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Confidence interval for a Mann-Whitney parameter

Source: R/statpsych1.R
ci.mann.Rd

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

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.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

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)
#>  Estimate        SE        LL UL
#>   0.86875 0.1222202 0.6292028  1

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