---
title: "IPS9 in R: Two-way analysis of variance (Chapter 13)"
author: "Bonnie Lin and Nicholas Horton (nhorton@amherst.edu)"
date: "July 20, 2018"
output: 
  pdf_document:
    fig_height: 3
    fig_width: 5
  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)
```

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

## Introduction and background 

These documents are intended to help describe how to undertake analyses introduced 
as examples in the Ninth Edition of \emph{Introduction to the Practice of Statistics} (2017) by Moore, McCabe, and Craig.

More information about the book can be found [here](https://macmillanlearning.com/Catalog/product/introductiontothepracticeofstatistics-ninthedition-moore).
The data used in these documents can be found under Data Sets in the [Student Site](https://www.macmillanlearning.com/catalog/studentresources/ips9e?_ga=2.29224888.526668012.1531487989-1209447309.1529940008#). This
file as well as the associated R Markdown reproducible analysis source file used to create it can be found at https://nhorton.people.amherst.edu/ips9/.

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 13: Two-way analysis of variance
This file replicates the analyses from Chapter 13: Two-way analysis of variance.

First, load the packages that will be needed for this document: 
```{r load-packages}
library(mosaic)
library(readr)
```

### Section 13.1: The two-way ANOVA model
```{r eg13-8, message=FALSE}
HRTRATE <- read_csv("https://nhorton.people.amherst.edu/ips9/data/chapter13/EG13-08HRTRATE.csv") 
head(HRTRATE)
```

By default, the `read_csv()` function will output the types of columns, as we see above. 
To improve readability for future coding, we will suppress the "Parsed with column 
specification" message by adding `message = FALSE` at the top of the code chunks.

We need to transform the data from wide to tall format using the `gather()` function.

```{r}
HRTRATE_tidy <- HRTRATE %>%
  tidyr::gather(key = Group, value = Heart_Rate, Control, Runners)
head(HRTRATE_tidy)
```

```{r}
## Figure 13.4, age 710
favstats(Heart_Rate ~ Sex + Group, data = HRTRATE_tidy)

## Figure 13.5, age 711
lm_HRTRATE <- lm(Heart_Rate ~ Group * Sex, data = HRTRATE_tidy)
msummary(lm_HRTRATE)
anova(lm_HRTRATE)
```

We see that there is a significant interaction (p=0.007): the sex difference between the heart rates differs by groups.  

```{r}
### Figure 13.6, page 712
with(HRTRATE_tidy, interaction.plot(Group, Sex, Heart_Rate))
```


### Section 13.2: Inference for two-way ANOVA

