lsr (version 0.5.2)

cohensD: Cohen's d


Calculates the Cohen's d measure of effect size.


  x = NULL,
  y = NULL,
  data = NULL,
  method = "pooled",
  mu = 0,
  formula = NULL



A numeric variable containing the data for group 1, or possibly a formula of the form outcome ~ group


If x is a numeric variable, the y argument should be a numeric variable containing the data for group 2. If a one-sample calculation is desired, then no value for y should be specified.


If x is a formula, then data is an optional argument specifying data frame containing the variables in the formula.


Which version of the d statistic should we calculate? Possible values are "pooled" (the default), "", "", "corrected", "raw", "paired" and "unequal". See below for specifics.


The "null" value against which the effect size should be measured. This is almost always 0 (the default), so this argument is rarely specified.


An alias for x if a formula input is used. Included for the sake of consistency with the t.test function.


Numeric variable containing the effect size, d. Note that it does not show the direction of the effect, only the magnitude. That is, the value of d returned by the function is always positive or zero.


The cohensD function calculates the Cohen's d measure of effect size in one of several different formats. The function is intended to be called in one of two different ways, mirroring the t.test function. That is, the first input argument x is a formula, then a command of the form cohensD(x = outcome~group, data = data.frame) is expected, whereas if x is a numeric variable, then a command of the form cohensD(x = group1, y = group2) is expected.

The method argument allows the user to select one of several different variants of Cohen's d. Assuming that the original t-test for which an effect size is desired was an independent samples t-test (i.e., not one sample or paired samples t-test), then there are several possibilities for how the normalising term (i.e., the standard deviation estimate) in Cohen's d should be calculated. The most commonly used method is to use the same pooled standard deviation estimate that is used in a Student t-test (method = "pooled", the default). If method = "raw" is used, then the same pooled standard deviation estimate is used, except that the sample standard deviation is used (divide by N) rather than the unbiased estimate of the population standard deviation (divide by N-2). Alternatively, there may be reasons to use only one of the two groups to estimate the standard deviation. To do so, use method = "" to select the x variable, or the first group listed in the grouping factor; and method = "" to normalise by y, or the second group listed in the grouping factor. The last of the "Student t-test" based measures is the unbiased estimator of d (method = "corrected"), which multiplies the "pooled" version by (N-3)/(N-2.25).

For other versions of the t-test, there are two possibilities implemented. If the original t-test did not make a homogeneity of variance assumption, as per the Welch test, the normalising term should mirror the Welch test (method = "unequal"). Or, if the original t-test was a paired samples t-test, and the effect size desired is intended to be based on the standard deviation of the differences, then method = "paired" should be used.

The last argument to cohensD is mu, which represents the mean against which one sample Cohen's d calculation should be assessed. Note that this is a slightly narrower usage of mu than the t.test function allows. cohensD does not currently support the use of a non-zero mu value for a paired-samples calculation.


Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.


# calculate Cohen's d for two independent samples:
gradesA <- c(55, 65, 65, 68, 70) # 5 students with teacher A
gradesB <- c(56, 60, 62, 66)     # 4 students with teacher B
cohensD(gradesA, gradesB)

# calculate Cohen's d for the same data, described differently:
grade <- c(55, 65, 65, 68, 70, 56, 60, 62, 66) # grades for all students
teacher <- c("A", "A", "A", "A", "A", "B", "B", "B", "B") # teacher for each student
cohensD(grade ~ teacher)

# calculate Cohen's d for two paired samples:
pre  <- c(100, 122, 97, 25, 274) # a pre-treatment measure for 5 cases
post <- c(104, 125, 99, 29, 277) # the post-treatment measure for the same 5 cases
cohensD(pre, post, method = "paired") # ... explicitly indicate that it's paired, or else
cohensD(post - pre)  # ... do a "single-sample" calculation on the difference

# support for data frames:
exams <- data.frame(grade, teacher)
cohensD(exams$grade ~ exams$teacher)    # using $
cohensD(grade ~ teacher, data = exams)  # using the 'data' argument

# }