Deep dive: stats + scales + guides

Lecture 5

Dr. Benjamin Soltoff

Cornell University
INFO 3312/5312 - Spring 2026

February 3, 2026

Announcements

Announcements

• Waitlist update
  • 15 pins distributed so far
  • INFO 3312: 0 seats available and 10 on the waitlist (4 IS majors)
  • INFO 5312: 2 seats available and 0 on the waitlist
• Must use PIN by 11:59pm tonight
• Homework 02 due tomorrow
• Project 01

Project 01

• Project description
• Team assignments on Thursday
• Deliverables
• Complete team preference survey

• What is the story?
• What challenges do you see with the design?

Learning objectives

• Define the statistical adjustment and scales components of the grammar of graphics
• Demonstrate how to use stat_*() functions from {ggplot2}
• Implement scale transformations for \(x\) and \(y\) axes
• Modify guides to change the visual appearance of scales on plots

Setup

World Bank indicators

world_bank <- read_rds("data/wb-indicators.rds")
world_bank

# A tibble: 174 × 8
   iso2c country               year gdp_per_cap female_labor_pct life_exp      pop income_level     
   <chr> <chr>                <dbl>       <dbl>            <dbl>    <dbl>    <dbl> <fct>            
 1 AF    Afghanistan           2023        414.             6.85     66.0 41454761 Low income       
 2 AO    Angola                2023       2916.            49.4      64.6 36749906 Lower middle inc…
 3 AL    Albania               2023       9731.            46.4      79.6  2414095 Upper middle inc…
 4 AE    United Arab Emirates  2023      49851.            22.3      82.9 10483751 High income      
 5 AR    Argentina             2023      14262.            43.2      77.4 45538401 Upper middle inc…
 6 AM    Armenia               2023       8159.            47.2      77.5  2964300 Upper middle inc…
 7 AU    Australia             2023      65058.            47.4      83.1 26659922 High income      
 8 AT    Austria               2023      56580.            46.9      81.5  9131761 High income      
 9 AZ    Azerbaijan            2023       7133.            49.9      74.4 10153958 Upper middle inc…
10 BI    Burundi               2023        251.            51.6      63.7 13689450 Low income       
# ℹ 164 more rows

Stats

Stats < > geoms

• Statistical transformation (stat) transforms the data, typically by summarizing
• Many of {ggplot2}’s stats are used behind the scenes to generate many important geoms

stat	geom
stat_bin()	geom_bar(), geom_freqpoly(), geom_histogram()
stat_bin2d()	geom_bin2d()
stat_bindot()	geom_dotplot()
stat_binhex()	geom_hex()
stat_boxplot()	geom_boxplot()
stat_contour()	geom_contour()
stat_quantile()	geom_quantile()
stat_smooth()	geom_smooth()
stat_sum()	geom_count()

stat_boxplot()

Layering with stats

ggplot(world_bank, aes(x = income_level, y = life_exp)) +
  geom_point(alpha = 0.5) +
  stat_summary(geom = "point", fun = "median", color = "red", size = 5, pch = 4, stroke = 2)

Alternate: layering with stats

ggplot(world_bank, aes(x = income_level, y = life_exp)) +
  geom_point(alpha = 0.5) +
  geom_point(stat = "summary", fun = "median", color = "red", size = 5, pch = 4, stroke = 2)

Alternate alternate: do it with {dplyr}

world_bank |>
  group_by(income_level) |>
  summarize(median_life_exp = median(life_exp)) |>
  ggplot(mapping = aes(x = income_level)) +
  geom_point(data = world_bank, mapping = aes(y = life_exp), alpha = 0.5) +
  geom_point(mapping = aes(y = median_life_exp), color = "red", size = 5, pch = 4, stroke = 2)

Scales

What is a scale?

