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Compute effect sizes between two samples

Source: R/statistics-effects.R
cr_effect_size.Rd

Standardized effect sizes for a comparison of two independent samples, each with a confidence interval. Confidence intervals are analytic by default (deterministic and cheap on large samples); a bootstrap interval is available for cases where the analytic approximation is not wanted.

Usage

cr_effect_size(
  x,
  y,
  method = c("cohens_d", "hedges_g", "cliffs_delta", "rank_biserial", "glass_delta"),
  ci = 0.95,
  ci_method = c("analytic", "bootstrap"),
  n_boot = 200,
  seed = NULL
)

Arguments

x

Numeric vector (treatment group).

y

Numeric vector (control / reference group).

method

Character vector of methods to compute. Allowed: "cohens_d", "hedges_g", "cliffs_delta", "rank_biserial", "glass_delta".

ci

Confidence level for the interval (default 0.95). Set NULL to skip interval estimation.

ci_method

"analytic" (default) or "bootstrap".

n_boot

Number of bootstrap resamples used when ci_method = "bootstrap".

seed

Optional integer seed for the bootstrap. The global random number stream is restored on exit.

Value

A tibble with columns method, estimate, ci_low, ci_high and magnitude.

Details

Cohen's d uses the pooled standard deviation without small-sample correction and its interval is the large-sample (Hedges-Olkin) approximation with a t quantile on n_x + n_y - 2 degrees of freedom. Hedges' g applies the bias correction \(J = 1 - 3 / (4 \cdot df - 1)\) to both estimate and interval. Glass's delta standardizes by the standard deviation of y only. Cliff's delta uses the consistent variance estimator with the interval on the transformed scale, so the bounds always lie inside \([-1, 1]\). The rank-biserial correlation of two independent samples equals Cliff's delta and is reported on the same scale.

See also

cr_effect_grid() for a whole grid of contrasts, cr_power() for the sample size implied by an effect size.

Other effect sizes: cr_compare_levels(), cr_effect_grid()

Examples

set.seed(1)
cr_effect_size(stats::rnorm(100, 1), stats::rnorm(100, 0))
#> # A tibble: 5 × 5
#>   method        estimate ci_low ci_high magnitude
#>   <chr>            <dbl>  <dbl>   <dbl> <chr>    
#> 1 cohens_d         1.23   0.930   1.54  large    
#> 2 hedges_g         1.23   0.927   1.53  large    
#> 3 cliffs_delta     0.616  0.481   0.723 large    
#> 4 rank_biserial    0.616  0.481   0.723 large    
#> 5 glass_delta      1.20   0.872   1.52  large    

# bootstrap interval with a reproducible seed
cr_effect_size(stats::rnorm(50, 1), stats::rnorm(50, 0),
               method = "cliffs_delta",
               ci_method = "bootstrap", n_boot = 50, seed = 42)
#> # A tibble: 1 × 5
#>   method       estimate ci_low ci_high magnitude
#>   <chr>           <dbl>  <dbl>   <dbl> <chr>    
#> 1 cliffs_delta    0.470  0.319   0.648 medium