Visualizing distributions 1

class: center, middle, title-slide

.title[
# Visualizing distributions 1
]
.author[
### Claus O. Wilke
]
.date[
### last updated: 2024-01-29
]

---

class: center middle

## Histograms and density plots

---

## Passengers on the Titanic

.center.small-font[
<table>
 <thead>
  <tr>
   <th style="text-align:right;"> age </th>
   <th style="text-align:left;"> sex </th>
   <th style="text-align:left;"> class </th>
   <th style="text-align:left;"> survived </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 0.17 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 0.33 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> died </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 0.80 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 0.83 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 0.83 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 0.92 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 1st </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 1.00 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 1.00 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 1.00 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 1.00 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
</tbody>
</table>
&nbsp;&nbsp;&nbsp;&nbsp;
<table>
 <thead>
  <tr>
   <th style="text-align:right;"> age </th>
   <th style="text-align:left;"> sex </th>
   <th style="text-align:left;"> class </th>
   <th style="text-align:left;"> survived </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 1.0 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 1.5 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> died </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 1.5 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> died </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 1st </td>
   <td style="text-align:left;"> died </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> died </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> died </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
</tbody>
</table>
&nbsp;&nbsp;&nbsp;&nbsp;
<table>
 <thead>
  <tr>
   <th style="text-align:right;"> age </th>
   <th style="text-align:left;"> sex </th>
   <th style="text-align:left;"> class </th>
   <th style="text-align:left;"> survived </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:left;"> male </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 2nd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:left;"> female </td>
   <td style="text-align:left;"> 3rd </td>
   <td style="text-align:left;"> survived </td>
  </tr>
</tbody>
</table>
]

---

## Histogram: Define bins and count cases

.pull-left.small-font[
<table>
 <thead>
  <tr>
   <th style="text-align:left;"> age range </th>
   <th style="text-align:right;"> count </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 0–5 </td>
   <td style="text-align:right;"> 36 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 6–10 </td>
   <td style="text-align:right;"> 19 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 11–15 </td>
   <td style="text-align:right;"> 18 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 16–20 </td>
   <td style="text-align:right;"> 99 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 21–25 </td>
   <td style="text-align:right;"> 139 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 26–30 </td>
   <td style="text-align:right;"> 121 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 31–35 </td>
   <td style="text-align:right;"> 76 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 36–40 </td>
   <td style="text-align:right;"> 74 </td>
  </tr>
</tbody>
</table>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<table>
 <thead>
  <tr>
   <th style="text-align:left;"> age range </th>
   <th style="text-align:right;"> count </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 41–45 </td>
   <td style="text-align:right;"> 54 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 46–50 </td>
   <td style="text-align:right;"> 50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 51–55 </td>
   <td style="text-align:right;"> 26 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 56–60 </td>
   <td style="text-align:right;"> 22 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 61–65 </td>
   <td style="text-align:right;"> 16 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 66–70 </td>
   <td style="text-align:right;"> 3 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 71–75 </td>
   <td style="text-align:right;"> 3 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 76–80 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
</tbody>
</table>
]

.pull-right[
<img src="visualizing-distributions-1_files/figure-html/titanic-age-hist-1.svg" width="100%" />
]

???

Figure redrawn from [Claus O. Wilke. Fundamentals of Data Visualization. O'Reilly, 2019.](https://clauswilke.com/dataviz)

---

# Histograms depend on the chosen bin width

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-age-hist-binwidth-1.svg" width="75%" />
]

???

Figure redrawn from [Claus O. Wilke. Fundamentals of Data Visualization. O'Reilly, 2019.](https://clauswilke.com/dataviz)

---

## Alternative to histogram: Kernel density estimate (KDE)

.pull-left[
![](visualizing-distributions-1_files/figure-html/titanic-age-hist2-1.svg)
]

.pull-right[
![](visualizing-distributions-1_files/figure-html/titanic-age-kde-1.svg)
]

Histograms show raw counts, KDEs show proportions. (Total area = 1)

???

