How to calculate ecd

[joethorley]

In small sample size bias vignette it is as follows:

Ag$ecdf <- (rank(Ag$Conc)+.25)/(nrow(Ag)+.5)

which gives

# A tibble: 9 × 6
  Chemical Species                Conc Group        Units  ecdf
  <chr>    <chr>                 <dbl> <fct>        <chr> <dbl>
1 Silver   Oncorhynchus mykiss    0.24 Fish         ug/L  0.132
2 Silver   Lemna gibba            0.63 Plant        ug/L  0.237
3 Silver   Ceriodaphnia dubia     0.78 Invertebrate ug/L  0.342
4 Silver   Pimephales promelas    0.83 Fish         ug/L  0.447
5 Silver   Ictalurus punctatus    1.9  Fish         ug/L  0.553
6 Silver   Daphnia magna          2.12 Invertebrate ug/L  0.658
7 Silver   Hyalella azteca        4    Invertebrate ug/L  0.763
8 Silver   Chironomus tentans    13    Invertebrate ug/L  0.868
9 Silver   Micropterus salmoides 23    Fish         ug/L  0.974

[1] 0.1315789 0.2368421 0.3421053 0.4473684 0.5526316 0.6578947 0.7631579 0.8684211 0.9736842

but in the functions it is

function(x, ties.method = "first") {
  (rank(x, ties.method = ties.method) - 0.5) / length(x)
}

which gives

[1] 0.05555556 0.16666667 0.27777778 0.38888889 0.50000000 0.61111111 0.72222222 0.83333333 0.94444444

[joethorley]

The following reprex developed with @beckyfisher demonstrates that the vignette code is suboptimal but ppoints may have better properties than the package function.

ecdf_function <- ssdtools::ssd_ecd

print(ssdtools::ssd_ecd)
#> function (x, ties.method = "first") 
#> {
#>     (rank(x, ties.method = ties.method) - 0.5)/length(x)
#> }
#> <bytecode: 0x129c99a88>
#> <environment: namespace:ssdtools>

ecdf_vignette <- function(x, ties.method = "first") {
  (rank(x, ties.method = ties.method) + 0.25) / (length(x) + 0.5)
}

ecdf_function(1)
#> [1] 0.5
ecdf_vignette(1)
#> [1] 0.8333333
stats::ppoints(1)
#> [1] 0.5

ecdf_function(1:2)
#> [1] 0.25 0.75
ecdf_vignette(1:2)
#> [1] 0.5 0.9
stats::ppoints(1:2)
#> [1] 0.2777778 0.7222222

ecdf_function(1:3)
#> [1] 0.1666667 0.5000000 0.8333333
ecdf_vignette(1:3)
#> [1] 0.3571429 0.6428571 0.9285714
stats::ppoints(1:3)
#> [1] 0.1923077 0.5000000 0.8076923

ecdf_function(1:4)
#> [1] 0.125 0.375 0.625 0.875
ecdf_vignette(1:4)
#> [1] 0.2777778 0.5000000 0.7222222 0.9444444
stats::ppoints(1:4)
#> [1] 0.1470588 0.3823529 0.6176471 0.8529412

ecdf_function(c(1,1))
#> [1] 0.25 0.75
ecdf_vignette(c(1,1))
#> [1] 0.5 0.9
stats::ppoints(c(1,1))
#> [1] 0.2777778 0.7222222

^{Created on 2024-10-23 with reprex v2.1.1}

[beckyfisher]

For completeness, the code for ppoints is:

function (n, a = if (n <= 10) 3/8 else 1/2) 
{
    if (length(n) > 1L) 
        n <- length(n)
    if (n > 0) 
        (1L:n - a)/(n + 1 - 2 * a)
    else numeric()
}