety of utility functions. MBESS (pronounced 'em-bes') was originally an acronym for 'Methods for the Behavioral, Educational, and Social Sciences,' but at this point MBESS contains methods applicable and used in a wide variety of fields and is an orphan acronym, in the sense that what was an acronym is now literally its name. MBESS has greatly benefited from others, see <http://nd.edu/~kkelley/site/MBESS.html> for a detailed list of those that have contributed and other details.

## Functions in MBESS

 Name Description HS.data Complete Data Set of Holzinger and Swineford's (1939) Study MBESS MBESS F.and.R2.Noncentral.Conversion Conversion functions from noncentral noncentral values to their corresponding and vice versa, for those related to the F-test and R Square. CFA.1 One-factor confirmatory factor analysis model Cor.Mat.Lomax Correlation matrix for Lomax (1983) data set Gardner.LD The Gardner learning data, which was used by L.R. Tucker ci.c Confidence interval for a contrast in a fixed effects ANOVA ci.c.ancova Confidence interval for an (unstandardized) contrast in ANCOVA with one covariate ci.cc Confidence interval for the population correlation coefficient ci.cv Confidence interval for the coefficient of variation ci.pvaf Confidence Interval for the Proportion of Variance Accounted for (in the dependent variable by knowing the levels of the factor) ci.rc Confidence Interval for a Regression Coefficient ci.reg.coef Confidence interval for a regression coefficient ci.reliability Confidence Interval for a Reliability Coefficient Sigma.2.SigmaStar Construct a covariance matrix with specified error of approximation Variance.R2 Variance of squared multiple correlation coefficient aipe.smd Sample size planning for the standardized mean different from the accuracy in parameter estimation approach ancova.random.data Generate random data for an ANCOVA model ci.sc.ancova Confidence interval for a standardized contrast in ANCOVA with one covariate ci.sm Confidence Interval for the Standardized Mean ci.srsnr Confidence Interval for the Square Root of the Signal-To-Noise Ratio conf.limits.nc.chisq Confidence limits for noncentral chi square parameters power.equivalence.md.plot Plot power of Two One-Sided Tests Procedure (TOST) for Equivalence prof.salary Cohen et. al. (2003)'s professor salary data set cor2cov Correlation Matrix to Covariance Matrix Conversion covmat.from.cfm Covariance matrix from confirmatory (single) factor model. smd Standardized mean difference smd.c Standardized mean difference using the control group as the basis of standardization Cor.Mat.MM Correlation matrix for Maruyama & McGarvey (1980) data set Expected.R2 Expected value of the squared multiple correlation coefficient ci.rmsea Confidence interval for the population root mean square error of approximation ci.sc Confidence Interval for a Standardized Contrast in a Fixed Effects ANOVA intr.plot Regression Surface Containing Interaction mediation Effect sizes and confidence intervals in a mediation model mediation.effect.bar.plot Bar plots of mediation effects mediation.effect.plot Visualizing mediation effects ci.snr Confidence Interval for the Signal-To-Noise Ratio ci.src Confidence Interval for a Standardized Regression Coefficient cv Function to calculate the regular (which is also biased) estimate of the coefficient of variation or the unbiased estimate of the coefficient of variation. ss.aipe.reg.coef Sample size necessary for the accuracy in parameter estimation approach for a regression coefficient of interest ss.aipe.reg.coef.sensitivity Sensitivity analysis for sample size planning from the Accuracy in Parameter Estimation Perspective for the (standardized and unstandardized) regression coefficient ss.aipe.sc.sensitivity Sensitivity analysis for sample size planning for the standardized ANOVA contrast from the Accuracy in Parameter Estimation (AIPE) Perspective ss.aipe.sem.path Sample size planning for SEM targeted effects ss.aipe.sc.ancova Sample size planning from the AIPE perspective for standardized ANCOVA contrasts ss.aipe.sc.ancova.sensitivity Sensitivity analysis for the sample size planning method for standardized ANCOVA contrast ss.aipe.src.sensitivity Sensitivity analysis for sample size planing from the Accuracy in Parameter Estimation Perspective for the standardized regression coefficient ss.power.R2 Function to plan sample size so that the test of the squared multiple correlation coefficient is sufficiently powerful. t.and.smd.conversion Conversion functions for noncentral t-distribution ss.aipe.crd Find target sample sizes for the accuracy in unstandardized conditions means