Cohen's d

Calculates the Cohen's d measure of effect size.

Usage

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

Arguments

x

A numeric vector of data for group 1, or a formula of the form outcome ~ group (in which case data can be used to supply a data frame).

y

A numeric vector of data for group 2. Omit for a one-sample calculation.

data

An optional data frame containing the variables in x when x is a formula.

method

Which version of Cohen's d to calculate. Options are "pooled" (default), "x.sd", "y.sd", "corrected", "raw", "paired", and "unequal". See Details.

mu

The null value for a one-sample calculation. Almost always 0 (the default).

formula

A formula of the form outcome ~ group. This is an alternative way to supply the formula instead of using x.

Value

A single positive number: the magnitude of the effect size d. The sign of the mean difference is dropped, so the value is always zero or greater.

Details

The function can be used in two main ways. For two separate numeric vectors, call cohensD(x = group1, y = group2). For data in a data frame with a grouping variable, use a formula: cohensD(outcome ~ group, data = mydata).

The method argument controls how the standard deviation is estimated:

"pooled"

Pooled SD from both groups (matches Student's t-test). This is the default.

"corrected"

Bias-corrected version of "pooled", multiplied by (N-3)/(N-2.25).

"raw"

Like "pooled" but divides by N rather than N-2.

"x.sd"

SD of the first group only.

"y.sd"

SD of the second group only.

"unequal"

Square root of the average of the two group variances (matches Welch's t-test).

"paired"

SD of the within-person differences (matches a paired-samples t-test).

For a one-sample calculation, supply only x (and optionally mu). The result is abs(mean(x) - mu) / sd(x).

References

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

Examples

# two independent groups supplied as separate vectors
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)
#> [1] 0.699892

# the same comparison using a formula and a data frame
grade <- c(55, 65, 65, 68, 70, 56, 60, 62, 66)
teacher <- c("A", "A", "A", "A", "A", "B", "B", "B", "B")
cohensD(grade ~ teacher)
#> [1] 0.699892

# paired samples: use method = "paired" (SD of within-person differences)
pre <- c(100, 122, 97, 25, 274)
post <- c(104, 125, 99, 29, 277)
cohensD(pre, post, method = "paired")
#> [1] 3.824732

# equivalent one-sample calculation on the difference scores
cohensD(post - pre)
#> [1] 3.824732

# formula interface with a data frame
exams <- data.frame(grade, teacher)
cohensD(grade ~ teacher, data = exams)
#> [1] 0.699892