11-STAT_220_ChiSquarePreLab-tidy.Rmd

---
title: 'Inference for many proportions (Chi-square) - tidy'
author: "Professor McNamara"
output:
  html_document:
    toc: true
    toc_depth: 3
    toc_float: true
---

## Setup and packages

We use three packages in this course: `Lock5Data`, `tidyverse` and `infer`. To load a package, you use the `library()` function, wrapped around the name of a package. I've put the code to load one package into the chunk below. Add the other two you need. 

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, error = TRUE)
library(Lock5Data)
# put in the other two packages you need here
```

## Loading in data

As always, we'll load the example data, `GSS_clean.csv`. It should be inside the `data` folder in your RStudio Cloud. We'll use the `read_csv()` function to read in the data. 

```{r data-load}
GSS <- read_csv("data/GSS_clean.csv")
```

## Chi-square tests

There are two main tasks we can use a Chi-square test for: goodness of fit tests (for one categorical variable) and tests for association (two categorical variables). We'll go through both of them. 

To use a $\chi^2$ distribution as a distributional approximation, we need to check the condition that each of the expected counts is at least 5.

## Chi-square for goodness of fit

For this example, we are going to consider the variable `general_happiness` from the `GSS` data. I would like to study the following hypotheses,

$$
H_0: p_{\text{not too happy}} = p_{\text{pretty happy}} = p_{\text{very happy}} = 0.33 \\
H_A: \text{at least one of the proportions is different}
$$


Let's start by looking at a summary of the data. 

```{r}
GSS |>
  drop_na(general_happiness) |>
  group_by(general_happiness) |>
  summarize(n = n()) |>
  mutate(prop = n/sum(n))
```

Are the conditions for inference met? 


Now, we can use the `chisq_test()` function to do the test!

```{r}
GSS |>
  chisq_test(response = general_happiness)
```


What is the conclusion to the test?


## Chi-square for association

For a chi-square test for association, we are looking at the relationship between two categorical variables. For this example, let's consider the relationship between `marital_status` and `general_happiness`. 

$$
H_0: \text{there is no association between marital status and general happiness}\\
H_A: \text{there is an association between marital status and general happiness}
$$

Again, we should check to ensure the conditions are met before proceeding. 

```{r}
GSS |>
  drop_na(marital_status, general_happiness) |>
  group_by(marital_status, general_happiness) |>
  summarize(n = n())
```


Now, we can use `chisq_test()` to do the test!

```{r}
GSS |>
  chisq_test()
```



What is the conclusion of the test?