lrstat (version 0.2.14)

hedgesg: Hedges' g Effect Size

Description

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

Usage

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

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.

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.

Author

Kaifeng Lu,

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 $\tilde{n}=\frac{n_1{n}_2}{n_1+n_2}$ and $m=n_1+n_2-2$ for pooled variance estimate.

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)