library(tidyverse)
library(mosaic)
library(ggformula)
library(skimr)
##
# install.packages("remotes")
# library(remotes)
# remotes::install_github("wilkelab/ggridges")
library(ggridges) # Ridge Density Plots
##
library(janitor) # Data cleaning and tidying package
library(visdat) # Visualize whole dataframes for missing data
library(naniar) # Clean missing data
library(DT) # Interactive Tables for our data
library(tinytable) # Elegant Tables for our data
library(ggrepel) # Repel overlapping text labels in ggplot2
library(marquee) # Annotations in ggplot2
Distributions
The Hills are Shadows, said Tennyson
“Never let the future disturb you. You will meet it, if you have to, with the same weapons of reason which today arm you against the present.”
— Marcus Aurelius
1 Setting up R Packages
Plot Fonts and Theme
Show the Code
library(systemfonts)
library(showtext)
## Clean the slate
systemfonts::clear_local_fonts()
systemfonts::clear_registry()
##
showtext_opts(dpi = 96) # set DPI for showtext
sysfonts::font_add(
family = "Alegreya",
regular = "../../../../../../fonts/Alegreya-Regular.ttf",
bold = "../../../../../../fonts/Alegreya-Bold.ttf",
italic = "../../../../../../fonts/Alegreya-Italic.ttf",
bolditalic = "../../../../../../fonts/Alegreya-BoldItalic.ttf"
)
sysfonts::font_add(
family = "Roboto Condensed",
regular = "../../../../../../fonts/RobotoCondensed-Regular.ttf",
bold = "../../../../../../fonts/RobotoCondensed-Bold.ttf",
italic = "../../../../../../fonts/RobotoCondensed-Italic.ttf",
bolditalic = "../../../../../../fonts/RobotoCondensed-BoldItalic.ttf"
)
showtext_auto(enable = TRUE) # enable showtext
##
theme_custom <- function() {
theme_bw(base_size = 10) +
theme_sub_axis(
title = element_text(
family = "Roboto Condensed",
size = 8
),
text = element_text(
family = "Roboto Condensed",
size = 6
)
) +
theme_sub_legend(
text = element_text(
family = "Roboto Condensed",
size = 6
),
title = element_text(
family = "Alegreya",
size = 8
)
) +
theme_sub_plot(
title = element_text(
family = "Alegreya",
size = 14, face = "bold"
),
title.position = "plot",
subtitle = element_text(
family = "Alegreya",
size = 10
),
caption = element_text(
family = "Alegreya",
size = 6
),
caption.position = "plot"
)
}
## Use available fonts in ggplot text geoms too!
ggplot2::update_geom_defaults(geom = "text", new = list(
family = "Roboto Condensed",
face = "plain",
size = 3.5,
color = "#2b2b2b"
))
ggplot2::update_geom_defaults(geom = "label", new = list(
family = "Roboto Condensed",
face = "plain",
size = 3.5,
color = "#2b2b2b"
))
ggplot2::update_geom_defaults(geom = "marquee", new = list(
family = "Roboto Condensed",
face = "plain",
size = 3.5,
color = "#2b2b2b"
))
ggplot2::update_geom_defaults(geom = "text_repel", new = list(
family = "Roboto Condensed",
face = "plain",
size = 3.5,
color = "#2b2b2b"
))
ggplot2::update_geom_defaults(geom = "label_repel", new = list(
family = "Roboto Condensed",
face = "plain",
size = 3.5,
color = "#2b2b2b"
))
## Set the theme
ggplot2::theme_set(new = theme_custom())
## tinytable options
options("tinytable_tt_digits" = 2)
options("tinytable_format_num_fmt" = "significant_cell")
options(tinytable_html_mathjax = TRUE)
## Set defaults for flextable
flextable::set_flextable_defaults(font.family = "Roboto Condensed")
