# A suggested effect size and bootstrap Confidence Interval for a mediation effect

Preacher and Kelley (2011) suggest using a standardized effect size tor epresent the strength of the indirect effect of the independent variable, IV, on outcome, Y, through a mediator, M. Their effect size, kappa-squared, represents the proportion of the total possible effect that is shown by the sample. It may vary between 0 (no indirect effect) to 1 (maximum possible indirect effect attained by the data) and, they suggest, interpreting in an analogous way to a R-squared with 0.01, 0.09 and 0.25 representing small, medium and large effects respectively. They suggest quoting the effect (the product of the regression coefficients for IV -> M and M -> Y given IV) and its 95% bootstrapped confidence interval when performing the mediation analysis.

This estimate, together with its 95% bootstrap confidence interval, may be obtained using this spreadsheet which uses the bootstrap add-in for EXCEL (details of how to add this in and implement it to obtain 95% bootstrap confidence intervals are given here.) In the example in this spreadsheet the bootraw6 sheet contains the 95% confidence interval of (0.009, 0.39) suggesting a large mediation effect.

The estimate and its 95% confidence interval together with other effect sizes and power calculations using these effect sizes may be used in R using the MBESS package (Its manual is available in pdf format from here or here.)

Example R code is below which can be used to obtain kappa-squared and its 95% confidence interval for the SPSS data given here. You will have to replace the SPSS filename in the read.spss command line. Using the spreadsheet or R syntax below gives a kappa-squared for this data of 0.1687234 with an approximate 95% bootstrap confidence interval of [0.00641602, 0.368722].

install.packages(c("MBESS")) install.packages(c("foreign")) install.packages(c("gsl")) library(MBESS) library(foreign) library(gsl) library(MASS) meg <- read.spss("C:\\Documents and Settings\\peterw\\Desktop\\My Documents\\My Documents2\\SOBEL'S TEST\\MBESS R MEB EFF SIZE BOOT CIS\\MED BOOT CI TEST DATA.sav") meg <- data.frame(meg) attach(meg) meg <- na.omit(meg) medci <- mediation(IV,M,Y,conf.level=0.95,bootstrap=TRUE,B=1000)