Stats + scales + guides

Lecture 05

Dr. Benjamin Soltoff

Cornell University
INFO 3312/5312 - Fall 2026

September 8, 2026

Announcements

Announcements

• Homework 02 due tomorrow

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

• Scales should be designed in a manner that makes it easy for the viewer to interpret the 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

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(transform = "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(transform = "log10")

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

Select an optimal transformation

04:00

Countries with higher GDP tend to have higher life expectancy

Multiple scales

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)")

Guess the output

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.

“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 (percentage of total workforce)")

Dual-axis scales

02:00

Appropriate usage of secondary axis

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

Customizing scales and guides

Instructions

Identify improvements to the scales and guides for the following plot. Explain why they would improve the interpretability of the chart.

10:00

Live-code a solution

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