2 What graphs will we see today?
Variable #1 | Variable #2 | Chart Names | Chart Shape | |
---|---|---|---|---|
Quant | None | Density plot, Ridge Density Plot |
3 What kind of Data Variables will we choose?
No | Pronoun | Answer | Variable/Scale | Example | What Operations? |
---|---|---|---|---|---|
1 | How Many / Much / Heavy? Few? Seldom? Often? When? | Quantities, with Scale and a Zero Value.Differences and Ratios /Products are meaningful. | Quantitative/Ratio | Length,Height,Temperature in Kelvin,Activity,Dose Amount,Reaction Rate,Flow Rate,Concentration,Pulse,Survival Rate | Correlation |
4 Inspiration
Show the Code
ggplot2::theme_set(new = theme_custom())
lincoln_weather %>%
gf_density_ridges_gradient(Month ~ `Max Temperature [F]`,
group = ~Month
) %>%
gf_refine(scale_fill_viridis_c(
name = "Temperature [F]",
option = "B"
)) %>%
gf_labs(title = "Weather in Lincoln, Nebraska")
April is the cruelest month, said T.S Eliot. But December in Nebraska must be tough.
5 What is a “Density Plot”?
As we saw earlier, Histograms are best to show the distribution of raw Quantitative data, by displaying the number of values that fall within defined ranges, often called buckets or bins.
Sometimes it is useful to consider a chart where the bucket width shrinks to zero!
You might imagine a density chart as a histogram where the buckets are infinitesimally small, i.e. zero width. Think of the frequency density as a differentiation (as in calculus) of the histogram. By taking the smallest of steps \(\sim 0\), we get a measure of the slope of distribution. This may seem counter-intuitive, but densities have their uses in spotting the ranges in the data where there are more frequent values. In this, they serve a similar purpose as do histograms, but may offer insights not readily apparent with histograms, especially with default bucket widths. The chunkiness that we see in the histograms is removed and gives us a smooth curve showing in which range the data are more frequent.
6 Case Study-1: penguins
dataset
We will first look at at a dataset that is available as a part of the palmerpenguins package (and also directly available in R now), the penguins
dataset. Data were collected and made available by Dr. Kristen Gorman and the Palmer Station, Antarctica LTER, a member of the Long Term Ecological Research Network.
6.1 Read the Data
[1] "studyName" "Sample Number" "Species"
[4] "Region" "Island" "Stage"
[7] "Individual ID" "Clutch Completion" "Date Egg"
[10] "Culmen Length (mm)" "Culmen Depth (mm)" "Flipper Length (mm)"
[13] "Body Mass (g)" "Sex" "Delta 15 N (o/oo)"
[16] "Delta 13 C (o/oo)" "Comments"
6.2 Examine the Data
As per our Workflow, we will look at the data using all the three methods we have seen.
glimpse(penguins_raw)
Rows: 344
Columns: 17
$ studyName <chr> "PAL0708", "PAL0708", "PAL0708", "PAL0708", "PAL…
$ `Sample Number` <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1…
$ Species <chr> "Adelie Penguin (Pygoscelis adeliae)", "Adelie P…
$ Region <chr> "Anvers", "Anvers", "Anvers", "Anvers", "Anvers"…
$ Island <chr> "Torgersen", "Torgersen", "Torgersen", "Torgerse…
$ Stage <chr> "Adult, 1 Egg Stage", "Adult, 1 Egg Stage", "Adu…
