
Compute effect size indices for standardized differences: Cohen's d, Hedges' g and Glass<U+2019>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 (using the exact method) to Cohen's d for small sample sizes. For sample sizes > 20, the results for both statistics are roughly equivalent. Glass<U+2019>s delta is appropriate when the standard deviations are significantly different between the populations, as it uses only the second group's standard deviation.
cohens_d(
x,
y = NULL,
data = NULL,
pooled_sd = TRUE,
mu = 0,
paired = FALSE,
ci = 0.95,
verbose = TRUE,
...
)hedges_g(
x,
y = NULL,
data = NULL,
pooled_sd = TRUE,
mu = 0,
paired = FALSE,
ci = 0.95,
verbose = TRUE,
...,
correction
)
glass_delta(
x,
y = NULL,
data = NULL,
mu = 0,
ci = 0.95,
verbose = TRUE,
...,
iterations
)
A formula, a numeric vector, or a character name of one in data
.
A numeric vector, a grouping (character / factor) vector, a or a
character name of one in data
. Ignored if x
is a formula.
An optional data frame containing the variables.
If TRUE
(default), a sd_pooled()
is used (assuming equal
variance). Else the mean SD from both groups is used instead.
a number indicating the true value of the mean (or difference in means if you are performing a two sample test).
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
.
Confidence Interval (CI) level
Toggle warnings and messages on or off.
Arguments passed to or from other methods.
deprecated.
A data frame with the effect size ( Cohens_d
, Hedges_g
,
Glass_delta
) and their CIs (CI_low
and CI_high
).
Unless stated otherwise, confidence intervals are estimated using the
Noncentrality parameter method; These methods searches for a the best
non-central parameters (ncp
s) of the noncentral t-, F- or Chi-squared
distribution for the desired tail-probabilities, and then convert these
ncp
s to the corresponding effect sizes. (See full effectsize-CIs for
more.)
Keep in mind that ncp
confidence intervals are inverted significance tests,
and only inform us about which values are not significantly different than
our sample estimate. (They do not inform us about which values are
plausible, likely or compatible with our data.) Thus, when CIs contain the
value 0, this should not be taken to mean that a null effect size is
supported by the data; Instead this merely reflects a non-significant test
statistic - i.e. the p-value is greater than alpha (Morey et al., 2016).
For positive only effect sizes (Eta squared, Cramer's V, etc.; Effect sizes associated with Chi-squared and F distributions), this applies also to cases where the lower bound of the CI is equal to 0. Even more care should be taken when the upper bound is equal to 0 - this occurs when p-value is greater than 1-alpha/2 making, the upper bound cannot be estimated, and the upper bound is arbitrarily set to 0 (Steiger, 2004). For example:
eta_squared(aov(mpg ~ factor(gear) + factor(cyl), mtcars[1:7, ]))
## # Effect Size for ANOVA (Type I) ## ## Parameter | Eta2 (partial) | 90% CI ## -------------------------------------------- ## factor(gear) | 0.58 | [0.00, 0.84] ## factor(cyl) | 0.46 | [0.00, 0.78]
Set pooled_sd = FALSE
for effect sizes that are to accompany a Welch's
t-test (Delacre et al, 2021).
Algina, J., Keselman, H. J., & Penfield, R. D. (2006). Confidence intervals for an effect size when variances are not equal. Journal of Modern Applied Statistical Methods, 5(1), 2.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge.
Delacre, M., Lakens, D., Ley, C., Liu, L., & Leys, C. (2021, May 7). Why Hedges<U+2019> g*s based on the non-pooled standard deviation should be reported with Welch's t-test. https://doi.org/10.31234/osf.io/tu6mp
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.
d_to_common_language()
sd_pooled()
Other effect size indices:
effectsize()
,
eta_squared()
,
phi()
,
rank_biserial()
,
standardize_parameters()
# NOT RUN {
# 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)
glass_delta(mpg ~ am, data = mtcars)
print(cohens_d(mpg ~ am, data = mtcars), append_CL = TRUE)
# other acceptable ways to specify arguments
glass_delta(sleep$extra, sleep$group)
hedges_g("extra", "group", data = sleep)
cohens_d(sleep$extra[sleep$group == 1], sleep$extra[sleep$group == 2], paired = TRUE)
# cohens_d(Pair(extra[group == 1], extra[group == 2]) ~ 1,
# data = sleep, 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")
# }
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