# cohen.d {effsize}

### Description

Computes the Cohen's d and Hedges'g effect size statistics.

### Usage

cohen.d(d, ...) ## S3 method for class 'formula': cohen.d((formula,data=list(),...)) ## S3 method for class 'default': cohen.d((d,f,pooled=TRUE,paired=FALSE, na.rm=FALSE, hedges.correction=FALSE, conf.level=0.95,noncentral=FALSE, ...))

### Arguments

- 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
- pooled
- a logical indicating whether compute pooled standard deviation or the whole sample standard deviation
- paired
- a logical indicating whether to consider the values as paired
- na.rm
- logical indicating whether
`NA`

s should be removed before computation; if`paired==TRUE`

then all incomplete pairs are removed. - hedges.correction
- logical indicating whether apply the Hedges correction
- conf.level
- confidence level of the confidence interval
- formula
- a formula of the form
`y ~ f`

, where`y`

is a numeric variable giving the data values and`f`

a factor with two levels giving the corresponding groups - data
- an optional matrix or data frame containing the variables in the formula
`formula`

. By default the variables are taken from`environment(formula)`

. - noncentral
- logical indicating whether to use non-central t distributions for computing the confidence interval.
- ...
- further arguments to be passed to or from methods.

### Details

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, if `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).

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 variace of the `d`

is computed using the conversion formula reportead at page 238 of Cooper et al. (2009):

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

### Values

A list of class `effsize`

containing the following components:

- estimate
- the statistics estimate
- conf.int
- the confidence interval of the statistic
- var
- the estimated variance of the statistic
- 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"`

### References

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.

The Handbook of Research Synthesis and Meta-Analysis (Cooper, Hedges, & Valentine, 2009)

David C. Howell (2010). Confidence Intervals on Effect Size. Available at: https://www.uvm.edu/%7Edhowell/methods7/Supplements/Confidence%20Intervals%20on%20Effect%20Size.pdf

Cumming, G.; Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervalsthat are based on central and noncentral distributions. Educational and Psychological Measurement, 61, 633-649.

### See Also

`cliff.delta`

, `VD.A`

, `print.effsize`

### Examples

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)

Documentation reproduced from package effsize, version 0.6.2. License: GPL-2