$ `Individual ID` <chr> "N1A1", "N1A2", "N2A1", "N2A2", "N3A1", "N3A2", …
$ `Clutch Completion` <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "No", …
$ `Date Egg` <date> 2007-11-11, 2007-11-11, 2007-11-16, 2007-11-16,…
$ `Culmen Length (mm)` <dbl> 39.1, 39.5, 40.3, NA, 36.7, 39.3, 38.9, 39.2, 34…
$ `Culmen Depth (mm)` <dbl> 18.7, 17.4, 18.0, NA, 19.3, 20.6, 17.8, 19.6, 18…
$ `Flipper Length (mm)` <dbl> 181, 186, 195, NA, 193, 190, 181, 195, 193, 190,…
$ `Body Mass (g)` <dbl> 3750, 3800, 3250, NA, 3450, 3650, 3625, 4675, 34…
$ Sex <chr> "MALE", "FEMALE", "FEMALE", NA, "FEMALE", "MALE"…
$ `Delta 15 N (o/oo)` <dbl> NA, 8.94956, 8.36821, NA, 8.76651, 8.66496, 9.18…
$ `Delta 13 C (o/oo)` <dbl> NA, -24.69454, -25.33302, NA, -25.32426, -25.298…
$ Comments <chr> "Not enough blood for isotopes.", NA, NA, "Adult…
skim(penguins_raw)
Name | penguins_raw |
Number of rows | 344 |
Number of columns | 17 |
_______________________ | |
Column type frequency: | |
character | 9 |
Date | 1 |
numeric | 7 |
________________________ | |
Group variables | None |
Variable type: character
skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
---|---|---|---|---|---|---|---|
studyName | 0 | 1.00 | 7 | 7 | 0 | 3 | 0 |
Species | 0 | 1.00 | 33 | 41 | 0 | 3 | 0 |
Region | 0 | 1.00 | 6 | 6 | 0 | 1 | 0 |
Island | 0 | 1.00 | 5 | 9 | 0 | 3 | 0 |
Stage | 0 | 1.00 | 18 | 18 | 0 | 1 | 0 |
Individual ID | 0 | 1.00 | 4 | 6 | 0 | 190 | 0 |
Clutch Completion | 0 | 1.00 | 2 | 3 | 0 | 2 | 0 |
Sex | 11 | 0.97 | 4 | 6 | 0 | 2 | 0 |
Comments | 290 | 0.16 | 18 | 68 | 0 | 10 | 0 |
Variable type: Date
skim_variable | n_missing | complete_rate | min | max | median | n_unique |
---|---|---|---|---|---|---|
Date Egg | 0 | 1 | 2007-11-09 | 2009-12-01 | 2008-11-09 | 50 |
Variable type: numeric
skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
---|---|---|---|---|---|---|---|---|---|---|
Sample Number | 0 | 1.00 | 63.15 | 40.43 | 1.00 | 29.00 | 58.00 | 95.25 | 152.00 | ▇▇▆▅▃ |
Culmen Length (mm) | 2 | 0.99 | 43.92 | 5.46 | 32.10 | 39.23 | 44.45 | 48.50 | 59.60 | ▃▇▇▆▁ |
Culmen Depth (mm) | 2 | 0.99 | 17.15 | 1.97 | 13.10 | 15.60 | 17.30 | 18.70 | 21.50 | ▅▅▇▇▂ |
Flipper Length (mm) | 2 | 0.99 | 200.92 | 14.06 | 172.00 | 190.00 | 197.00 | 213.00 | 231.00 | ▂▇▃▅▂ |
Body Mass (g) | 2 | 0.99 | 4201.75 | 801.95 | 2700.00 | 3550.00 | 4050.00 | 4750.00 | 6300.00 | ▃▇▆▃▂ |
Delta 15 N (o/oo) | 14 | 0.96 | 8.73 | 0.55 | 7.63 | 8.30 | 8.65 | 9.17 | 10.03 | ▃▇▆▅▂ |
Delta 13 C (o/oo) | 13 | 0.96 | -25.69 | 0.79 | -27.02 | -26.32 | -25.83 | -25.06 | -23.79 | ▆▇▅▅▂ |
inspect(penguins_raw)
categorical variables:
name class levels n missing
1 studyName character 3 344 0
2 Species character 3 344 0
3 Region character 1 344 0
4 Island character 3 344 0
5 Stage character 1 344 0
6 Individual ID character 190 344 0
7 Clutch Completion character 2 344 0
8 Sex character 2 333 11
9 Comments character 10 54 290
distribution
1 PAL0910 (34.9%), PAL0809 (33.1%) ...
2 (%) ...
3 Anvers (100%)
4 Biscoe (48.8%), Dream (36%) ...
5 Adult, 1 Egg Stage (100%)
6 N13A1 (0.9%), N13A2 (0.9%) ...
7 Yes (89.5%), No (10.5%)
8 MALE (50.5%), FEMALE (49.5%)
9 (%) ...
