Cohen's h for a 2x2 Table

Computes Cohen's \(h\), a standardized effect size for the difference between two proportions in a 2x2 contingency table.

Usage

cohenH(
  x,
  y = NULL,
  conf.level = NA,
  sides = c("two.sided", "left", "right"),
  ...
)

Arguments

x

a 2x2 contingency table or matrix, or a categorical vector when y is supplied

y

an optional second variable used together with x to create a contingency table via table(x, y, ...)

conf.level

confidence level of the interval. If set to NA (the default), only the point estimate is returned.

sides

character string specifying the sidedness of the confidence interval (one of "two.sided" (default), "left" or "right"). See ConfidenceIntervals().

...

additional arguments passed to table()

Value

if conf.level = NA, a numeric scalar containing Cohen's \(h\); otherwise a named numeric vector with elements:

est

point estimate of Cohen's \(h\).

lci

lower confidence interval bound.

uci

upper confidence interval bound.

Details

Cohen's \(h\) is defined as:

$$ h = 2\arcsin(\sqrt{p_1}) - 2\arcsin(\sqrt{p_2}) $$

where \(p_1\) and \(p_2\) are the event probabilities in the first and second row, respectively.

Optionally, an approximate asymptotic confidence interval is computed.

Cohen's \(h\) is a variance-stabilized standardized effect size for comparing two proportions.

Approximate interpretation thresholds suggested by Cohen are:

|h| < 0.2	negligible effect
|h| >= 0.2	small effect
|h| >= 0.5	medium effect
|h| >= 0.8	large effect

The confidence interval is based on the asymptotic standard error:

$$ SE(h) = \sqrt{\frac{1}{n_1} + \frac{1}{n_2}} $$

sides names the side on which the finite bound lies: "left" yields \([lci, \infty)\), "right" yields \((-\infty, uci]\).

References

Cohen J (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.

See also

Other effect.size: cohenD(), etaSq(), glassDelta(), oddsRatio(), relRisk()

Examples

tab <- matrix(
  c(26, 26,
    6, 7),
  nrow = 2,
  byrow = TRUE
)

cohenH(tab)
#> [1] 0.07699914
cohenH(tab, conf.level = 0.95)
#>         est         lci         uci 
#>  0.07699914 -0.53075989  0.68475817 

x <- c(rep("A", 52), rep("B", 13))
y <- c(rep(c("yes", "no"), c(26, 26)),
       rep(c("yes", "no"), c(6, 7)))

cohenH(x, y, conf.level = 0.95)
#>         est         lci         uci 
#> -0.07699914 -0.68475817  0.53075989