ci.mann: Confidence interval for a Mann-Whitney parameter

In statpsych: Statistical Methods for Psychologists

Confidence interval for a Mann-Whitney parameter

Description

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.

For more details, see Section 2.12 of Bonett (2021, Volume 1)

Usage

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

\insertRef

Sen1967statpsych

\insertRef

Bonett2021statpsych

Examples

y1 <- c(9.4, 10.3, 58.3, 106.0, 31.0, 46.2, 12.0, 19.0, 135.0, 159.0)
y2 <- c(14.6, 5.1, 8.1, 22.7, 6.4, 4.4, 19.0, 3.2)
ci.mann(.05, y1, y2)

# Should return:
# Estimate        SE        LL UL
#  0.86875 0.1222202 0.6292028  1

statpsych documentation built on Jan. 13, 2026, 1:07 a.m.