Date variables:
name class first last min_diff max_diff n missing
1 Date Egg Date 2007-11-09 2009-12-01 0 days 349 days 344 0
quantitative variables:
name class min Q1 median Q3
1 Sample Number numeric 1.00000 29.00000 58.000000 95.250000
2 Culmen Length (mm) numeric 32.10000 39.22500 44.450000 48.500000
3 Culmen Depth (mm) numeric 13.10000 15.60000 17.300000 18.700000
4 Flipper Length (mm) numeric 172.00000 190.00000 197.000000 213.000000
5 Body Mass (g) numeric 2700.00000 3550.00000 4050.000000 4750.000000
6 Delta 15 N (o/oo) numeric 7.63220 8.29989 8.652405 9.172123
7 Delta 13 C (o/oo) numeric -27.01854 -26.32030 -25.833520 -25.062050
max mean sd n missing
1 152.00000 63.151163 40.4301990 344 0
2 59.60000 43.921930 5.4595837 342 2
3 21.50000 17.151170 1.9747932 342 2
4 231.00000 200.915205 14.0617137 342 2
5 6300.00000 4201.754386 801.9545357 342 2
6 10.02544 8.733382 0.5517703 330 14
7 -23.78767 -25.686292 0.7939612 331 13
6.3 Data Munging
Among the variables that define the physical measurements of the penguins, there are a couple of entries that show missing data. Elsewhere there are more. The variable names also are human-readable, but not really computer-readable.
So let us follow through with our Data Munging Process:
penguins_clean <- penguins_raw %>%
naniar::replace_with_na_all(condition = ~ .x %in% common_na_strings) %>% # replace common NA strings with actual NA
naniar::replace_with_na_all(condition = ~ .x %in% common_na_numbers) %>%
janitor::clean_names(case = "snake") %>% # clean names
dplyr::mutate(across(where(is.character), as_factor)) %>% # make factors
dplyr::relocate(where(is.factor)) # move factors to the right of rownames
glimpse(penguins_clean)
Rows: 344
Columns: 17
$ study_name <fct> PAL0708, PAL0708, PAL0708, PAL0708, PAL0708, PAL0708…
$ species <fct> Adelie Penguin (Pygoscelis adeliae), Adelie Penguin …
$ region <fct> Anvers, Anvers, Anvers, Anvers, Anvers, Anvers, Anve…
$ island <fct> Torgersen, Torgersen, Torgersen, Torgersen, Torgerse…
$ stage <fct> "Adult, 1 Egg Stage", "Adult, 1 Egg Stage", "Adult, …
$ individual_id <fct> N1A1, N1A2, N2A1, N2A2, N3A1, N3A2, N4A1, N4A2, N5A1…
$ clutch_completion <fct> Yes, Yes, Yes, Yes, Yes, Yes, No, No, Yes, Yes, Yes,…
$ sex <fct> MALE, FEMALE, FEMALE, NA, FEMALE, MALE, FEMALE, MALE…
$ comments <fct> Not enough blood for isotopes., NA, NA, Adult not sa…
$ sample_number <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1…
$ date_egg <date> 2007-11-11, 2007-11-11, 2007-11-16, 2007-11-16, 200…
$ culmen_length_mm <dbl> 39.1, 39.5, 40.3, NA, 36.7, 39.3, 38.9, 39.2, 34.1, …
$ culmen_depth_mm <dbl> 18.7, 17.4, 18.0, NA, 19.3, 20.6, 17.8, 19.6, 18.1, …
$ flipper_length_mm <dbl> 181, 186, 195, NA, 193, 190, 181, 195, 193, 190, 186…
$ body_mass_g <dbl> 3750, 3800, 3250, NA, 3450, 3650, 3625, 4675, 3475, …
$ delta_15_n_o_oo <dbl> NA, 8.94956, 8.36821, NA, 8.76651, 8.66496, 9.18718,…
$ delta_13_c_o_oo <dbl> NA, -24.69454, -25.33302, NA, -25.32426, -25.29805, …
Show the Code
penguins_clean %>%
DT::datatable(
caption = htmltools::tags$caption(
style = "caption-side: top; text-align: left; color: black; font-size: 150%;",
"Penguins Dataset (Clean)"
),
options = list(pageLength = 10, autoWidth = TRUE)
) %>%
DT::formatStyle(
columns = names(penguins_clean),
fontFamily = "Roboto Condensed",
fontSize = "12px"
)
6.4 Data Dictionary
We will restrict ourselves to some of the variables that pertain, by and large, to the body dimensions of our penguins:
-
sex
: male and female penguins -
species
: Three adorable types! -
island
: they have islands to themselves!! -
region
: Antarctica, duh!! Hmmm….
