FAQ/medmax - CBU statistics Wiki

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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 [attachment:abmax.xls 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 [:FAQ/EXCELmed given here.])

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 [ http://cran.r-project.org/web/packages/MBESS/ here] or [attachment:MBESS.pdf here.])

Example R code is below which can be used to obtain kappa-squared and its 95% confidence interval for the SPSS data given [attachment: medeg.sav here].

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)