# cohen.d {effsize}

Cohen's d and Hedges g effect size
Package:
effsize
Version:
0.6.2

### 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.

`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)```

### Author(s)

Marco Torchiano http://softeng.polito.it/torchiano/

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