Kendall Tau Score for Ranking Quiz — kendall_tau

Computes how well a user's ranking matches the correct ranking using the Kendall tau distance. Counts concordant pairs (user agrees with correct order) vs discordant pairs (user disagrees).

Usage

kendall_tau_score(user_order, correct_order)

Arguments

user_order: Integer vector of item indices in the user's order (first element = user's #1 pick, i.e. most risky).
correct_order: Integer vector of item indices in the correct order.

Value

A list with:

score: number of concordant pairs
max_score: total number of pairs = k*(k-1)/2
n_concordant: same as score
n_discordant: pairs where user and correct order disagree
pct: percentage score (0-100)

Examples

# Perfect score
kendall_tau_score(c(1, 2, 3), c(1, 2, 3))
#> $score
#> [1] 3
#> 
#> $max_score
#> [1] 3
#> 
#> $n_concordant
#> [1] 3
#> 
#> $n_discordant
#> [1] 0
#> 
#> $pct
#> [1] 100
#> 

# Completely reversed
kendall_tau_score(c(3, 2, 1), c(1, 2, 3))
#> $score
#> [1] 0
#> 
#> $max_score
#> [1] 3
#> 
#> $n_concordant
#> [1] 0
#> 
#> $n_discordant
#> [1] 3
#> 
#> $pct
#> [1] 0
#> 

# One swap
kendall_tau_score(c(2, 1, 3), c(1, 2, 3))
#> $score
#> [1] 2
#> 
#> $max_score
#> [1] 3
#> 
#> $n_concordant
#> [1] 2
#> 
#> $n_discordant
#> [1] 1
#> 
#> $pct
#> [1] 66.7
#>