Figures redrawn from [Claus O. Wilke. Fundamentals of Data Visualization. O'Reilly, 2019.](https://clauswilke.com/dataviz)

---

## KDEs also depend on parameter settings

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-age-kde-grid-1.svg" width="75%" />
]

???

Figure redrawn from [Claus O. Wilke. Fundamentals of Data Visualization. O'Reilly, 2019.](https://clauswilke.com/dataviz)

---

## Careful: KDEs can show non-sensical data

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-age-kde-wrong-1.svg" width="70%" />
]

???

Figure redrawn from [Claus O. Wilke. Fundamentals of Data Visualization. O'Reilly, 2019.](https://clauswilke.com/dataviz)

---

## Careful: Are bars stacked or overlapping?

.pull-left[
![](visualizing-distributions-1_files/figure-html/titanic-age-hist-stacked-1.svg)
]

.pull-right[
![](visualizing-distributions-1_files/figure-html/titanic-age-hist-overlap-1.svg)
]

Stacked or overlapping histograms are rarely a good choice.

???

Figures redrawn from [Claus O. Wilke. Fundamentals of Data Visualization. O'Reilly, 2019.](https://clauswilke.com/dataviz)

---

## Alternatively: Age pyramid

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-age-pyramid-1.svg" width="70%" />
]

???

Figures redrawn from [Claus O. Wilke. Fundamentals of Data Visualization. O'Reilly, 2019.](https://clauswilke.com/dataviz)

---

## Alternatively: KDEs showing proportions of total

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-age-props-1.svg" width="75%" />
]

???

Figures redrawn from [Claus O. Wilke. Fundamentals of Data Visualization. O'Reilly, 2019.](https://clauswilke.com/dataviz)

[//]: # "segment ends here"

---
class: center middle

## Histograms and density plots in **ggplot2**

---

## Getting the data

All examples will use the `titanic` dataset:

.tiny-font[

```r
titanic <- read_csv("https://wilkelab.org/SDS375/datasets/titanic.csv") %>%
  select(age, sex, class, survived)
```
]

---

## Making histograms with ggplot: `geom_histogram()`

.small-font[

```r
ggplot(titanic, aes(age)) +
  geom_histogram()
```
]

.center.small-font[

```
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
```

<img src="visualizing-distributions-1_files/figure-html/titanic-hist-ggplot-demo-out-1.svg" width="50%" />
]

---

## Setting the bin width

.small-font[

```r
ggplot(titanic, aes(age)) +
  geom_histogram(binwidth = 5)
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-hist-ggplot-demo2-out-1.svg" width="50%" />
]

Do you like the bin placement?

---

## Always set the center as well

.small-font[

```r
ggplot(titanic, aes(age)) +
  geom_histogram(
    binwidth = 5,  # width of the bins
    center = 2.5   # center of the bin containing that value
  )
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-hist-ggplot-demo3-out-1.svg" width="50%" />
]

---

## Always set the center as well

.small-font[

```r
ggplot(titanic, aes(age)) +
  geom_histogram(
    binwidth = 5,  # width of the bins
    center = 12.5  # center of the bin containing that value
  )
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-hist-ggplot-demo4-out-1.svg" width="50%" />
]

---

## Making density plots with ggplot: `geom_density()`

.small-font[

```r
ggplot(titanic, aes(age)) +
  geom_density(fill = "skyblue")
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-dens-ggplot-demo-out-1.svg" width="50%" />
]

---

## Making density plots with ggplot: `geom_density()`

.small-font[

```r
ggplot(titanic, aes(age)) +
  geom_density() # without fill
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-dens-ggplot-demo2-out-1.svg" width="50%" />
]

---

## Modifying bandwidth (`bw`) and kernel parameters

.tiny-font[

