---
title: "SDM4 in R: Comparing Counts (Chapter 24)"
author: "Nicholas Horton (nhorton@amherst.edu)"
date: "January 2, 2017"
output: 
  html_document:
    fig_height: 5
    fig_width: 7
  pdf_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}
# Some customization.  You can alter or delete as desired (if you know what you are doing).

# This changes the default colors in lattice plots.
trellis.par.set(theme=theme.mosaic())  

# 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 \emph{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).

## 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).  

```{r fig.height=5}
area <- c(rep("agriculture", 209), rep("arts/science", 198), 
          rep("engineering", 177), rep("ILR", 101),
	  rep("agriculture", 104), rep("arts/science", 171), 
          rep("engineering", 158), rep("ILR", 33),
	  rep("agriculture", 135), rep("arts/science", 115), 
          rep("engineering", 39), rep("ILR", 16))
activity <- c(rep("Employed", 685), rep("Grad school", 466), 
              rep("Other", 305))
tally(~ activity + area, margins=TRUE)
mosaicplot(tally(~ activity + area), main="mosaicplot of activity by area",
  color=TRUE)
xchisq.test(tally(~ activity + area))
```

### 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 (page 668).