des: Mean Difference (d) to Effect size

Description

Converts $d$ (mean difference) to an effect size of $g$ (unbiased estimate of $d$), $r$ (correlation coefficient), $z'$ (Fisher's $z$), and log odds ratio. The variances, confidence intervals and p-values of these estimates are also computed, along with NNT (number needed to treat), U3 (Cohen's $U_(3)$ overlapping proportions of distributions), CLES (Common Language Effect Size) and Cliff's Delta.

Usage

des(d, n.1, n.2, level=95, dig=2, id=NULL, data=NULL)

Arguments

Mean difference statistic ($d$).

n.1

Sample size of group one.

n.2

Sample size of group one.

level

Confidence level. Default is 95%.

dig

Number of digits to display. Default is 2 digits.

Study identifier. Default is NULL, assuming a scalar is used as input. If input is a vector dataset (i.e., data.frame, with multiple values to be computed), enter the name of the study identifier here.

data

name of data.frame. Default is NULL, assuming a scalar is used as input. If input is a vector dataset (i.e., data.frame, with multiple values to be computed), enter the name of the data.frame here.

Value

dStandardized mean difference ($d$).
var.dVariance of $d$.
l.dlower confidence limits for $d$.
u.dupper confidence limits for $d$.
U3.dCohen's $U_(3)$, for $d$.
cl.dCommon Language Effect Size for $d$.
cliffs.dCliff's Delta for $d$.
p.dp-value for $d$.
gUnbiased estimate of $d$.
var.gVariance of $g$.
l.glower confidence limits for $g$.
u.gupper confidence limits for $g$.
U3.gCohen's $U_(3)$, for $g$.
cl.gCommon Language Effect Size for $g$.
p.gp-value for $g$.
rCorrelation coefficient.
var.rVariance of $r$.
l.rlower confidence limits for $r$.
u.rupper confidence limits for $r$.
p.rp-value for $r$.
zFisher's z ($z'$).
var.zVariance of $z'$.
l.zlower confidence limits for $z'$.
u.zupper confidence limits for $z'$.
p.zp-value for $z'$.
OROdds ratio.
l.orlower confidence limits for $OR$.
u.orupper confidence limits for $OR$.
p.orp-value for $OR$.
lORLog odds ratio.
var.lorVariance of log odds ratio.
l.lorlower confidence limits for $lOR$.
u.lorupper confidence limits for $lOR$.
p.lorp-value for $lOR$.
N.totalTotal sample size.
NNTNumber needed to treat.

Details

Information regarding input (d): In a study comparing means from independent groups, the population standardized mean difference is defined as $$\delta= \frac{\mu_{2}-\mu_{1}} {\sigma}$$ where $\mu_{2}$ is the population mean of the second group, $\mu_{1}$ is the population mean of the first group, and $\sigma$ is the population standard deviation (assuming $\sigma_{2}$ = $\sigma_{1}$). The estimate of $\delta$ from independent groups is defined as $$d= \frac{\bar Y_{2}-\bar Y_{1}} {S_{within}}$$ where $\bar Y_{2}$ and $\bar Y_{1}$ are the sample means in each group and $S_{within}$ is the standard deviation pooled across both groups and is defined as $$S_{within}= \sqrt{\frac{(n_{1}-1)S^2_{1}+(n_{2}-1)S^2_{2}} {n_{1}+n_{2}-2}}$$ where $n_{1}$ and $n_{2}$ are the sample sizes of group 1 and 2 respectively and $S^2_{1}$ and $S^2_{2}$ are the standard deviations of each group. The variance of $d$ is then defined as $$v_{d}= \frac{n_{1}+n_{2}} {n_{1}n_{2}}+ \frac{d^2} {2(n_{1}n_{2})}$$

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation. Cohen, J. (1988). Statistical power for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum. Furukawa, T. A., & Leucht, S. (2011). How to obtain NNT from Cohen's d: comparison of two methods. PloS one, 6(4), e19070. McGraw, K. O. & Wong, S. P. (1992). A common language effect size statistic. Psychological Bulletin, 111, 361-365. Valentine, J. C. & Cooper, H. (2003). Effect size substantive interpretation guidelines: Issues in the interpretation of effect sizes. Washington, DC: What Works Clearinghouse.