QQreflimits (version 1.0.3)

nonp_limits: Nonparametric Limits

Description

Calculate shortest nonparametric reference limits, at given confidence level.

Usage

nonp_limits(X, RR=TRUE, perc=0.95, cover=0.9)

Value

A list containing the following components:

lower

the lower limit and confidence interval

upper

the upper limit and confidence interval

a

the index of the order statistic defining the lower limit of the CI

b

the index of the order statistic defining the upper limit of the CI

coverage

the actual confidence level the interval achieves

Arguments

X

the data set whose reference limit is sought.

RR

optional (default of TRUE) - the way percentiles are defined:

• FALSE -- use the Weibull limit i/(n+1),

• TRUE -- use the Hazen limit (i-0.5)/n.

perc

optional (default of 0.95) - the two-sided probability.

cover

optional (default of 0.9) - the confidence level of the CI for the reference limit.

Author

Douglas M. Hawkins, Jessica J. Kraker

Details

The reference limits are estimated as lower and upper percentiles of the sample. There are many ways of defining sample percentiles of which the code has two options – the Hazen limit (preferred) and the Weibull limit (which has historical precedents).

The confidence limits on these percentiles come from standard binomial methodology.

• Each interval is a pair of order statistics from the sample.

• The codes find the order statistics with the required 90% coverage but use order statistics with indices as close together as possible.

• An implication of this is that the 90% confidence interval on each reference limit has a total tail area less than 10% but does not necessarily have less than 5% in each tail.

If the sample size is too small (<91 for the default settings), confidence limits can not be computed and will be returned as NA. If it is even smaller (<21 for the default settings) the estimated reference limits will also be returned as NA.

References

Horn PS, Peske AJ (2005). Reference intervals: a user’s guide. Washington (DC): AACC Press.

Examples

# parameters
mu    <- 40
sigma <- 10
n     <- 120

# replicable randomization
set.seed(1069)
X     <- mu + sigma*rnorm(n)

# evaluate and review
perc_used = 0.95
nonp_results <- nonp_limits(X, perc=perc_used)
cat("\nThe reference limits are the", 100*(1-perc_used)/2, "th percentile",
    signif(nonp_results$lower[1],5), "and the", 100*(1+perc_used)/2, "th percentile",
    signif(nonp_results$upper[1],5), ".\n")

cat("\nAnd with ", round(100*nonp_results$coverage,2),"% confidence, the lower limit is between",
    signif(nonp_results$lower[2],5), "and", signif(nonp_results$lower[3],5),
    ";\n while the upper limit is between",
    signif(nonp_results$upper[2],5),"and",signif(nonp_results$upper[3],5),".\n\n")