hedgesg {lrstat}

Hedges' g effect size

Description

Obtains Hedges' g estimate and confidence interval of effect size.

Usage

hedgesg(tstat, m, ntilde, cilevel = 0.95)

Arguments

tstat

The value of the t-test statistic for comparing two treatment conditions.

m

The degrees of freedom for the t-test.

ntilde

The normalizing sample size to convert the standardized treatment difference to the t-test statistic, i.e., tstat = sqrt(ntilde)*meanDiff/stDev.

cilevel

The confidence interval level. Defaults to 0.95.

Details

Hedges' g is an effect size measure commonly used in meta-analysis to quantify the difference between two groups. It's an improvement over Cohen's d, particularly when dealing with small sample sizes.

The formula for Hedges' g is

g = c(m) d,

where d is Cohen's d effect size estimate, and c(m) is the bias correction factor,

d = (\hat{\mu}_1 - \hat{\mu}_2)/\hat{\sigma},

c(m) = 1 - \frac{3}{4m-1}.

Since c(m) < 1, Cohen's d overestimates the true effect size. \delta = (\mu_1 - \mu_2)/\sigma. Since

t = \sqrt{\tilde{n}} d,

we have

g = \frac{c(m)}{\sqrt{\tilde{n}}} t,

where t has a noncentral t distribution with m degrees of freedom and noncentrality parameter \sqrt{\tilde{n}} \delta.

The asymptotic variance of g can be approximated by

Var(g) = \frac{1}{\tilde{n}} + \frac{g^2}{2m}.

The confidence interval for \delta can be constructed using normal approximation.

For two-sample mean difference with sample size n_1 for the treatment group and n_2 for the control group, we have \tilde{n} = \frac{n_1n_2}{n_1+n_2} and m=n_1+n_2-2 for pooled variance estimate.

Value

A data frame with the following variables:

• tstat: The value of the t test statistic.

• m: The degrees of freedom for the t-test.

• ntilde: The normalizing sample size to convert the standardized treatment difference to the t-test statistic.

• g: Hedges' g effect size estimate.

• varg: Variance of g.

• lower: The lower confidence limit for effect size.

• upper: The upper confidence limit for effect size.

• cilevel: The confidence interval level.

Author(s)

Kaifeng Lu, [e-mail]

References

Larry V. Hedges. Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics 1981; 6:107-128.

Examples

n1 = 7
n2 = 8
meanDiff = 0.444
stDev = 1.201
m = n1+n2-2
ntilde = n1*n2/(n1+n2)
tstat = sqrt(ntilde)*meanDiff/stDev

hedgesg(tstat, m, ntilde)