Function returns a tibble of quantiles and confidence interval of quantiles for a range of probabilities. '

## Usage

getCIforQuantiles(
vecDat = NA,
vecQuantiles = NA,
method = c("Nyblom", "Exact", "Bootstrap"),
ci = 0.95,
R = 9999,
type = NULL
)

## Arguments

vecDat

Vector of the data

vecQuantiles

Vector of the quantiles you want

method

Method you want to use to get the confidence intervals

ci

Confidence interval (default .95)

R

Number of bootstrap replications if using bootstrap method

type

Type of quantile (default is 8)

## Value

A tibble of the results with variables: prob: the quantile required, i.e. .05, .5 would give the median, .95 the 95th (per)centile n: total n nOK: number of non-missing values nMiss: number of missing values quantile: the quantile for that value of prob LCL: lower confidence limit for that quantile UCL: upper confidence limt for that quantile

## Background

Quantiles, like percentiles, can be a very useful way of understanding a distribution, in MH research, typically a distribution of scores, often either help-seeking sample distribution or a non-help-seeking sample.

For example, you might want to see if a score you have for someone is above the 95% (per)centile, i.e. above the .95 quantile of the non-help-seeking sample distribution.

The catch is that, like any sample statistic, a quantile/percentile is generally being used as an estimate of a population value. That is to say we are really interested in whether the score we have is above the 95% percentile of a non-help-seeking population. That means that the quantiles/percentiles from a sample are only approximate guides to the population values.

As usual, a confidence interval (CI) around an observed quantile is a way of seeing how precisely, assuming random sampling of course, the sample quantile can guide us about the population quantile.

Again as usual, the catch is that there are different ways of compute the CI around a quantile. This function is a wrapper around three methods from Michael Höhle's quantileCI package:

• the Nyblom method

• the "exact" method

• the bootstrap method

As I understand the quantileCI package the classic paper by Nyblom, generally the Nyblom method will be as good or better than the exact method and much faster than bootstrapping so the Nyblom method is the default here but I have put the others in for completeness.

Started 4.vii.23

## References

• Nyblom, J. (1992). Note on interpolated order statistics. Statistics & Probability Letters, 14(2), 129–131. https://doi.org/10.1016/0167-7152(92)90076-H

• https://github.com/mhoehle/quantileCI

Other CI functions, quantile functions: plotQuantileCIsfromDat()

Chris Evans

## Examples

if (FALSE) {
### will need tidyverse to run
library(tidyverse)
### will need quantileCI to run
### if you don't have quantileCI package you need to get it from github:
# devtools::install_github("hoehleatsu/quantileCI")
library(quantileCI)

### use the exact method
getCIforQuantiles(1:1000, c(.1, .5, .95), "e", ci = .95, R = 9999, type = 8)
### use the Nyblom method
getCIforQuantiles(1:1000, c(.1, .5, .95), "n", ci = .95, R = 9999, type = 8)
### use the bootstrap method
getCIforQuantiles(1:1000, c(.1, .5, .95), "b", ci = .95, R = 9999, type = 8)
}