effectsize: cohens_d – R documentation

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cohens_d

Effect size for differences

Description

Compute effect size indices for standardized differences: Cohen's d, Hedges' g and Glass’s delta. (This function returns the population estimate.)

Both Cohen's d and Hedges' g are the estimated the standardized difference between the means of two populations. Hedges' g provides a bias correction to Cohen's d for small sample sizes. For sample sizes > 20, the results for both statistics are roughly equivalent. Glass’s delta is appropriate when the standard deviations are significantly different between the populations, as it uses only the second group's standard deviation.

Usage

cohens_d(
  x,
  y = NULL,
  data = NULL,
  pooled_sd = TRUE,
  mu = 0,
  paired = FALSE,
  ci = 0.95,
  verbose = TRUE,
  ...,
  correction
)

hedges_g(
  x,
  y = NULL,
  data = NULL,
  correction = 1,
  pooled_sd = TRUE,
  mu = 0,
  paired = FALSE,
  ci = 0.95,
  verbose = TRUE,
  ...
)

glass_delta(
  x,
  y = NULL,
  data = NULL,
  mu = 0,
  ci = 0.95,
  iterations = 200,
  verbose = TRUE,
  ...,
  correction
)

Arguments

`x`	A formula, a numeric vector, or a character name of one in `data`.
`y`	A numeric vector, a grouping (character / factor) vector, a or a character name of one in `data`. Ignored if `x` is a formula.
`data`	An optional data frame containing the variables.
`pooled_sd`	If `TRUE` (default), a `sd_pooled()` is used (assuming equal variance). Else the mean SD from both groups is used instead.
`mu`	a number indicating the true value of the mean (or difference in means if you are performing a two sample test).
`paired`	If `TRUE`, the values of `x` and `y` are considered as paired. This produces an effect size that is equivalent to the one-sample effect size on `x - y`.
`ci`	Confidence Interval (CI) level
`verbose`	Toggle warnings and messages on or off.
`...`	Arguments passed to or from other methods.
`correction`	Type of small sample bias correction to apply to produce Hedges' g. Can be `1` for Hedges and Olkin's original correction (default) or `2` for Hunter and Schmidt's correction (see McGrath & Meyer, 2006).
`iterations`	The number of bootstrap replicates for computing confidence intervals. Only applies when `ci` is not `NULL`.

Details

Confidence Intervals for Glass' delta

Confidence Intervals for Glass' delta are estimated using the bootstrap method.

Value

A data frame with the effect size ( Cohens_d, Hedges_g, Glass_delta) and their CIs (CI_low and CI_high).

Confidence Intervals

Unless stated otherwise, confidence intervals are estimated using the Noncentrality parameter method; These methods searches for a the best non-central parameters (ncps) of the noncentral t-, F- or Chi-squared distribution for the desired tail-probabilities, and then convert these ncps to the corresponding effect sizes. (See full effectsize-CIs for more.)

Note

The indices here give the population estimated standardized difference. Some statistical packages give the sample estimate instead (without applying Bessel's correction).

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge.
Hedges, L. V. & Olkin, I. (1985). Statistical methods for meta-analysis. Orlando, FL: Academic Press.
Hunter, J. E., & Schmidt, F. L. (2004). Methods of meta-analysis: Correcting error and bias in research findings. Sage.
McGrath, R. E., & Meyer, G. J. (2006). When effect sizes disagree: the case of r and d. Psychological methods, 11(4), 386.

Examples

# two-sample tests -----------------------

# using formula interface
cohens_d(mpg ~ am, data = mtcars)
cohens_d(mpg ~ am, data = mtcars, pooled_sd = FALSE)
cohens_d(mpg ~ am, data = mtcars, mu = -5)
hedges_g(mpg ~ am, data = mtcars)
if (require(boot)) glass_delta(mpg ~ am, data = mtcars)
print(cohens_d(mpg ~ am, data = mtcars), append_CL = TRUE)

# other acceptable ways to specify arguments
cohens_d(sleep$extra, sleep$group)
hedges_g("extra", "group", data = sleep)
cohens_d(sleep$extra[sleep$group == 1], sleep$extra[sleep$group == 2], paired = TRUE)

# one-sample tests -----------------------

cohens_d("wt", data = mtcars, mu = 3)
hedges_g("wt", data = mtcars, mu = 3)

# interpretation -----------------------

interpret_d(0.4, rules = "cohen1988")
d_to_common_language(0.4)
interpret_g(0.4, rules = "sawilowsky2009")
interpret_delta(0.4, rules = "gignac2016")

effectsize

Indices of Effect Size and Standardized Parameters

v0.4.4-1

GPL-3

Authors

Mattan S. Ben-Shachar [aut, cre] (<https://orcid.org/0000-0002-4287-4801>), Dominique Makowski [aut] (<https://orcid.org/0000-0001-5375-9967>), Daniel Lüdecke [aut] (<https://orcid.org/0000-0002-8895-3206>), Indrajeet Patil [ctb] (<https://orcid.org/0000-0003-1995-6531>, @patilindrajeets), Ken Kelley [ctb], David Stanley [ctb]

Initial release