Confidence interval for a Mann-Whitney parameter

Source: R/statpsych1.R

Computes a distribution-free confidence interval for the Mann-Whitney parameter (a "common language effect size"). In a 2-group experiment, this parameter is the proportion of members in the population with scores that would be higher under treatment 1 than treatment 2. In a 2-group nonexperiment where participants are sampled from two subpopulations of sizes N1 and N2, the parameter is the proportion of all N1 x N2 pairs in which a member from subpopulation 1 has a larger score than a member from subpopulation 2.

ci.mann(alpha, y1, y2)

Arguments

alpha

alpha level for 1-alpha confidence

y1

vector of scores for group 1

y2

vector of scores for group 2

Value

Returns a 1-row matrix. The columns are:

  • Estimate - estimated proportion

  • SE - standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Sen PK (1967). “A note on asymptotically distribution-free confidence bounds for P(X < Y), based on two independent samples.” The Indian Journal of Statistics, Series A, 29(1), 95--102.

Examples

y2 <- c(36, 44, 47, 42, 49, 39, 46, 31, 33, 48)
y1 <- c(32, 39, 26, 35, 43, 27, 40, 37, 34, 29)
ci.mann(.05, y1, y2)
#>  Estimate        SE LL        UL
#>     0.205 0.1401834  0 0.4797544

# Should return:
# Estimate        SE        LL UL
#    0.795 0.1401834 0.5202456  1