```r
ggplot(titanic, aes(age)) +
  geom_density(
    fill = "skyblue",
    bw = 0.5,               # a small bandwidth
    kernel = "gaussian"     # Gaussian kernel (the default)
  )
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-dens-ggplot-demo3-out-1.svg" width="50%" />
]

---

## Modifying bandwidth (`bw`) and kernel parameters

.tiny-font[

```r
ggplot(titanic, aes(age)) +
  geom_density(
    fill = "skyblue",
    bw = 2,                 # a moderate bandwidth
    kernel = "rectangular"  # rectangular kernel
  )
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-dens-ggplot-demo4-out-1.svg" width="50%" />
]

[//]: # "segment ends here"

---
class: center middle

## Setting stats explicitly in **ggplot2**

---

## Statistical transformations (stats) can be set explicitly

.tiny-font[

```r
ggplot(titanic, aes(age)) +
  geom_density(
    stat = "density",    # the default for geom_density()
    fill = "skyblue"
  )
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-stat-demo1-out-1.svg" width="50%" />
]

---

## Statistical transformations (stats) can be set explicitly

.tiny-font[

```r
ggplot(titanic, aes(age)) +
  geom_area(  # geom_area() does not normally use stat = "density"
    stat = "density",
    fill = "skyblue"
  )
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-stat-demo2-out-1.svg" width="50%" />
]

---

## Statistical transformations (stats) can be set explicitly

.tiny-font[

```r
ggplot(titanic, aes(age)) +
  geom_line(  # neither does geom_line()
    stat = "density"
  )
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-stat-demo3-out-1.svg" width="50%" />
]

---

## Statistical transformations (stats) can be set explicitly

.tiny-font[

```r
ggplot(titanic, aes(age)) +
  # we can use multiple geoms on top of each other
  geom_area(stat = "density", fill = "skyblue") +
  geom_line(stat = "density")
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-stat-demo4-out-1.svg" width="50%" />
]

---

## Parameters are handed through to the stat

.pull-left.tiny-font[

```r
ggplot(titanic, aes(age)) +
  geom_line(stat = "density", bw = 3)
```

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-stat-demo5-out-1.svg" width="90%" />
]]

.pull-right.tiny-font[

```r
ggplot(titanic, aes(age)) +
  geom_line(stat = "density", bw = 0.3)
```

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-stat-demo6-out-1.svg" width="90%" />
]]

Here, `bw` is a parameter of `stat_density()`, not of `geom_line()`.

---

## We can explicitly map results from stat computations

.tiny-font[

```r
ggplot(titanic, aes(age)) +
  geom_tile( # geom_tile() draws rectangular colored areas
    aes(
      y = 1, # draw all tiles at the same y location
      fill = after_stat(density)  # use computed density for fill
    ),
    stat = "density",
    n = 20    # number of points calculated by stat_density() 
  ) 
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-stat-demo7-out-1.svg" width="90%" />
]

---

## We can explicitly map results from stat computations

.tiny-font[

```r
ggplot(titanic, aes(age)) +
  geom_tile( # geom_tile() draws rectangular colored areas
    aes(
      y = 1, # draw all tiles at the same y location
      fill = after_stat(density)  # use computed density for fill
    ),
    stat = "density",
    n = 200   # number of points calculated by stat_density() 
  ) 
```
]

.center[
<img src="visualizing-distributions-1_files/figure-html/titanic-stat-demo8-out-1.svg" width="90%" />
]

[//]: # "segment ends here"

---

## Further reading

- Fundamentals of Data Visualization: [Chapter 7: Visualizing distributions](https://clauswilke.com/dataviz/histograms-density-plots.html)
- Data Visualization—A Practical Introduction: [4.6 Histograms and density plots](https://socviz.co/groupfacettx.html#histograms)
- **ggplot2** reference documentation: [`geom_histogram()`](https://ggplot2.tidyverse.org/reference/geom_histogram)
- **ggplot2** reference documentation: [`geom_density()`](https://ggplot2.tidyverse.org/reference/geom_density)