Standardized mean difference

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Description

Function to calculate the standardized mean difference (regular or unbiased) using either raw data or summary measures.

Usage

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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).

Value

Returns the estimated standardized mean difference.

Author(s)

Ken Kelley (University of Notre Dame; KKelley@ND.Edu)

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.

See Also

smd.c, conf.limits.nct, ss.aipe

Examples

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# 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)

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