Comparing the distributions of several numeric variables is a common task in dataviz. The distribution of a variable can be represented using a histogram or a density chart, and it is very tempting to represent many distributions on the same axis.

Here is an example showing how people perceive probability vocabulary. On the /r/samplesize thread of reddit, questions like What probability would you assign to the phrase “Highly likely” were asked. Here is the distribution of the score given by people to each question:

#library
library(tidyverse)
library(hrbrthemes)
library(viridis)
library(patchwork)


# Load dataset from github
data <- read.table("https://raw.githubusercontent.com/zonination/perceptions/master/probly.csv", header=TRUE, sep=",")
data <- data %>% 
  gather(key="text", value="value") %>%
  mutate(text = gsub("\\.", " ",text)) %>%
  mutate(value = round(as.numeric(value),0))

# A dataframe for annotations
annot <- data.frame(
  text = c("Almost No Chance", "About Even", "Probable", "Almost Certainly"),
  x = c(5, 53, 65, 79),
  y = c(0.15, 0.4, 0.06, 0.1)
)

# Plot
data %>%
  filter(text %in% c("Almost No Chance", "About Even", "Probable", "Almost Certainly")) %>%
  mutate(text = fct_reorder(text, value)) %>%
  ggplot( aes(x=value, color=text, fill=text)) +
    geom_density(alpha=0.6) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    geom_text( data=annot, aes(x=x, y=y, label=text, color=text), hjust=0, size=4.5) +
    theme_ipsum() +
    theme(
      legend.position="none",
      panel.spacing = unit(0.1, "lines"),
      strip.text.x = element_text(size = 8)
    ) +
    xlab("") +
    ylab("Assigned Probability (%)")

In this case, the figure is quite neat. People give a probability between 0 and 20% for the sentence “Almost No chance”, and between 75 and 100% for “Almost Certainly”. Let’s check what happens with more groups:

# Plot
data %>%
  mutate(text = fct_reorder(text, value)) %>%
  ggplot( aes(x=value, color=text, fill=text)) +
    geom_density(alpha=0.6) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    theme_ipsum() +
    theme(
      panel.spacing = unit(0.1, "lines"),
      strip.text.x = element_text(size = 8)
    ) +
    xlab("") +
    ylab("Assigned Probability (%)")

Now the figure is way too cluttered and it is impossible to distinguish groups: there are too many distributions represented on the same graphic. How to avoid that?

Workaround

Several workarounds exist and are presented in detail in this dedicated page. Here is just an overview of the possibilities:

data %>%
  mutate(text = fct_reorder(text, value)) %>%
  ggplot( aes(x=text, y=value, fill=text)) +
    geom_boxplot() +
    geom_jitter(color="grey", alpha=0.3, size=0.9) +
    scale_fill_viridis(discrete=TRUE) +
    theme_ipsum() +
    theme(
      legend.position="none"
    ) +
    coord_flip() +
    xlab("") +
    ylab("Assigned Probability (%)")

Violin

data %>%
  mutate(text = fct_reorder(text, value)) %>%
  ggplot( aes(x=text, y=value, fill=text, color=text)) +
    geom_violin(width=2.1, size=0.2) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    theme_ipsum() +
    theme(
      legend.position="none"
    ) +
    coord_flip() +
    xlab("") +
    ylab("Assigned Probability (%)")

Ridgeline

library(ggridges)

## 
## Attaching package: 'ggridges'

## The following object is masked from 'package:ggplot2':
## 
##     scale_discrete_manual

data %>%
  mutate(text = fct_reorder(text, value)) %>%
  ggplot( aes(y=text, x=value,  fill=text)) +
    geom_density_ridges(alpha=0.6, bandwidth=4) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    theme_ipsum() +
    theme(
      legend.position="none",
      panel.spacing = unit(0.1, "lines"),
      strip.text.x = element_text(size = 8)
    ) +
    xlab("") +
    ylab("Assigned Probability (%)")

Faceting

data %>%
  mutate(text = fct_reorder(text, value)) %>%
  ggplot( aes(x=value, color=text, fill=text)) +
    geom_density(alpha=0.6) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    theme_ipsum() +
    theme(
      legend.position="none",
      panel.spacing = unit(0.1, "lines"),
      strip.text.x = element_text(size = 8)
    ) +
    xlab("") +
    ylab("Assigned Probability (%)") +
    facet_wrap(~text, scale="free_y")

Going further

Disclaimer: This idea originally comes from a publication of the CIA which resulted in this figure. Then, Zoni Nation cleaned the reddit dataset and built graphics with R. I heavily rely on his work in this post.

Other link:

Doing boxplots in R and Python
Doing violin plots in R and Python

Comments

Any thoughts on this? Found any mistake? Disagree? Please drop me a word on twitter or in the comment section below: