# Standardized mean difference Function to calculate the standardized mean difference (regular or unbiased) using either raw data or summary measures. ```r smd(Group.1 = NULL, Group.2 = NULL, Mean.1 = NULL, Mean.2 = NULL, s.1 = NULL, s.2 = NULL, s = NULL, n.1 = NULL, n.2 = NULL, Unbiased=FALSE) ``` ## Arguments - `Group.1`: Raw data for group 1. - `Group.2`: Raw data for group 2. - `Mean.1`: The mean of group 1. - `Mean.2`: The mean of group 2. - `s.1`: The standard deviation of group 1 (i.e., the square root of the unbiased estimator of the population variance). - `s.2`: The standard deviation of group 2 (i.e., the square root of the unbiased estimator of the population variance). - `s`: The pooled group standard deviation (i.e., the square root of the unbiased estimator of the population variance). - `n.1`: The sample size within group 1. - `n.2`: The sample size within group 2. - `Unbiased`: Returns the unbiased estimate of the standardized mean difference. ## Details When `Unbiased=TRUE`, the unbiased estimate of the standardized mean difference is returned (Hedges, 1981). ## Returns Returns the estimated standardized mean difference. ## References Cohen, J. (1988). **Statistical power analysis for the behavioral sciences** (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum. Cumming, G. & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions, **Educational and Psychological Measurement, 61**, 532--574. Hedges, L. V. (1981). Distribution theory for Glass's Estimator of effect size and related estimators. **Journal of Educational Statistics, 2**, 107--128. Kelley, K. (2005) The effects of nonnormal distributions on confidence intervals around the standardized mean difference: Bootstrap and parametric confidence intervals, **Educational and Psychological Measurement, 65**, 51--69. Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. **Journal of Statistical Software, 20** (8), 1--24. Steiger, J. H., & Fouladi, R. T. (1997). Noncentrality interval estimation and the evaluation of statistical methods. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.), **What if there were no significance tests?** (pp. 221--257). Mahwah, NJ: Lawrence Erlbaum. ## Author(s) Ken Kelley (University of Notre Dame; KKelley@ND.Edu ) ## See Also `smd.c`, `conf.limits.nct`, `ss.aipe` ## Examples ```r # Generate sample data. set.seed(113) g.1 <- rnorm(n=25, mean=.5, sd=1) g.2 <- rnorm(n=25, mean=0, sd=1) smd(Group.1=g.1, Group.2=g.2) M.x <- .66745 M.y <- .24878 sd <- 1.048 smd(Mean.1=M.x, Mean.2=M.y, s=sd) M.x <- .66745 M.y <- .24878 n1 <- 25 n2 <- 25 sd.1 <- .95817 sd.2 <- 1.1311 smd(Mean.1=M.x, Mean.2=M.y, s.1=sd.1, s.2=sd.2, n.1=n1, n.2=n2) smd(Mean.1=M.x, Mean.2=M.y, s.1=sd.1, s.2=sd.2, n.1=n1, n.2=n2, Unbiased=TRUE) ```

smd function