---
title: "SDM4 in R: Paired Samples and Blocks (Chapter 23)"
author: "Nicholas Horton (nhorton@amherst.edu) and Sarah McDonald"
date: "June 13, 2018"
output: 
  pdf_document:
    fig_height: 2.4
    fig_width: 7
  html_document:
    fig_height: 3
    fig_width: 5
  word_document:
    fig_height: 4
    fig_width: 6
---


```{r, include = FALSE}
# Don't delete this chunk if you are using the mosaic package
# This loads the mosaic and dplyr packages
require(mosaic)
options(digits = 5)
```

```{r, include=FALSE}
# knitr settings to control how R chunks work.
require(knitr)
opts_chunk$set(
  tidy = FALSE,     # display code as typed
  size = "small"    # slightly smaller font for code
)
```

## Introduction and background 

This document is intended to help describe how to undertake analyses introduced 
as examples in the Fourth Edition of *Stats: Data and Models* (2014) by De Veaux, Velleman, and Bock.
More information about the book can be found at http://wps.aw.com/aw_deveaux_stats_series.  This
file as well as the associated R Markdown reproducible analysis source file used to create it can be found at http://nhorton.people.amherst.edu/sdm4.

This work leverages initiatives undertaken by Project MOSAIC (http://www.mosaic-web.org), an NSF-funded effort to improve the teaching of statistics, calculus, science and computing in the undergraduate curriculum. In particular, we utilize the `mosaic` package, which was written to simplify the use of R for introductory statistics courses. A short summary of the R needed to teach introductory statistics can be found in the mosaic package vignettes (http://cran.r-project.org/web/packages/mosaic).
A paper describing the mosaic approach was published in the *R Journal*: https://journal.r-project.org/archive/2017/RJ-2017-024.

## Chapter 23: Paired samples and blocks

### Section 23.1: Paired data

The example on page 631 compares the mileage of 11 field workers using
either a 5 day or 4 day schedule.
```{r}
fiveday <- c(2798, 7724, 7505, 838, 4592, 8107, 1228, 8718, 1097, 8089, 3807)
fourday <- c(2914, 6112, 6177, 1102, 3281, 4997, 1695, 6606, 1063, 6392, 3362)
ds <- data.frame(fiveday, fourday)
ds <- mutate(ds, diff = fiveday - fourday)
ds
```

### Section 23.2: Assumptions and conditions

```{r}
gf_histogram(~ diff, binwidth = 500, center = 500/2, data = ds)   # page 634
t.test(~ diff, data = ds)
```

### Section 23.3: Confidence intervals for matched pairs

The same result is seen as on page 640 for the confidence interval
for the population difference in mileage using the (results not shown).
```{r eval = FALSE}
t.test(~ diff, data = ds)$conf.int
```

### Section 23.4: Blocking

The sign test on page 642 can be calculated using the `binom.test()` function.
```{r}
binom.test(119, 151)
```