• Each scale is a function from a region in data space (the domain of the scale) to a region in aesthetic space (the range of the scale)

• The axis or legend (also known as a guide) is the inverse function: it allows you to convert visual properties back to data

Scale specification

Every aesthetic in your plot is associated with exactly one scale:

• Code
• Plot

# automatic scales
ggplot(world_bank, aes(x = female_labor_pct, y = life_exp, color = income_level)) +
  geom_point(alpha = 0.8)

# manual scales
ggplot(world_bank, aes(x = female_labor_pct, y = life_exp, color = income_level)) +
  geom_point(alpha = 0.8) +
  scale_x_continuous() +
  scale_y_continuous() +
  scale_color_discrete()

Anatomy of a scale function

scale_<aes>_<type>()

• Always starts with scale
• <aes>: Name of the primary aesthetic (e.g., color, shape, x)
• <type>: Name of the scale (e.g., continuous, discrete, brewer)

Some scale functions add a fourth component to the function name

scale_color_viridis_b()
scale_color_viridis_c()
scale_color_viridis_d()

1

Binned palette

2

Continuous palette

3

Discrete palette

Guess the output

What will the x-axis label of the following plot say?

ggplot(world_bank, aes(x = female_labor_pct, y = life_exp, color = income_level)) +
  geom_point(alpha = 0.8) +
  scale_x_continuous(name = "female_labor_pct") +
  scale_x_continuous(name = "Female labor (percentage of total workforce)")

“Address” messages

ggplot(world_bank, aes(x = female_labor_pct, y = life_exp, color = income_level)) +
  geom_point(alpha = 0.8) +
  scale_x_continuous(name = "female_labor_pct") +
  scale_x_continuous(name = "Female labor (percentage of total workforce)")

Scale for x is already present.
Adding another scale for x, which will replace the existing scale.

What happens if incorrect pairing?

• Plots
• Results

ggplot(
  data = world_bank,
  mapping = aes(
    x = income_level,
    y = life_exp
  )
) +
  geom_point(alpha = 0.5) +
  scale_x_continuous()

ggplot(
  data = world_bank,
  mapping = aes(
    x = income_level,
    y = life_exp
  )
) +
  geom_point(alpha = 0.5) +
  scale_y_discrete()

Error in `scale_x_continuous()`:
! Discrete value supplied to a continuous scale.
ℹ Example values: Low income, Lower middle income, Upper middle income, and High income.

Transformations

When working with continuous data, the default is to map linearly from the data space onto the aesthetic space, but this scale can be transformed

• Linear
• Transformed

ggplot(
  world_bank,
  aes(x = female_labor_pct, y = gdp_per_cap)
) +
  geom_point(alpha = 0.5)

ggplot(
  world_bank,
  aes(x = female_labor_pct, y = gdp_per_cap)
) +
  geom_point(alpha = 0.5) +
  scale_y_continuous(trans = "log10")

Common scale transformations

Box-Cox scale transformations

Continuous scale transformations

Name	Function \(f(x)\)	Inverse \(f^{-1}(y)\)
asn	\(\tanh^{-1}(x)\)	\(\tanh(y)\)
exp	\(e ^ x\)	\(\log(y)\)
identity	\(x\)	\(y\)
log	\(\log(x)\)	\(e ^ y\)
log10	\(\log_{10}(x)\)	\(10 ^ y\)
log2	\(\log_2(x)\)	\(2 ^ y\)
logit	\(\log(\frac{x}{1 - x})\)	\(\frac{1}{1 + e(y)}\)
pow10	\(10^x\)	\(\log_{10}(y)\)
probit	\(\Phi(x)\)	\(\Phi^{-1}(y)\)
reciprocal	\(x^{-1}\)	\(y^{-1}\)
reverse	\(-x\)	\(-y\)
sqrt	\(x^{1/2}\)	\(y ^ 2\)

Convenience functions for transformations

ggplot(
  world_bank,
  aes(x = female_labor_pct, y = life_exp)
) +
  geom_point(alpha = 0.5) +
  scale_y_continuous(trans = "log10")

ggplot(
  world_bank,
  aes(x = female_labor_pct, y = life_exp)
) +
  geom_point(alpha = 0.5) +
  scale_y_log10()

Application exercise

ae-04

Instructions

• Go to the course GitHub org and find your ae-04 (repo name will be suffixed with your GitHub name).
• Clone the repo in Positron, run renv::restore() to install the required packages, open the Quarto document in the repo, and follow along and complete the exercises.
• Render, commit, and push your edits by the AE deadline – end of the day

Work through part 1

Implement log transformations.

