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Cohen's f Effect Size

Source: R/cohen_f.R
cohen_f.Rd

Computes Cohen's f = \(\sigma_m / \sigma\), the population standard deviation of means relative to the within-group standard deviation, by any of three equivalent specifications:

  1. raw population means and within-group variance,

  2. the population proportion of variance accounted for, \(\eta^2\),

  3. \(\sigma_m\) and \(\sigma\) directly.

Cohen's f is a population quantity; supplied with population parameters it returns the population value, supplied with sample estimates it returns the corresponding sample value.

Usage

cohen_f(
  mu = NULL,
  sigma_squared = NULL,
  n = NULL,
  eta_squared = NULL,
  sigma_m = NULL,
  sigma = NULL
)

Arguments

mu

Numeric vector of population means (one per group). Use together with sigma_squared.

sigma_squared

The within-group variance. Use together with mu.

n

Optional. Per-group sample sizes (a single number for equal group sizes, or a vector of length length(mu) for unequal). When NULL, equal weighting across groups is used (i.e., the population variance of mu is computed with the \(1/k\) divisor).

eta_squared

The population proportion of variance accounted for. Use this argument alone.

sigma_m

The population standard deviation of the means (\(\sigma_m\)). Use together with sigma.

sigma

The within-group standard deviation (\(\sigma\)). Use together with sigma_m.

Value

A 1-row data.frame with columns term and value; term is "cohen_f" and value is the computed value.

Details

All three calling modes return the same value when applied to compatible inputs (Cohen 1988, eq. 8.2.1):

  • Raw form: \(f = \sqrt{\sum n_j (\mu_j - \bar\mu)^2 / N \cdot 1/\sigma^2}\).

  • From \(\eta^2\): \(f = \sqrt{\eta^2 / (1 - \eta^2)}\).

  • From the variance ratio: \(f = \sigma_m / \sigma\).

References

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

See also

ci_srsnr, ci_snr, ss_power_R2

Author

Ken Kelley kkelley@nd.edu

Examples

# (1) From raw means and within-group variance:
cohen_f(mu = c(94, 91, 92, 83), sigma_squared = 67.375)
#>  term    value
#>  cohen_f 0.51 

# Equal n weights are the default; equivalent with explicit equal n:
cohen_f(mu = c(94, 91, 92, 83), sigma_squared = 67.375, n = 6)
#>  term    value
#>  cohen_f 0.51 

# Unequal n:
cohen_f(mu = c(94, 91, 92, 83), sigma_squared = 67.375, n = c(4, 6, 5, 5))
#>  term    value
#>  cohen_f 0.498

# (2) From eta_squared:
cohen_f(eta_squared = 0.10)
#>  term    value
#>  cohen_f 0.333

# (3) From sigma_m and sigma directly:
cohen_f(sigma_m = 4, sigma = 8)
#>  term    value
#>  cohen_f 0.5