cohen.d: Cohen's d and Hedges g effect size
In effsize: Efficient Effect Size Computation

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/CohenD.R

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` is a factor) or the treatment group values (if `f` is a numeric vector)
`f`	either a factor with two levels or a numeric vector of values, if `NA` a single sample effect size is computed
`formula`	a formula of the form `y ~ f`, where `y` is a numeric variable giving the values and `f` a factor with two levels giving the corresponding groups. If using a paired computation (`paired=TRUE`) it is possible to specify the ids of the subjects using the form `y ~ f \| Subject(id)` which allow the correct pairing of the pre and post values. A single sample effect size can be specified with the form `y ~ .`.
`data`	an optional matrix or data frame containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.
`pooled`	a logical indicating whether compute pooled standard deviation or the whole sample standard deviation. If `pooled=TRUE` (default) pooled sd is used, if `pooled=FALSE` the standard deviation of the the control group (the second argument or the one corresponding the the second level of the factor) is used instead.
`hedges.correction`	logical indicating whether apply the Hedges correction
`conf.level`	confidence level of the confidence interval
`noncentral`	logical indicating whether to use non-central t distributions for computing the confidence interval.
`paired`	a logical indicating whether to consider the values as paired, a warning is issued if `paired==TRUE` with the formula interface and not `\| Subject(id)` or with data and factor and no `subject` is provided
`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 `\| Subject(id)`, where `id` is the column in the data that contains and id of the subjects to be paired.
`mu`	numeric indicating the reference mean for single sample effect size.
`na.rm`	logical indicating whether `NA`s should be removed before computation; if `paired==TRUE` then all incomplete pairs are removed.
`...`	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 non-central Student-t 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):

((n1+n2)/(n1*n2) + .5*d^2/df) * ((n1+n2)/df)

A list of class effsize containing the following components:

`estimate`	the statistic estimate
`conf.int`	the confidence interval of the statistic
`sd`	the within-groups 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 `"Cohen's d"` or `"Hedges' g"`

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 meta-analysis. Orlando, FL: Academic Press.

Cohen, J. (1992). A power primer. Psychological Bulletin, 112, 155-159.

Cooper, Hedges, and Valentin (2009). The Handbook of Research Synthesis and Meta-Analysis

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, 633-649.

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, 271-279.

M. Borenstein, L. V. Hedges, J. P. T. Higgins and H. R. Rothstein (2009) Introduction to Meta-Analysis. 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)

Cohen's d

d estimate: -2.017103 (large)
95 percent confidence interval:
      inf       sup 
-2.359643 -1.674563 

Cohen's d

d estimate: -2.017103 (large)
95 percent confidence interval:
      inf       sup 
-2.359643 -1.674563 

Cohen's d

d estimate: -2.017103 (large)
95 percent confidence interval:
      inf       sup 
-2.359643 -1.674563 

Hedges's g

g estimate: -2.009453 (large)
95 percent confidence interval:
      inf       sup 
-2.351556 -1.667351