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Kruskal-Wallis Effect Size

Source: R/kruskal_effesize.R
kruskal_effsize.Rd

Compute the effect size for Kruskal-Wallis test as the eta squared based on the H-statistic: eta2[H] = (H - k + 1)/(n - k); where H is the value obtained in the Kruskal-Wallis test; k is the number of groups; n is the total number of observations.

The eta-squared estimate assumes values from 0 to 1 and multiplied by 100 indicates the percentage of variance in the dependent variable explained by the independent variable. The interpretation values commonly in published litterature are: 0.01- < 0.06 (small effect), 0.06 - < 0.14 (moderate effect) and >= 0.14 (large effect).

Note that eta2[H] is a bias-corrected estimator, so the raw formula can return a small negative value for a near-null effect (very small H). In that case the estimate is floored to 0, keeping the reported effect size within its valid [0, 1] range.

Confidence intervals are calculated by bootstap.

See the Datanovia tutorial Kruskal-Wallis Test in R for a worked walkthrough.

Usage

kruskal_effsize(
  data,
  formula,
  ci = FALSE,
  conf.level = 0.95,
  ci.type = "perc",
  nboot = 1000,
  boot.parallel = getOption("boot.parallel", "no"),
  boot.ncpus = getOption("boot.ncpus", 1L),
  method = c("eta2", "epsilon2")
)

Arguments

data

a data.frame containing the variables in the formula.

formula

a formula of the form x ~ group where x is a numeric variable giving the data values and group is a factor with one or multiple levels giving the corresponding groups. For example, formula = TP53 ~ cancer_group.

ci

If TRUE, returns confidence intervals by bootstrap. May be slow.

conf.level

The level for the confidence interval.

ci.type

The type of confidence interval to use. Can be any of "norm", "basic", "perc", or "bca". Passed to boot::boot.ci.

nboot

The number of replications to use for bootstrap.

boot.parallel

The type of parallel operation to be used when computing the bootstrap confidence interval. Allowed values are "no" (default), "multicore" and "snow". Passed to boot(). Defaults to getOption("boot.parallel", "no"), so it can also be set globally with options(boot.parallel = "multicore"). Only used when ci = TRUE.

boot.ncpus

Integer. The number of processes to be used in the parallel bootstrap. Defaults to getOption("boot.ncpus", 1L). Note that boot.parallel has no effect unless boot.ncpus > 1. Only used when ci = TRUE.

method

the effect-size metric. Either "eta2" (default) for the bias-corrected eta-squared eta2[H] = (H - k + 1)/(N - k), or "epsilon2" for the rank epsilon-squared H/(N - 1) (Tomczak & Tomczak, 2014), which equals effectsize::rank_epsilon_squared() and is not bias-corrected (so a little larger than eta2[H]).

Value

return a data frame with some of the following columns:

  • .y.: the y variable used in the test.

  • n: Sample counts.

  • effsize: estimate of the effect size.

  • magnitude: magnitude of effect size.

  • conf.low,conf.high: lower and upper bound of the effect size confidence interval.

References

Maciej Tomczak and Ewa Tomczak. The need to report effect size estimates revisited. An overview of some recommended measures of effect size. Trends in Sport Sciences. 2014; 1(21):19-25.

http://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/effectSize

http://www.psy.gla.ac.uk/~steve/best/effect.html

See also

The Datanovia tutorial: Kruskal-Wallis Test in R.

Examples

# Load data
#:::::::::::::::::::::::::::::::::::::::
data("ToothGrowth")
df <- ToothGrowth

# Kruskal-wallis rank sum test
#:::::::::::::::::::::::::::::::::::::::::
df %>% kruskal_effsize(len ~ dose)
#> # A tibble: 1 × 5
#>   .y.       n effsize method  magnitude
#> * <chr> <int>   <dbl> <chr>   <ord>    
#> 1 len      60   0.678 eta2[H] large    

# Grouped data
df %>%
  group_by(supp) %>%
  kruskal_effsize(len ~ dose)
#> # A tibble: 2 × 6
#>   supp  .y.       n effsize method  magnitude
#> * <fct> <chr> <int>   <dbl> <chr>   <ord>    
#> 1 OJ    len      30   0.611 eta2[H] large    
#> 2 VC    len      30   0.855 eta2[H] large