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Cohen's and Hedges' Effect Size

Source: R/cohenD.R
cohenD.Rd

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

Usage

cohenD(
  x,
  y = NULL,
  conf.level = NA,
  sides = c("two.sided", "left", "right"),
  correct = FALSE,
  na.rm = FALSE
)

Arguments

x

a non-empty numeric vector of data values

y

an optional non-empty numeric vector of data values

conf.level

confidence level of the interval. If set to NA (the default), only the point estimate is returned.

sides

character string specifying the sidedness of the confidence interval (one of "two.sided" (default), "left" or "right"). See ConfidenceIntervals().

correct

logical; whether to apply the Hedges correction. Defaults to FALSE.

na.rm

logical. Should missing values be removed? Defaults to FALSE.

Value

if conf.level = NA, a numeric scalar containing the effect size; otherwise a named numeric vector with elements:

est

point estimate of Cohen's \(d\) or Hedges' \(g\).

lci

lower confidence interval bound.

uci

upper confidence interval bound.

The magnitude category and pooled standard deviation are stored in the attributes magnitude and sdPooled, respectively.

Details

For a single sample, \(d = \bar{x} / s\); for two samples, \(d = (\bar{x} - \bar{y}) / s_{pooled}\). With correct = TRUE Hedges' bias correction \(J = 1 - 3/(4\nu - 1)\), with \(\nu\) the residual degrees of freedom, is applied to the estimate and, where computed, to the interval.

Confidence intervals invert the noncentral \(t\) distribution (Steiger & Fouladi): the noncentrality parameter is \(d\sqrt{n}\) with \(n - 1\) degrees of freedom in the one-sample case, and \(d / \sqrt{1/n_x + 1/n_y}\) with \(n_x + n_y - 2\) degrees of freedom in the two-sample case.

sides names the side on which the finite bound lies: "left" yields \([lci, \infty)\), "right" yields \((-\infty, uci]\).

Note

Based on code by William Revelle.

References

Cohen, J. (1988) Statistical power analysis for the behavioral sciences (2nd ed.) Academic Press, New York.

Hedges, L. V. & Olkin, I. (1985) Statistical methods for meta-analysis Academic Press, Orlando, FL

Smithson, M.J. (2003) Confidence Intervals, Quantitative Applications in the Social Sciences Series, No. 140. Thousand Oaks, CA: Sage. pp. 39-41

See also

glassDelta(), meanX(), varX()

Other effect.size: cohenH(), etaSq(), glassDelta(), oddsRatio(), relRisk()

Examples


x <- Pizza$price[Pizza$driver == "Carter"]
y <- Pizza$price[Pizza$driver == "Miller"]

cohenD(x, y, conf.level = 0.95, na.rm = TRUE)
#>          est          lci          uci 
#> -0.212277884 -0.430316026  0.006058519 
#> attr(,"magnitude")
#> [1] "small"
#> attr(,"sdPooled")
#> [1] 21.54513

# Hedges' g
cohenD(x, y, conf.level = 0.95, correct = TRUE, na.rm = TRUE)
#>          est          lci          uci 
#> -0.211827825 -0.429403695  0.006045674 
#> attr(,"magnitude")
#> [1] "small"
#> attr(,"sdPooled")
#> [1] 21.54513

# one-sided: the finite bound lies on the left
cohenD(x, y, conf.level = 0.95, sides = "left", na.rm = TRUE)
#>        est        lci        uci 
#> -0.2122779 -0.3952370        Inf 
#> attr(,"magnitude")
#> [1] "small"
#> attr(,"sdPooled")
#> [1] 21.54513