07:00

Guides

What is a guide?

Guides are axes and legends:

Customizing axes

ggplot(world_bank, aes(x = gdp_per_cap, y = life_exp)) +
  geom_point(alpha = 0.5) +
  scale_y_continuous(
    name = "Life expectancy at birth"
  )

Customizing axes

Why do 50 and 90 not appear on the \(y\)-axis?

ggplot(world_bank, aes(x = gdp_per_cap, y = life_exp)) +
  geom_point(alpha = 0.5) +
  scale_y_continuous(
    name = "Life expectancy at birth",
    breaks = seq(from = 50, to = 90, by = 10)
  )

Customizing axes

ggplot(world_bank, aes(x = gdp_per_cap, y = life_exp)) +
  geom_point(alpha = 0.5) +
  scale_y_continuous(
    name = "Life expectancy at birth",
    breaks = seq(from = 50, to = 90, by = 10),
    limits = c(50, 90)
  )

Customizing axes

ggplot(world_bank, aes(x = gdp_per_cap, y = life_exp)) +
  geom_point(alpha = 0.5) +
  scale_y_continuous(
    name = "Life expectancy at birth",
    breaks = seq(from = 50, to = 90, by = 10),
    limits = c(50, 90)
  ) +
  scale_x_continuous(
    name = "GDP per capita",
    breaks = c(0, 5e04, 1e05),
    labels = c("$0", "$50,000", "$100,000")
  )

Customizing axes

library(scales)

ggplot(world_bank, aes(x = gdp_per_cap, y = life_exp)) +
  geom_point(alpha = 0.5) +
  scale_y_continuous(
    name = "Life expectancy at birth",
    breaks = seq(from = 50, to = 90, by = 10),
    limits = c(50, 90)
  ) +
  scale_x_continuous(
    name = "GDP per capita",
    labels = label_currency()
  )

Customizing axes

ggplot(world_bank, aes(x = gdp_per_cap, y = life_exp)) +
  geom_point(alpha = 0.5) +
  scale_y_continuous(
    name = "Life expectancy at birth",
    breaks = seq(from = 50, to = 90, by = 10),
    limits = c(50, 90)
  ) +
  scale_x_continuous(
    name = "GDP per capita",
    labels = label_currency(scale_cut = cut_short_scale())
  )

Modifying scale guides

Scale guides

Scale guides

Scale type	Default guide type	Function
Continuous scales for color/fill aesthetics	colorbar	guide_colorbar()
Binned scales for color/fill aesthetics	colorsteps	guide_colorsteps()
Position scales (continuous, binned and discrete)	axis	guide_axis()
Discrete scales (except position scales)	legend	guide_legend()
Binned scales (except position/color/fill scales)	bins	guide_bins()

Implementation

... +
  guides(color = guide_colorbar(theme = theme(...), ...))

... +
  scale_color_gradient(guide = guide_colorbar(theme = theme(...), ...))

Example implementation

• Reverse direction
• Change bar height
• Horizontal bar
• Label position

base_plot + guides(color = guide_colorbar(reverse = TRUE))

base_plot + guides(color = guide_colorbar(theme = theme(legend.key.height = unit(2, "cm"))))

base_plot + guides(color = guide_colorbar(theme = theme(legend.direction = "horizontal")))

base_plot + guides(color = guide_colorbar(theme = theme(legend.text.position = "left")))

Application exercise

ae-04

Work through part 2

Recreate this plot.

10:00

Wrap up

Recap

• {ggplot2} implements statistical transformations (typically as defaults)
• Scales visually encode data to mappings
• Guides control the appearance of scales
• {scales} package provides a wide range of transformation and formatting functions
• Use guide_*() functions to customize the appearance of guides

Acknowledgements

• Slides derived in part from STA 313: Advanced Data Visualization