---
title: "IS4 in R: The Standard Deviation as a Ruler and the Normal Model (Chapter 5)"
author: "Patrick Frenett, Vickie Ip, and Nicholas Horton (nhorton@amherst.edu)"
date: "July 17, 2017"
output: 
  pdf_document:
    fig_height: 3
    fig_width: 6
  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}
# 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
  fig.align="center"
)
```

## Introduction and background 

This document is intended to help describe how to undertake analyses introduced 
as examples in the Fourth Edition of \emph{Intro Stats} (2013) 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 https://nhorton.people.amherst.edu/is4.

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 5: The Standard Deviation as a Ruler and the Normal Model

### Section 5.1: Standardizing with z-scores

From page 111

```{r}
library(mosaic); library(readr); library(ggformula)
options(na.rm=TRUE)
options(digits=3)
(6.54-5.91)/0.56  # Dobrynska's jump was 2.18 SD's greater than the mean
```

```{r}
twohund<-as.vector(c(23.2,23.3,23.3,23.6,23.9,23.9,24.2,24.2,24.3,
                     24.3,24.3,24.3,24.3,24.4,24.5,24.5,24.6,24.6,24.6,24.7,24.7,24.9,
                     24.9,24.9,25.0,25.0,25.0,25.2,25.3,25.4,25.4,25.4,25.4,25.5,25.9,
                     25.9,26.1))
twohund <- data.frame(twohund)
df_stats(~., data=twohund)
```

### Section 5.2: Shifting and Scaling

### Section 5.3: Normal Models

The 68-95-99.7 rule

```{r, message=FALSE, warning=FALSE}
xpnorm(c(-3, -1.96, -1, 1, 1.96, 3), mean=0, sd=1, verbose=FALSE)
xpnorm(c(-3, -1.96, 1.96, 3), mean=0, sd=1, verbose=FALSE)
xpnorm(c(-3, 3), mean=0, sd=1, verbose=FALSE)
```

Step-by-step (page 120)

```{r}
xpnorm(600, mean=500, sd=100)
```

### Section 5.4: Finding normal percentiles

as on page 121

```{r}
xpnorm(680, mean=500, sd=100)
qnorm(0.964, mean=500, sd=100)   # inverse of pnorm()
qnorm(0.964, mean=0, sd=1)   # what is the z-score?
```

or on page 122

```{r}
xpnorm(450, mean=500, sd=100)
```

and page 123

```{r}
qnorm(.9, mean=500, sd=100)
qnorm(.9, mean=0, sd=1)   # or as a Z-score
```

### Section 5.5: Normal Probability Plots

See Figure 5.8 on page 127

```{r message=FALSE}
Nissan <- 
read_delim("http://nhorton.people.amherst.edu/sdm4/data/Nissan.txt",
  delim="\t")
```
```{r}
gf_histogram(..density..~ mpg, binwidth=1, center=0.5, data=Nissan, fill = "royalblue2", col=TRUE)
gf_qq(~ mpg, data=Nissan) %>%
  gf_labs(x="qnorm",y="mpg")
```