Friedman Test Effect Size (Kendall's W Value) — friedman

Compute the effect size estimate (referred to as w) for Friedman test: W = X2/N(K-1); where W is the Kendall's W value; X2 is the Friedman test statistic value; N is the sample size. k is the number of measurements per subject.

The Kendall’s W coefficient assumes the value from 0 (indicating no relationship) to 1 (indicating a perfect relationship).

Kendalls uses the Cohen’s interpretation guidelines of 0.1 - < 0.3 (small effect), 0.3 - < 0.5 (moderate effect) and >= 0.5 (large effect)

Confidence intervals are calculated by bootstap.

friedman_effsize(
  data,
  formula,
  ci = FALSE,
  conf.level = 0.95,
  ci.type = "perc",
  nboot = 1000,
  ...
)

Arguments

data: a data.frame containing the variables in the formula.
formula: a formula of the form a ~ b | c, where a (numeric) is the dependent variable name; b is the within-subjects factor variables; and c (factor) is the column name containing individuals/subjects identifier. Should be unique per individual.
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.
...: other arguments passed to the function friedman.test()

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.

Examples

# Load data
#:::::::::::::::::::::::::::::::::::::::
data("ToothGrowth")
df <- ToothGrowth %>%
    filter(supp == "VC") %>%
    mutate(id = rep(1:10, 3))
head(df)
#>    len supp dose id
#> 1  4.2   VC  0.5  1
#> 2 11.5   VC  0.5  2
#> 3  7.3   VC  0.5  3
#> 4  5.8   VC  0.5  4
#> 5  6.4   VC  0.5  5
#> 6 10.0   VC  0.5  6

# Friedman test effect size
#:::::::::::::::::::::::::::::::::::::::::
df %>% friedman_effsize(len ~ dose | id)
#> # A tibble: 1 × 5
#>   .y.       n effsize method    magnitude
#> * <chr> <int>   <dbl> <chr>     <ord>    
#> 1 len      10       1 Kendall W large