SMD | R Documentation |
The function computes the standardized mean difference, where a bias correction can be applied.
SMD(x, y, bias.cor = TRUE, var.equal = FALSE, na.rm = FALSE)
x |
numeric vector, data of group 1. |
y |
numeric vector, data of group 2. |
bias.cor |
a logical variable indicating whether a bias correction should be performed. |
var.equal |
a logical variable indicating whether to treat the two variances
as being equal. If |
na.rm |
logical. Should missing values be removed? |
The function compute the (bias-corrected) standardized mean difference.
If bias.cor = FALSE
and var.equal = TRUE
, the result corresponds
to Cohen's d (Cohen (1988)).
If bias.cor = TRUE
and var.equal = TRUE
, the result corresponds to
Hedges' g (Hedges (1981)).
If bias.cor = FALSE
and var.equal = FALSE
, the result is closely
related to the test statistic of Welch's t test (Aoki (2020)).
If bias.cor = TRUE
and var.equal = FALSE
, the result corresponds to
Aoki's e (Aoki (2020)) which incorporates a Welch-Satterthwaite approximation
in combination with a bias correction.
SMD value.
Matthias Kohl Matthias.Kohl@stamats.de
Aoki, S. (2020). Effect sizes of the differences between means without assuming variance equality and between a mean and a constant. Heliyon, 6(1), e03306.
Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. Routledge. ISBN 978-1-134-74270-7.
Hedges, L. V. (1981). Distribution theory for Glass's estimator of effectsize and related estimators. Journal of Educational Statistics 6, 107-128.
n1 <- 200 x <- rnorm(n1) n2 <- 300 y <- rnorm(n2, mean = 3, sd = 2) ## true value (0-3)/sqrt((1 + n1/n2*2^2)/(n1/n2+1)) ## estimates ## Aoki's e SMD(x, y) ## Hedges' g SMD(x, y, var.equal = TRUE) ## standardized test statistic of Welch's t-test SMD(x, y, bias.cor = FALSE) ## Cohen's d SMD(x, y, bias.cor = FALSE, var.equal = TRUE) ## Example from Aoki (2020) SMD(0:4, c(0, 0, 1, 2, 2)) SMD(0:4, c(0, 0, 1, 2, 2), var.equal = TRUE) SMD(0:4, c(0, 0, 1, 2, 2), bias.cor = FALSE) SMD(0:4, c(0, 0, 1, 2, 2), bias.cor = FALSE, var.equal = TRUE)
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