97_Appendix_A_Alternative_Bootstrap_Methods.Rmd

# Appendix B : Alternative Bootstrap Code {-}

```{r, echo=FALSE}
# Unattach any packages that happen to already be loaded. In general this is unecessary
# but is important for the creation of the book to not have package namespaces
# fighting unexpectedly.
pkgs = names(sessionInfo()$otherPkgs)
if( length(pkgs > 0)){
  pkgs = paste('package:', pkgs, sep = "")
  for( i in 1:length(pkgs)){
    detach(pkgs[i], character.only = TRUE, force=TRUE)
  }
}
# Set my default chunk options 
knitr::opts_chunk$set( fig.height=3, cache=TRUE )
```

## Mosaic Package {-}

```{r, message=FALSE, warning=FALSE}
library(ggplot2)    # graphing functions
library(dplyr)      # data summary tools
library(mosaic)     # using Mosaic for iterations

# Set default behavior of ggplot2 graphs to be black/white theme
theme_set(theme_bw())
```

This method uses the `mosaic` package and can work very well when everything is in data frames.

```{r, cache=TRUE, warning=FALSE, message=FALSE}
# read the Lakes data set
Lakes <- read.csv('http://www.lock5stat.com/datasets/FloridaLakes.csv')

# create the Estimated Sampling Distribution of xbar
BootDist <- mosaic::do(10000) * 
  mosaic::resample(Lakes) %>% 
  summarise(xbar = mean(AvgMercury))

# what columns does the data frame "BootDist" have?
head(BootDist)

# show a histogram of the estimated sampling distribution of xbar
ggplot(BootDist, aes(x=xbar)) +
  geom_histogram() + 
  ggtitle('Estimated Sampling distribution of xbar' )

# calculate a quantile-based confidence interval
quantile(BootDist$xbar, c(0.025, 0.975))
```

## Base R Code {-}

Here, no packages are used and the steps of the bootstrap are more explicit.

```{r, echo=TRUE}
AvgMerc <- Lakes$AvgMercury
Boot.Its<-10000  ### Numer of iterations, like `R` in `boot`
Sample.Size<-length(AvgMerc)
BS.means<-numeric() ### where each estimate is saved
for(j in 1:Boot.Its) BS.means[j]<-mean(sample(AvgMerc, Sample.Size, replace=T))
hist(BS.means)
```

Then the 95% confidence interval can be found in a similar manner to above.

```{r, echo=TRUE}
quantile(BS.means, c(0.025, 0.975))
```