Distributions

class: center middle main-title section-title-4

# Distributions

.class-info[

**Week 8**

AEM 2850 / 5850 : R for Business Analytics 
Cornell Dyson 
Fall 2025

Acknowledgements: 
[Andrew Heiss](https://datavizm20.classes.andrewheiss.com), 
[Claus Wilke](https://wilkelab.org/SDS375/)

]

---

# Announcements

Welcome back from Fall Break!

Prelim 1 grades will be released on this afternoon

The average grade was 74%. Great work -- it was a tough prelim!

**I plan to curve final letter grades** so that the average is in the B+ to A- range

Please see the canvas announcement and gradescope for more information

**We will accept regrade requests through Thursday, October 23**

_**Please**_ see me if you are concerned about your ability to succeed in this course

---

# Announcements

We will provide details on the group project soon

Questions before we get started?

---

# Plan for this week

.pull-left[
### Tuesday
  - *Fall Break: No class on Oct 14*
]

.pull-right[
### Thursday
  - [Distributions](#distributions)
  - [example-08-2](#example-2)
]

---

class: inverse, center, middle
name: distributions

# Distributions

---

# Problems with single numbers
  
.pull-left[

<img src="08-slides_files/figure-html/animal-weight-bar-1.png" width="100%" style="display: block; margin: auto;" />
 
]

.pull-right[
 
<img src="08-slides_files/figure-html/animal-weight-points-1.png" width="100%" style="display: block; margin: auto;" />
]

---
  
# More information is (almost) always better
  
**Avoid visualizing single numbers when you have a whole range or distribution of numbers**

--
  
Uncertainty in single variables

Uncertainty across multiple variables

Uncertainty in models and simulations

**What are some common methods for visualizing distributions?**

Histograms, densities, box plots

---

# Histograms

What are they?

Put data into equally spaced buckets (or "bins") based on values of a variable, plot how many rows of the data frame are in each bucket

---
  
# Histograms

How would we use the grammar of graphics to make a histogram of `lifeExp`?

``` r
library(gapminder)

gapminder_2002 <- gapminder |> 
 filter(year == 2002)

head(gapminder_2002)
```

```
## # A tibble: 6 × 6
## country continent year lifeExp pop gdpPercap
## <fct> <fct> <int> <dbl> <int> <dbl>
## 1 Afghanistan Asia 2002 42.1 25268405 727.
## 2 Albania Europe 2002 75.7 3508512 4604.
## 3 Algeria Africa 2002 71.0 31287142 5288.
## 4 Angola Africa 2002 41.0 10866106 2773.
## 5 Argentina Americas 2002 74.3 38331121 8798.
## 6 Australia Asia 2002 80.4 19546792 30688.
```

---
  
# Histograms

.left-code[

``` r
gapminder_2002 |> 
* ggplot(aes(x = lifeExp)) +
* geom_histogram()
```
]

.right-plot[
  ![](08-slides_files/figure-html/basic-histogram-1.png)
]

---
  
# Histograms: binwidth argument
  
No official rule for what makes a good bin width

.pull-left-3[
.center.small[Too narrow:]

.center.tiny[`geom_histogram(binwidth = .2)`]

<img src="08-slides_files/figure-html/hist-too-narrow-1.png" width="100%" style="display: block; margin: auto;" />
 
]

--
  
.pull-middle-3[
.center.small[Too wide:]

.center.tiny[`geom_histogram(binwidth = 50)`]

<img src="08-slides_files/figure-html/hist-too-wide-1.png" width="100%" style="display: block; margin: auto;" />
]

--
  
.pull-right-3[
.center.small[(One type of) just right:]

.center.tiny[`geom_histogram(binwidth = 5)`]
 
<img src="08-slides_files/figure-html/hist-just-right-1.png" width="100%" style="display: block; margin: auto;" />
]

---
  
# Histograms: tips using other arguments

.pull-left[
.center[Add a border to the bars for readability]

.center.tiny[`geom_histogram(..., color = "white")`]
 
<img src="08-slides_files/figure-html/hist-border-1.png" width="100%" style="display: block; margin: auto;" />
]

--
 
.pull-right[
.center.small[Set the boundary; bucket now 50–55, not 47.5–52.5]

.center.tiny[`geom_histogram(..., boundary = 50)`]

]

---
  
# Density plots
  
What are they?

Estimates of the **probability *density* function** of a random variable

Histograms show raw counts; density plots show proportions (integrate to 1)

How would we use the grammar of graphics to make a density plot of `lifeExp`?

