# Using 'confintr'" In confintr: Confidence Intervals

```knitr::opts_chunk\$set(
collapse = TRUE,
comment = "#>",
warning = FALSE,
message = FALSE
)
```

## Overview

{confintr} is dedicated to confidence intervals (CI). The following parameters are covered:

• 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),
• CramÃ©r'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 CIs on this list are discussed in @smithson2003.

In line with the {boot} backend, the following bootstrap CIs are (usually) available:

1. Normal ("norm") bootstrap CI: This is the Wald/Student CI using bootstrap standard error and bootstrap bias correction. Simple, but only first-order accurate, and not transformation respecting.

2. Percentile ("perc") bootstrap CI: Uses quantiles of the bootstrap distribution as confidence limits. Simple, but only first-order accurate. Transformation respecting.

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

4. Bias-corrected and accelerated ("bca") CI: Refined version of the percentile bootstrap. Second-order accurate and transformation respecting. Needs more replications than observations. The default (except for the mean and the mean difference, see below).

5. Student-t ("stud") bootstrap CI: Refined version of the normal bootstrap that replaces the Student quantile by a custom quantile obtained from bootstrapping the variance of the 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 CIs, we refer to @efron1993.

## Installation

```# From CRAN
install.packages("confintr")

# Development version
devtools::install_github("mayer79/confintr")
```

## Usage

```library(confintr)

set.seed(1)

# Mean
ci_mean(1:100)

ci_mean(1:100, type = "bootstrap")

# 95% value at risk
ci_quantile(rexp(1000), q = 0.95)

# IQR
ci_IQR(rexp(100))

# Correlation
ci_cor(iris[1:2], method = "spearman", type = "bootstrap")

# Proportions
ci_proportion(10, n = 100, type = "Wilson")

ci_proportion(10, n = 100, type = "Clopper-Pearson")

# R-squared
fit <- lm(Sepal.Length ~ ., data = iris)
ci_rsquared(fit, probs = c(0.05, 1))

# Kurtosis
ci_kurtosis(1:100)

# Mean difference
ci_mean_diff(10:30, 1:15)

ci_mean_diff(10:30, 1:15, type = "bootstrap")

# Median difference
ci_median_diff(10:30, 1:15)
```

## Try the confintr package in your browser

Any scripts or data that you put into this service are public.

confintr documentation built on June 7, 2023, 6:24 p.m.