lsr (version 1.0.0)

cohensD: Cohen's d

Description

Calculates the Cohen's d measure of effect size.

Usage

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

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.

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.

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)

# 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)

# 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")

# equivalent one-sample calculation on the difference scores
cohensD(post - pre)

# formula interface with a data frame
exams <- data.frame(grade, teacher)
cohensD(grade ~ teacher, data = exams)