Somers' D

somers_d() computes Somers' D for a two-way contingency table of ordinal variables.

Usage

somers_d(
  x,
  direction = c("row", "column", "symmetric"),
  detail = FALSE,
  conf_level = 0.95,
  digits = 3L,
  .include_se = FALSE
)

Arguments

x

A contingency table (of class table).

direction

Direction of prediction: "row" (default, column predicts row), "column" (row predicts column), or "symmetric" (average of both directions).

detail

Logical. If FALSE (default), return the estimate as a numeric scalar. If TRUE, return a named numeric vector including confidence interval and p-value.

conf_level

A number between 0 and 1 giving the confidence level (default 0.95). Only used when detail = TRUE. Set to NULL to omit the confidence interval.

digits

Number of decimal places used when printing the result (default 3). Only affects the detail = TRUE output.

.include_se

Internal parameter; do not use.

Value

Same structure as cramer_v(): a scalar when detail = FALSE, a named vector when detail = TRUE. The p-value tests H0: D = 0 (Wald z-test).

Details

Somers' D is an asymmetric ordinal measure defined as \(d = (C - D) / (C + D + T)\), where \(T\) is the number of pairs tied on the independent variable. The symmetric version is the harmonic mean of the two asymmetric values. Standard error formulas follow the DescTools implementations (Signorell et al., 2024); see cramer_v() for full references.

See also

kendall_tau_b(), gamma_gk(), assoc_measures()

Examples

tab <- table(sochealth$education, sochealth$self_rated_health)
somers_d(tab, direction = "row")
#> [1] 0.2015369
somers_d(tab, direction = "column", detail = TRUE)
#> Estimate  CI lower  CI upper        p
#>    0.208     0.157     0.258  < 0.001