estimation in CRD ss.aipe.crd.es Find target sample sizes for the accuracy in standardized conditions means estimation in CRD theta.2.Sigma.theta Compute the model-implied covariance matrix of an SEM model vit Visualize individual trajectories vit.fitted Visualize individual trajectories with fitted curve and quality of fit ci.R Confidence interval for the multiple correlation coefficient ci.R2 Confidence interval for the population squared multiple correlation coefficient ci.smd Confidence limits for the standardized mean difference. intr.plot.2d Plotting Conditional Regression Lines with Interactions in Two Dimensions power.density.equivalence.md Density for power of two one-sided tests procedure (TOST) for equivalence power.equivalence.md Power of Two One-Sided Tests Procedure (TOST) for Equivalence ss.aipe.cv.sensitivity Sensitivity analysis for sample size planning given the Accuracy in Parameter Estimation approach for the coefficient of variation. ci.smd.c Confidence limits for the standardized mean difference using the control group standard deviation as the divisor. conf.limits.ncf Confidence limits for noncentral F parameters conf.limits.nct Confidence limits for a noncentrality parameter from a t-distribution s.u Unbiased estimate of the population standard deviation signal.to.noise.R2 Signal to noise using squared multiple correlation coefficient ss.aipe.R2 Sample Size Planning for Accuracy in Parameter Estimation for the multiple correlation coefficient. ss.aipe.R2.sensitivity Sensitivity analysis for sample size planning with the goal of Accuracy in Parameter Estimation (i.e., a narrow observed confidence interval) ss.aipe.c Sample size planning for an ANOVA contrast from the Accuracy in Parameter Estimation (AIPE) perspective ss.aipe.c.ancova Sample size planning for a contrast in randomized ANCOVA from the Accuracy in Parameter Estimation (AIPE) perspective ss.aipe.rc Sample size necessary for the accuracy in parameter estimation approach for an unstandardized regression coefficient of interest mr.cv Minimum risk point estimation of the population coefficient of variation mr.smd Minimum risk point estimation of the population standardized mean difference ss.aipe.c.ancova.sensitivity Sensitivity analysis for sample size planning for the (unstandardized) contrast in randomized ANCOVA from the Accuracy in Parameter Estimation (AIPE) Perspective ss.aipe.reliability Sample Size Planning for Accuracy in Parameter Estimation for Reliability Coefficients. ss.aipe.rmsea Sample size planning for RMSEA in SEM ss.aipe.smd.sensitivity Sensitivity analysis for sample size given the Accuracy in Parameter Estimation approach for the standardized mean difference. ss.aipe.src sample size necessary for the accuracy in parameter estimation approach for a standardized regression coefficient of interest ss.power.reg.coef sample size for a targeted regression coefficient ss.power.sem Sample size planning for structural equation modeling from the power analysis perspective ss.aipe.cv Sample size planning for the coefficient of variation given the goal of Accuracy in Parameter Estimation approach to sample size planning ss.power.pcm Sample size planning for power for polynomial change models ss.power.rc sample size for a targeted regression coefficient upsilon This function implements the upsilon effect size statistic as described in Lachowicz, Preacher, & Kelley (in press) for mediation. verify.ss.aipe.R2 Internal MBESS function for verifying the sample size in ss.aipe.R2 ss.aipe.pcm Sample size planning for polynomial change models in longitudinal study ss.aipe.rmsea.sensitivity a priori Monte Carlo simulation for sample size planning for RMSEA in SEM ss.aipe.sc Sample size planning for Accuracy in Parameter Estimation (AIPE) of the standardized contrast in ANOVA ss.aipe.sm.sensitivity Sensitivity analysis for sample size planning for the standardized mean from the Accuracy in Parameter Estimation (AIPE) Perspective ss.aipe.smd Sample size planning for the standardized mean difference from the Accuracy in Parameter Estimation (AIPE) perspective ss.aipe.rc.sensitivity Sensitivity analysis for sample size planing from the Accuracy in Parameter Estimation Perspective for the unstandardized regression coefficient ss.aipe.sem.path.sensitiv a priori Monte Carlo simulation for sample size planning for SEM targeted effects ss.aipe.sm Sample size planning for Accuracy in Parameter Estimation (AIPE) of the standardized mean transform_Z.r Transform Fischer's Z into the scale of a correlation coefficient transform_r.Z Transform a correlation coefficient (r) into the scale of Fischer's Z No Results!