propes: Proportions to Effect Size

Description

Converts proportions (typically seen in studies reporting odds ratios) to an effect size of $d$ (mean difference), $g$ (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

propes(p1, p2, n.ab, n.cd, level=95, dig=2, id=NULL, data=NULL)

Arguments

Proportion one.

Proportion two.

n.ab

Total sample size for group A and B.

n.cd

Total sample size for group C and D.

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

This formula will first compute an odds ratio and then transform to log odds and its variance. Then, Cohen's $d$ will be calculated and this value will then be used to compute the remaining effect size estimates. The odds ratio is derived as follows $$or= \frac{p_{1}(1-p_{2})} {p_{2}(1-p_{1})}$$ The conversion to a log odds and its variance is defined as $$ln(o)= log(or)$$ $$v_{ln(o)}= \frac{1} {n_{AB}p_{1}(1-p_{1})}+ \frac{1} {n_{CD}p_{2}(1-p_{2})}$$ where $n_{AB}$ is the sum of group A and B sample size, $n_{CD}$ is the sum of group C and D sample size, $p_{1}$ is the proportion for group 1 and $p_{2}$ is the proportion for group 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.

Description

Usage

Arguments

Value

Details

References

See Also