-
bill_length_mm
: The length of the penguins’ bills -
bill_depth_mm
: See the picture!! -
flipper_length_mm
: Flippers! Penguins have “hands”!! -
body_mass_g
: Mass in grams. Grams? Grams??? Why, these penguins are like human babies!!❤️ -
culmen_depth_mm
: Depth of the culmen (the upper ridge of the bill) -
culmen_length_mm
: Length of the culmen
penguins
dataset
- This is a smallish dataset (344 rows, 8 columns).
- They define the various physical dimensions of the penguins, along with other variables pertaining to their study.
6.5 Plotting Densities
ggplot2::theme_set(new = theme_custom())
gf_density(~body_mass_g, data = penguins_clean) %>%
gf_labs(title = "Plot A: Penguin Masses", caption = "ggformula")
ggplot2::theme_set(new = theme_custom())
penguins_clean %>%
gf_density(~body_mass_g,
fill = ~species,
color = "black"
) %>%
gf_refine(scale_color_viridis_d(
option = "magma",
aesthetics = c("colour", "fill")
)) %>%
gf_labs(
title = "Plot B: Penguin Body Mass by Species",
caption = "ggformula"
)
ggplot2::theme_set(new = theme_custom())
penguins_clean %>%
gf_density(
~body_mass_g,
fill = ~species,
color = "black",
alpha = 0.3
) %>%
gf_facet_wrap(vars(sex)) %>%
gf_labs(title = "Plot C: Penguin Body Mass by Species and facetted by Sex", caption = "ggformula")
ggplot2::theme_set(new = theme_custom())
penguins_clean %>%
gf_density(~body_mass_g, fill = ~species, color = "black") %>%
gf_facet_wrap(vars(sex), scales = "free_y", nrow = 2) %>%
gf_labs(
x = "Body Mass of Penguins", title = "Plot D: Penguin Body Mass by Species and facetted by Sex",
subtitle = "Free y-scale",
caption = "ggformula"
) %>%
gf_refine(scale_fill_brewer(palette = "Set1")) %>%
gf_theme(theme(axis.text.x = element_text(
angle = 45,
hjust = 1
)))
ggplot2::theme_set(new = theme_custom())
penguins_clean %>%
ggplot() +
geom_density(aes(x = body_mass_g, fill = species),
alpha = 0.3,
color = "black"
) +
scale_color_brewer(
palette = "Set1",
aesthetics = c("colour", "fill")
) +
labs(
title = "Plot B: Penguin Body Mass by Species",
caption = "ggplot"
)
ggplot2::theme_set(new = theme_custom())
penguins_clean %>% ggplot() +
geom_density(aes(x = body_mass_g, fill = species),
color = "black",
alpha = 0.3
) +
facet_wrap(vars(sex)) +
labs(title = "Plot C: Penguin Body Mass by Species and facetted by Sex", caption = "ggplot")
ggplot2::theme_set(new = theme_custom())
penguins_clean %>% ggplot() +
geom_density(aes(x = body_mass_g, fill = species),
alpha = 0.3,
color = "black"
) +
facet_wrap(vars(sex), scales = "free_y", nrow = 2) +
labs(
title = "Plot D: Penguin Body Mass by Species and facetted by Sex",
subtitle = "Free y-scale", caption = "ggplot"
) +
scale_fill_brewer(palette = "Set1") +
theme(theme(axis.text.x = element_text(angle = 45, hjust = 1)))
penguin
Densities
Pretty much similar conclusions as with histograms. Although densities may not be used much in business contexts, they are better than histograms when comparing multiple distributions! So you should use them!
