Which pairs a noisy ranking orders

People (or areas, or courts) ranked by estimated scores are ordered correctly whatever the noise only when their estimates differ by more than their two interval half-widths together: below that, admissible errors can reverse them, above it none can. rnkres() says which pairs that holds for, and the share it fails for; the resolution of the ranking is twice the largest half-width. A league table whose intervals are wide orders few of its pairs (Goldstein and Spiegelhalter 1996). See proof("rnkres").

Usage

rnkres(est, hw)

Arguments

est

The estimates: finite numbers, named or not, at least two.

hw

The half-width of each estimate's interval: one number from 0, or one per estimate.

Value

A list: id, a logical matrix, TRUE where the pair's order is identified (NA on the diagonal), with the estimates' names; npair, nunid (the pairs not identified), share (their share) and res.

References

Goldstein, H. and Spiegelhalter, D. J. (1996). League tables and their limitations: statistical issues in comparisons of institutional performance. Journal of the Royal Statistical Society, Series A, 159(3), 385-443. doi:10.2307/2983325

Examples

rnkres(c(a = 0.2, b = 0.35, c = 0.8), hw = c(0.1, 0.1, 0.05))
#> $id
#>       a     b    c
#> a    NA FALSE TRUE
#> b FALSE    NA TRUE
#> c  TRUE  TRUE   NA
#> 
#> $npair
#> [1] 3
#> 
#> $nunid
#> [1] 1
#> 
#> $share
#> [1] 0.3333333
#> 
#> $res
#> [1] 0.2
#>