Jonckheere-Terpstra ordered-alternatives test (Gibbons Ch 10.6)

Tests H0: F_1 = ... = F_k against the ordered alternative H1: F_1 <= F_2 <= ... <= F_k. J = sum over i<j of U_ij (Mann-Whitney counts with 1/2 weight for ties).

Usage

morie_ordered_alternatives_test(groups)

Arguments

groups

List of numeric vectors in monotone hypothesised order.

Value

Named list: statistic, p_value, z, E_J, Var_J, n, k, method.

Details

Normal approximation: E_J = (N^2 - sum n_i^2) / 4 Var_J = (N^2 (2N + 3) - sum n_i^2 (2 n_i + 3)) / 72

Examples

morie_ordered_alternatives_test(groups = list(rnorm(20), rnorm(20), rnorm(20)))
#> $statistic
#> [1] 440
#> 
#> $p_value
#> [1] 0.02995877
#> 
#> $z
#> [1] -2.170635
#> 
#> $E_J
#> [1] 600
#> 
#> $Var_J
#> [1] 5433.333
#> 
#> $n
#> [1] 60
#> 
#> $k
#> [1] 3
#> 
#> $method
#> [1] "Jonckheere-Terpstra ordered-alternatives test"
#>