---
title: "SDM4 in R: Comparing Counts (Chapter 24)"
author: "Nicholas Horton (nhorton@amherst.edu) and Sarah McDonald"
date: "June 28, 2018"
output:
pdf_document:
fig_height: 2.8
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 24: Comparing Counts
### Section 24.1: Goodness-of-fit tests
Here we verify the calculations of expected counts for
ballplayers by month (page 656).
```{r}
ballplayer <- c(137, 121, 116, 121, 126, 114,
102, 165, 134, 115, 105, 122)
national <- c(0.08, 0.07, 0.08, 0.08, 0.08, 0.08,
0.09, 0.09, 0.09, 0.09, 0.08, 0.09)
n <- sum(~ ballplayer)
n
sum(~ national)
expect <- n*national
cbind(ballplayer, expect)
```
The chi-square quantile values in the table on the bottom of page 658 can be verified using the `xqt()` function.
```{r}
xqchisq(c(.90, .95, .975, .99, .995), df = 1)
```
These results match the first row: other values can be calculated by changing the
`df` argument.
The goodness of fit test on page 659 can be verified by calculating the
chi-square statistic.
```{r}
chisq <- sum((ballplayer - expect)^2/expect)
chisq
1-xpchisq(chisq, df = 11)
```
### Section 24.2: Chi-square test of homogeneity
Data from one university regarding
the association between postgraduation activity and area of study
is displayed in Table 24.1 (page 663). The `do()` function can be used
to generate each of the rows in the table.
```{r}
schooldata <- rbind(
do(209) * data.frame(activity = "agriculture", area = "Employed"),
do(198) * data.frame(activity = "arts/science", area = "Employed"),
do(177) * data.frame(activity = "engineering", area = "Employed"),
do(101) * data.frame(activity = "ILR", area = "Employed"),
do(104) * data.frame(activity = "agriculture", area = "Grad school"),
do(171) * data.frame(activity = "arts/science", area = "Grad school"),
do(158) * data.frame(activity = "engineering", area = "Grad school"),
do(33) * data.frame(activity = "ILR", area = "Grad school"),
do(135) * data.frame(activity = "agriculture", area = "Other"),
do(115) * data.frame(activity = "arts/science", area = "Other"),
do(39) * data.frame(activity = "engineering", area = "Other"),
do(16) * data.frame(activity = "ILR", area = "Other")
)
tally(~ area + activity, margins = TRUE, data = schooldata)
```
```{r fig.height = 6}
vcd::mosaic(tally(~ activity + area, data = schooldata),
main = "mosaicplot of activity by area",
shade = TRUE)
```
```{r}
xchisq.test(tally(~ activity + area, data = schooldata))
```
### Section 24.3: Examining the residuals
Note that the `xchisq.test()` function displays the standardized
residuals as the last item in each cell of the table (and these
match the results in Table 24.4 on page 668).