The aim of this vignette is to introduce the R package
`confintr`

for calculating one- and two-sided classic and
bootstrap confidence intervals.

Confidence intervals for the following parameters are available:

mean (Student, Wald, bootstrap),

proportion (Wilson, Clopper-Pearson, Agresti-Coutts, bootstrap),

median and other quantiles (distribution-free binomial and bootstrap),

variance and standard deviation (chi-squared, bootstrap),

IQR and MAD (bootstrap only),

skewness and kurtosis (bootstrap only),

R-squared and the non-centrality parameter of the F distribution (parametric),

Cramér’s V and the non-centrality parameter of the chi-squared distribution (parametric and bootstrap),

the odds ratio of a 2x2 table (exact),

Pearson-, Spearman-, Kendall correlation coefficients (normal for Pearson, bootstrap for any),

Mean, quantile and median differences of two samples (for quantile/median only bootstrap).

Many of the classic confidence intervals on this list are discussed in (Smithson 2003).

We offer different types of bootstrap intervals:

Normal (“norm”) bootstrap confidence interval: This is the Wald/Student confidence interval using as standard error the standard deviation of the bootstrap distribution plus a bootstrap bias correction. Simple, but only first-order accurate and not transformation respecting.

Percentile (“perc”) bootstrap confidence interval: Uses quantiles of the bootstrap distribution as confidence limits. Simple, but only first order accurate. Transformation respecting.

Basic (“basic”) or reverse bootstrap confidence interval: Flipped version of the percentile approach, dealing with bias but at the price of having very unnaturally tailed sampling distributions. Only first order accurate.

Bias-corrected and accelerated (“bca”) confidence interval: Refined version of the percentile bootstrap which is second order accurate and transformation respecting. Needs more replications than observations.

**Usually our default.**Student-t (“stud”) bootstrap confidence interval: Refined version of the normal bootstrap that replaces the Student quantile by a custom quantile obtained from bootstrapping the variance of the bootstrapped statistic. Second order accurate but not transformation respecting. Requires a formula for the variance of the estimator, which

`confintr`

provides for the mean, the mean difference, the variance (and standard deviation) as well as for the proportion.**Used as the default for the mean and the mean difference.**

For details on bootstrap confidence intervals, we refer to (Efron
and Tibshirani 1993). We provide them through the widely used
`boot`

package (Canty and Ripley
2019).

From CRAN:

`install.packages("confintr")`

Latest version from github:

```
library(devtools)
install_github("mayer79/confintr")
```

```
library(confintr)
set.seed(1)
# Mean
ci_mean(1:100)
#>
#> Two-sided 95% t confidence interval for the population mean
#>
#> Sample estimate: 50.5
#> Confidence interval:
#> 2.5% 97.5%
#> 44.74349 56.25651
ci_mean(1:100, type = "bootstrap")
#>
#> Two-sided 95% bootstrap confidence interval for the population mean
#> based on 9999 bootstrap replications and the student method
#>
#> Sample estimate: 50.5
#> Confidence interval:
#> 2.5% 97.5%
#> 44.72913 56.34685
# 95% value at risk
ci_quantile(rexp(1000), q = 0.95)
#>
#> Two-sided 95% binomial confidence interval for the population 95%
#> quantile
#>
#> Sample estimate: 3.054989
#> Confidence interval:
#> 2.5% 97.5%
#> 2.745526 3.499928
# IQR
ci_IQR(rexp(100), R = 999)
#>
#> Two-sided 95% bootstrap confidence interval for the population IQR
#> based on 999 bootstrap replications and the bca method
#>
#> Sample estimate: 1.042259
#> Confidence interval:
#> 2.5% 97.5%
#> 0.8778725 1.3773426
# Correlation
ci_cor(iris[1:2], method = "spearman", type = "bootstrap", R = 999)
#>
#> Two-sided 95% bootstrap confidence interval for the true Spearman
#> correlation coefficient based on 999 bootstrap replications and the bca
#> method
#>
#> Sample estimate: -0.1667777
#> Confidence interval:
#> 2.5% 97.5%
#> -0.299445947 -0.005167341
# Proportions
ci_proportion(10, n = 100, type = "Wilson")
#>
#> Two-sided 95% Wilson confidence interval for the true proportion
#>
#> Sample estimate: 0.1
#> Confidence interval:
#> 2.5% 97.5%
#> 0.05522914 0.17436566
ci_proportion(10, n = 100, type = "Clopper-Pearson")
#>
#> Two-sided 95% Clopper-Pearson confidence interval for the true
#> proportion
#>
#> Sample estimate: 0.1
#> Confidence interval:
#> 2.5% 97.5%
#> 0.04900469 0.17622260
# R-squared
<- lm(Sepal.Length ~ ., data = iris)
fit ci_rsquared(fit, probs = c(0.05, 1))
#>
#> One-sided 95% F confidence interval for the population R-squared
#>
#> Sample estimate: 0.8673123
#> Confidence interval:
#> 5% 100%
#> 0.8312405 1.0000000
# Kurtosis
ci_kurtosis(1:100)
#>
#> Two-sided 95% bootstrap confidence interval for the population kurtosis
#> based on 9999 bootstrap replications and the bca method
#>
#> Sample estimate: 1.79976
#> Confidence interval:
#> 2.5% 97.5%
#> 1.584104 2.050858
# Mean difference
ci_mean_diff(10:30, 1:15)
#>
#> Two-sided 95% t confidence interval for the population value of
#> mean(x)-mean(y)
#>
#> Sample estimate: 12
#> Confidence interval:
#> 2.5% 97.5%
#> 8.383547 15.616453
ci_mean_diff(10:30, 1:15, type = "bootstrap", R = 999)
#>
#> Two-sided 95% bootstrap confidence interval for the population value of
#> mean(x)-mean(y) based on 999 bootstrap replications and the student
#> method
#>
#> Sample estimate: 12
#> Confidence interval:
#> 2.5% 97.5%
#> 8.531103 15.863771
# Median difference
ci_median_diff(10:30, 1:15, R = 999)
#>
#> Two-sided 95% bootstrap confidence interval for the population value of
#> median(x)-median(y) based on 999 bootstrap replications and the bca
#> method
#>
#> Sample estimate: 12
#> Confidence interval:
#> 2.5% 97.5%
#> 4.675892 16.000000
```

Canty, Angelo, and Brian D. Ripley. 2019. *Boot: Bootstrap r (s-Plus)
Functions*.

Efron, Bradley, and Robert J. Tibshirani. 1993. *An Introduction to
the Bootstrap*. Monographs on Statistics and Applied Probability 57.
Boca Raton, Florida, USA: Chapman & Hall/CRC.

Smithson, Michael. 2003. *Confidence Intervals*. Quantitative
Applications in the Social Sciences. SAGE Publications, New York.