cohen.d {effsize}  R Documentation 
Computes the Cohen's d and Hedges'g effect size statistics.
cohen.d(d, ...)
## S3 method for class 'formula'
cohen.d(formula,data=list(),...)
## Default S3 method:
cohen.d(d,f,pooled=TRUE,paired=FALSE,
na.rm=FALSE, mu=0, hedges.correction=FALSE,
conf.level=0.95,noncentral=FALSE,
within=TRUE, subject=NA, ...)
d 
a numeric vector giving either the data values (if 
f 
either a factor with two levels or a numeric vector of values, if 
formula 
a formula of the form If using a paired computation ( A single sample effect size can be specified with the form 
data 
an optional matrix or data frame containing the variables in the formula 
pooled 
a logical indicating whether compute pooled standard deviation or the whole sample standard deviation. If 
hedges.correction 
logical indicating whether apply the Hedges correction 
conf.level 
confidence level of the confidence interval 
noncentral 
logical indicating whether to use noncentral t distributions for computing the confidence interval. 
paired 
a logical indicating whether to consider the values as paired, a warning is issued if

within 
indicates whether to compute the effect size using the within subject variation, taking into consideration the correlation between pre and post samples. 
subject 
an array indicating the id of the subject for a paired computation, when the formula interface is used it can be indicated in the formula by adding 
mu 
numeric indicating the reference mean for single sample effect size. 
na.rm 
logical indicating whether 
... 
further arguments to be passed to or from methods. 
When f
in the default version is a factor or a character, it must have two values and it identifies the two groups to be compared. Otherwise (e.g. f
is numeric), it is considered as a sample to be compare to d
.
In the formula version, f
is expected to be a factor, if that is not the case it is coherced to a factor and a warning is issued.
The function computes the value of Cohen's d statistics (Cohen 1988).
If required (hedges.correction==TRUE
) the Hedges g statistics is computed instead (Hedges and Holkin, 1985).
When paired
is set, the effect size is computed using the approach suggested in (Gibbons et al. 1993). In particular a correction to take into consideration the correlation of the two samples is applied (see Borenstein et al., 2009)
It is possible to perform a single sample effect size estimation either using a formula ~x
or passing f=NA
.
The computation of the CI requires the use of noncentral Studentt distributions that are used when noncentral==TRUE
; otherwise a central distribution is used.
Also a quantification of the effect size magnitude is performed using the thresholds define in Cohen (1992).
The magnitude is assessed using the thresholds provided in (Cohen 1992), i.e. d<0.2 "negligible"
, d<0.5 "small"
, d<0.8 "medium"
, otherwise "large"
The variance of the d
is computed using the conversion formula reported at page 238 of Cooper et al. (2009):
S^2_d = \left( \frac{n_1+n_2}{n_1 n_2} + \frac{d^2}{2 df}\right) \left( \frac{n_1+n_2}{df} \right)
A list of class effsize
containing the following components:
estimate 
the statistic estimate 
conf.int 
the confidence interval of the statistic 
sd 
the withingroups standard deviation 
conf.level 
the confidence level used to compute the confidence interval 
magnitude 
a qualitative assessment of the magnitude of effect size 
method 
the method used for computing the effect size, either 
Marco Torchiano http://softeng.polito.it/torchiano/
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New York:Academic Press.
Hedges, L. V. & Olkin, I. (1985). Statistical methods for metaanalysis. Orlando, FL: Academic Press.
Cohen, J. (1992). A power primer. Psychological Bulletin, 112, 155159.
Cooper, Hedges, and Valentin (2009). The Handbook of Research Synthesis and MetaAnalysis
David C. Howell (2011). Confidence Intervals on Effect Size. Available at: https://www.uvm.edu/~statdhtx/methods8/Supplements/MISC/Confidence%20Intervals%20on%20Effect%20Size.pdf
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, 633649.
Gibbons, R. D., Hedeker, D. R., & Davis, J. M. (1993). Estimation of effect size from a series of experiments involving paired comparisons. Journal of Educational Statistics, 18, 271279.
M. Borenstein, L. V. Hedges, J. P. T. Higgins and H. R. Rothstein (2009) Introduction to MetaAnalysis. John Wiley & Son.
cliff.delta
, VD.A
, print.effsize
treatment = rnorm(100,mean=10)
control = rnorm(100,mean=12)
d = (c(treatment,control))
f = rep(c("Treatment","Control"),each=100)
## compute Cohen's d
## treatment and control
cohen.d(treatment,control)
## data and factor
cohen.d(d,f)
## formula interface
cohen.d(d ~ f)
## compute Hedges' g
cohen.d(d,f,hedges.correction=TRUE)