6.6 Ridge Plots
Sometimes we may wish to show the distribution/density of a Quant variable, against several levels of a Qual variable. For instance, the prices of different items of furniture, based on the furniture “style” variable. Or the sales
of a particular line of products, across different shops or cities. We did this with both histograms and densities, by colouring based on a Qual variable, and by facetting using a Qual variable. There is a third way, using what is called a ridge plot. ggformula supports this plot by importing/depending upon the ggridges package. ggridges provides direct support for ridge plots, and can be used as an extension to ggplot2 and ggformula.
ggplot2::theme_set(new = theme_custom())
gf_density_ridges(drv ~ hwy,
fill = ~drv,
alpha = 0.5, # colour saturation
data = mpg
) %>%
gf_refine(scale_fill_brewer(
name = "Drive Type",
palette = "Spectral"
)) %>%
gf_labs(
title = "Mileage vs Drive Type",
subtitle = "Ridge Plot",
x = "Highway Mileage",
y = "Drive Type"
)
ggplot2::theme_set(new = theme_custom())
ggplot(data = mpg, mapping = aes(x = hwy, y = drv, fill = drv)) +
geom_density_ridges(alpha = 0.5) +
scale_fill_brewer(name = "Drive Type", palette = "Spectral") +
labs(
title = "Mileage vs Drive Type",
subtitle = "Ridge Plot",
x = "Highway Mileage",
y = "Drive Type"
)
mpg
Ridge Plots
This is another way of visualizing multiple distributions, of a Quant variable at different levels of a Qual variable. We see that the distribution of hwy
mileage varies substantially with drv
type.
7 Wait, But Why?
- Densities are sometimes easier to compare side by side. That is what Claus Wilke says, at least. Perhaps because they look less “busy” than histograms.
- Ridge Density Plots are very cool when it comes to comparing the density of a Quant variable as it varies against the levels of a Qual variable, without having to
facet
orgroup
. - It is possible to plot 2D-densities too, for two Quant variables, which give very evocative contour-like plots. Try to do this with the
faithful
dataset in R.
8 Conclusion
- Histograms and Frequency Distributions are both used for Quantitative data variables
- Whereas Histograms “dwell upon” counts, ranges, means and standard deviations
- Frequency Density plots “dwell upon” probabilities and densities
- Ridge Plots are density plots used for describing one Quant and one Qual variable (by inherent splitting)
- We can split all these plots on the basis of another Qualitative variable.(Ridge Plots are already split)
- Long tailed distributions need care in visualization and in inference making!
9 Your Turn
Which would be the Group By
variables here? And what would you summarize? With which function?
10 References
- Winston Chang (2024). R Graphics Cookbook. https://r-graphics.org
- See the scrolly animation for a histogram at this website: Exploring Histograms, an essay by Aran Lunzer and Amelia McNamara
- Minimal R using
mosaic
. https://cran.r-project.org/web/packages/mosaic/vignettes/MinimalRgg.pdf
- Sebastian Sauer, Plotting multiple plots using purrr::map and ggplot
R Package Citations
Package | Version | Citation |
---|---|---|
ggridges | 0.5.7 | Wilke (2025) |
NHANES | 2.1.0 | Pruim (2015) |
resampledata3 | 1.0 | Chihara and Hesterberg (2022) |
rtrek | 0.5.2 | Leonawicz (2025) |
TeachHist | 0.2.1 | Lange (2023) |
TeachingDemos | 2.13 | Snow (2024) |
tidyplots | 0.3.1 | Engler (2025) |
tinyplot | 0.5.0 | McDermott, Arel-Bundock, and Zeileis (2025) |
tinytable | 0.13.0 | Arel-Bundock (2025) |
visualize | 4.5.0 | Balamuta (2023) |
Citation
@online{v.2024,
author = {V., Arvind},
title = {\textless Iconify-Icon Icon=“clarity:bell-Curve-Line”
Width=“1.2em”
Height=“1.2em”\textgreater\textless/Iconify-Icon\textgreater{}
{Distributions}},
date = {2024-06-22},
url = {https://madhatterguide.netlify.app/content/courses/Analytics/10-Descriptive/Modules/26-Distributions/},
langid = {en},
abstract = {Quant and Qual Variable Graphs and their Siblings}
}