---
title: "C05 Qualitative Explanatory Variable"
author: "David Housman"
format: html
editor: visual
fig-width: 6
fig-asp: 0.618
out-width: "70%"
fig-align: center
---

## Introduction

Previously, we considered techniques to describe a single variable.  We now examine techniques to describe the relationship between two variables.  We usually think of one variable as the *dependent* or *response* variable and the other variable as the *independent*, *predictor*, or *explanatory* variable.  Again, the description techniques used depend on the types of variables. 

Load the important packages. The `janitor` package provides a nice way to create tables based on the tidyverse.

```{r}
#| message: false
#| warning: false
library(tidyverse)
library(janitor)
```

Import the illustrative data set, and treat `Excitement` as an ordinal factor variable.

```{r}
##| eval: false
intro = read_csv("03 Introduction.csv") |>
  mutate(Excitement = factor(Excitement, levels = "5":"1"))
```

## Quantitative Response and Qualitative Explanatory Variables

The approach is to use the visualizations and statistics used for a quantitative variable for each value of the qualitative variable.

Consider `Weight` as a function of `Gender`.

1.  Exclude the non-binary students.

```{r}
intro |> filter(Gender == "N")
```

```{r}
intro2 = intro |> filter(Gender != "N")
```

1.  Obtain box plots. Overlay with blue jitter plots.

```{r}
ggplot(intro2, aes(y = Weight, x = Gender)) +
  geom_boxplot() +
  geom_jitter(height = 0, width = 0.1, color = "blue")
```

1.  Estimate and obtain the standard five-number summaries.

```{r}
intro2 |>
  group_by(Gender) |>
  summarise(
    min = min(Weight),
    Q1 = quantile(Weight, 0.25),
    med = median(Weight),
    Q3 = quantile(Weight, 0.75),
    max = max(Weight)
  )
```

```{r}
summary(intro2)
```

2.  Obtain overlaid density plots. Unlike the other graphs, the response variable is typically represented on the horizontal axis.

```{r}
ggplot(intro2, aes(x = Weight, color = Gender, fill = Gender)) +
  geom_density(alpha = 0.5) +
  xlab("Weight (lb)")
```

2.  Estimate and obtain counts, means, and standard deviations.

```{r}
intro2 |>
  group_by(Gender) |>
  summarise(
    n = n(),
    mean = mean(Weight),
    sd = sd(Weight)
  )
```

3.  Obtain vertically aligned histograms.

```{r}
ggplot(intro2, aes(x = Weight)) +
  geom_histogram(bins = 8, fill = "gray", color = "black") +
  facet_wrap(~Gender, nrow = 2) +
  xlab("Weight (lb)")
```

4.  Obtain grouped empirical cumulative distribution functions plot.

```{r}
ggplot(intro2, aes(x = Weight, color = Gender)) +
  stat_ecdf(geom = "step")
```

## Qualitative Response and Explanatory Variables

The approach is to use the visualizations and statistics used for a qualitative variable for each value of the explanatory qualitative variable.

Consider `Excitement` as a function of `Gender`.

1.  Obtain a stacked frequency bar chart.

```{r}
ggplot(intro, aes(fill = Excitement, x = Gender)) +
  geom_bar()
```

2.  Obtain a dodged frequency bar chart.

```{r}
ggplot(intro, aes(fill = Excitement, x = Gender)) +
  geom_bar(position = "dodge2")
```

2.  Obtain a relative frequency within each group stacked bar chart.

```{r}
ggplot(intro, aes(fill = Excitement, x = Gender)) +
  geom_bar(position = "fill")
```

4.  Obtain a table of frequencies.

```{r}
intro |>
  tabyl(Excitement, Gender)
```

4.  Obtain a table of percentages by group.

```{r}
intro |>
  tabyl(Excitement, Gender) |>
  adorn_percentages("col") |>
  adorn_pct_formatting(digits = 2)
```