---
title: "Regression and Other Stories: Earnings"
author: "Andrew Gelman, Jennifer Hill, Aki Vehtari"
date: "`r format(Sys.Date())`"
output:
  html_document:
    theme: readable
    toc: true
    toc_depth: 2
    toc_float: true
    code_download: true
---
Bootstrapping to simulate the sampling distribution. See Chapter 5 in
Regression and Other Stories.

-------------


```{r setup, include=FALSE}
knitr::opts_chunk$set(message=FALSE, error=FALSE, warning=FALSE, comment=NA)
```

#### Load packages

```{r }
library("rprojroot")
root<-has_file(".ROS-Examples-root")$make_fix_file()
```

#### Load data

```{r }
earnings <- read.csv(root("Earnings/data","earnings.csv"))
head(earnings)
```

#### Median of women's earnings, divided by the median of men's earnings

```{r }
earn <- earnings$earn
male <- earnings$male
print(median(earn[male==0]) / median(earn[male==1]))
```

#### A single bootstrap sample

```{r }
n <- nrow(earnings)
boot <- sample(n, replace=TRUE)
earn_boot <- earn[boot]
male_boot <- male[boot]
ratio_boot <- median(earn_boot[male_boot==0]) / median(earn_boot[male_boot==1])
```

#### A set of bootstrap simulations

```{r }
Boot_ratio <- function(data){
  n <- nrow(data)
  boot <- sample(n, replace=TRUE)
  earn_boot <- data$earn[boot]
  male_boot <- data$male[boot]
  ratio_boot <- median(earn_boot[male_boot==0]) / median(earn_boot[male_boot==1])
  return(ratio_boot)
}
n_sims <- 10000
output <- replicate(n_sims, Boot_ratio(data=earnings))
```

#### Summarize the results graphically and numerically

```{r }
hist(output)
round(sd(output), 2)
```