---
  
# Density plots
  
.left-code[

``` r
gapminder_2002 |> 
  ggplot(aes(x = lifeExp)) + 
* geom_density()
```
]

.right-plot[
  ![](08-slides_files/figure-html/basic-density-1.png)
]

---
  
# Density plots: add some color
  
.left-code[

``` r
gapminder_2002 |> 
  ggplot(aes(x = lifeExp)) +
* geom_density(fill = "skyblue")
```

We can use aesthetics as *parameters* inside a geom rather than inside an **aes()** statement

Here we used **fill = "skyblue"**
]

.right-plot[
  ![](08-slides_files/figure-html/basic-density-color-1.png)
]

---
  
# Box and whisker plots

What are they?

Graphical representations of specific points in a distribution

---
 
# Box and whisker plots
 
<img src="08-slides_files/figure-html/boxplot-explanation-1.png" width="100%" style="display: block; margin: auto;" />

---
  
# Box and whisker plots

What are they?

Graphical representations of specific points in a distribution

How could we use ggplot to make a boxplot of `lifeExp`?

---
  
# Box and whisker plots

.left-code[

``` r
gapminder_2002 |> 
  ggplot(aes(x = lifeExp)) + 
* geom_boxplot()
```

What do the y axis numbers mean?
]

.right-plot[
  ![](08-slides_files/figure-html/basic-boxplot-1.png)
]

---
  
# Box and whisker plots

Use `theme()` to customize the plot for this geom

.left-code[

``` r
gapminder_2002 |> 
  ggplot(aes(x = lifeExp)) +
  geom_boxplot() +
* theme(
*   axis.text.y = element_blank(),
*   axis.ticks.y = element_blank(),
*   panel.grid.major.y = element_blank(),
*   panel.grid.minor.y = element_blank()
* )
```

]

.right-plot[
  ![](08-slides_files/figure-html/basic-boxplot-no-y-1.png)
]

---
  
# Uncertainty across multiple variables

How could we visualize the distribution of a single variable across groups?

Add a `fill` aesthetic or use facets!

---
  
# Multiple histograms
  
Fill with a different variable

.left-code[

``` r
gapminder_2002 |> 
  ggplot(aes(x = lifeExp,
*            fill = continent)) +
  geom_histogram(binwidth = 5, 
                 color = "white", 
                 boundary = 50) +
  theme(legend.position = "bottom") +
  labs(fill = NULL)
```

This stacked histogram is bad and hard to read though
]

.right-plot[
  ![](08-slides_files/figure-html/histogram-fill-1.png)
]

---
  
# Multiple histograms
  
Facet with a different variable

.left-code[

``` r
gapminder_2002 |> 
  ggplot(aes(x = lifeExp,
             fill = continent)) +
  geom_histogram(binwidth = 5, 
                 color = "white", 
                 boundary = 50) +
* facet_wrap(vars(continent)) +
* guides(fill = "none")
```

Note: we could also omit `fill = continent`
]

.right-plot[
  ![](08-slides_files/figure-html/histogram-facet-1.png)
]

---

# Multiple densities: Transparency

.left-code[

``` r
gapminder_2002 |> 
  ggplot(aes(x = lifeExp,
             fill = continent)) +
* geom_density(alpha = 0.5) +
  theme(legend.position = "bottom") +
  labs(fill = NULL)
```

But be careful, these can get confusing quickly

With many groups, better to space them out using ridgeline plots
]

.right-plot[
![](08-slides_files/figure-html/density-fill-1.png)
]

---

# Multiple densities: Ridgeline plots

.left-code[

``` r
*library(ggridges)

gapminder_2002 |> 
  ggplot(aes(x = lifeExp,
             fill = continent,
*            y = continent)) +
  guides(fill = "none") +
  labs(y = NULL) +
* geom_density_ridges()
```

There is no explicit scale for the densities anymore (it is shared with y)

With many densities, use a single fill color to prevent distraction
]

.right-plot[
![](08-slides_files/figure-html/density-ridges-1.png)
]

---

# Multiple box and whisker plots

.left-code[

``` r
gapminder_2002 |> 
  ggplot(aes(
    x = lifeExp,
    fill = continent,
    y = continent
  )) + 
  guides(fill = "none") +
  labs(y = NULL) +
* geom_boxplot()
```
]

.right-plot[
![](08-slides_files/figure-html/multiple-boxplots-1.png)
]

---
class: inverse, center, middle
name: example-2

# example-08: distributions-practice.R