New effect size: Most Extreme (ECDF) Differences

[mattansb]

• Convert htest (ks.test())
• Better name than MED?
• merge pdf and y args somehow?

library(effectsize)

x <- rnorm(50)
y <- runif(30)

# Do x and y come from the same distribution?
ks.test(x, y)
#> 
#>  Exact two-sample Kolmogorov-Smirnov test
#> 
#> data:  x and y
#> D = 0.52, p-value = 3.885e-05
#> alternative hypothesis: two-sided
med(x, y)
#> d    |       95% CI
#> -------------------
#> 0.52 | [0.07, 0.97]

# Is the CDS of x larger than that of y?
ks.test(x, y, alternative = "l")
#> 
#>  Exact two-sample Kolmogorov-Smirnov test
#> 
#> data:  x and y
#> D^- = 0.1, p-value = 0.6509
#> alternative hypothesis: the CDF of x lies below that of y
med(x, y, alternative = "l")
#> d    |       95% CI
#> -------------------
#> 0.10 | [0.00, 0.48]
#> 
#> - One-sided CIs: lower bound fixed at [0.00].

plot(ecdf(x), xlim = range(c(x, y)), col = "blue")
lines(ecdf(y), col = "red")

# Does x come from a shifted gamma distribution with shape 3 and rate 2?
ks.test(x+2, "pgamma", 3, 2)
#> 
#>  Exact one-sample Kolmogorov-Smirnov test
#> 
#> data:  x + 2
#> D = 0.3478, p-value = 6.565e-06
#> alternative hypothesis: two-sided
med(x+2, pdf = "pgamma", shape = 3, rate = 2)
#> d    |       95% CI
#> -------------------
#> 0.35 | [0.07, 0.62]

plot(ecdf(x + 2), xlim = range(x + 2), col = "blue")
curve(pgamma(x, 3, 2), col = "red", add = TRUE)

^{Created on 2026-03-27 with reprex v2.1.1}