R: Cohen's d and Hedges g effect size

cohen.d {effsize} | R Documentation

## Cohen's d and Hedges g effect size

### 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(),...)

    ## Default S3 method:
    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).

When `paired` is set, the effect size is computed using the approach suggested in (Gibbons et al. 1993).

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)

### Value

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"`

### Author(s)

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

### 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 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.

### 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)

[Package effsize version 0.7.1 Index]