---
title: "IS5 in R: Sample Surveys (Chapter 10)"
author: "Nicholas Horton (nhorton@amherst.edu)"
date: "2025-01-15"
date-format: iso
format: pdf
toc: true
editor: source
---

```{r}
#| label: setup
#| include: false
library(mosaic)   
library(tidyverse)
```


## Introduction and background 

This document is intended to help describe how to undertake analyses introduced as examples in the Fifth Edition of *Intro Stats* (2018) by De Veaux, Velleman, and Bock.
This file as well as the associated Quarto reproducible analysis source file used to create it can be found at http://nhorton.people.amherst.edu/is5.

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 (https://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.

We begin by loading packages that will be required for our analyses.

```{r}
library(mosaic)
library(tidyverse)
```

## Chapter 10: Sample Surveys


### Section 10.1: The Three Big Ideas of Sampling

### Section 10.2: Populations and Parameters

### Section 10.3: Simple Random Samples

#### Random Matters

We begin by loading in the data on birthweights.

```{r}
#| message: false
#| warning: false
Births <- read_csv("http://nhorton.people.amherst.edu/is5/data/AllBirths1998.csv")
```

By default, `read_csv()` prints the variable names.
These messages were suppressed using the `message: false` code chunk option to save space and improve readability.  

```{r}
#| warning: false
# Histogram of known population
gf_histogram(~ birthweight, data = Births, binwidth = 125, center = 62.5) |>
  gf_labs(x = "Weight (g)", y = "Births")
```

The histogram shows the distribution of the population of nearly four million births.
Warning messages about missing values were suppressed using the `warnings: false` code chunk option.


Figure 10.2 (page 326):

```{r}
# Samples of 100
set.seed(12452)
gf_density(~ birthweight, data = sample(Births, size = 100), fill = 5) |>
  gf_density(~ birthweight, data = sample(Births, size = 100), fill = 4) |>
  gf_labs(x = "Birthweights", y = "", title = "Two Samples of Size 100")
```

Here we set an (arbitrary) random number seed (`12452`).
This sets our location in a long list of pseudo-random numbers.
Use of a seed in this manner allows us to rerun the code and get the same answer.

It's not necessarily a best practice to display overlapping densities (or histograms).
Perhaps a better approach would be to use `gf_dens()` to only display the line.

```{r}
set.seed(12452)
gf_dens(~ birthweight, data = sample(Births, size = 100)) |>
  gf_dens(~ birthweight, data = sample(Births, size = 100)) |>
  gf_labs(x = "Birthweights", y = "", title = "Two Samples of Size 100")
```

```{r}
# Samples of 250
set.seed(12452)
gf_density(~ birthweight, data = sample(Births, size = 250), fill = 5) |>
  gf_density(~ birthweight, data = sample(Births, size = 250), fill = 4) |>
  gf_labs(x = "Birthweights", y = "", title = "Two Samples of Size 250")
```

```{r}
# Samples of 1000
set.seed(12452)
gf_density(~ birthweight, data = sample(Births, size = 1000), fill = 5) |>
  gf_density(~ birthweight, data = sample(Births, size = 1000), fill = 4) |>
  gf_labs(x = "Birthweights", y = "", title = "Two Samples of Size 1000")
```

### Section 10.4: Other Sampling Designs

### Section 10.5: From the Population to the Sample: You Can't Always Get What You Want

### Section 10.6: The Valid Survey

### Section 10.7: Common Sampling Mistakes, or How to Sample Badly