library(tidyverse) ; library(here)
law <- read_csv(file = here("data", "law_data.csv")) |>
mutate(
sex = factor(sex, levels = c(1, 2), labels = c("Female", "Male")),
first_pf_fct = factor(first_pf, levels = c(0, 1), labels = c("Fail", "Pass"))
) |>
filter(region_first != "PO") |>
left_join(
tibble(
region_first = c("FW","GL","MS","MW","Mt","NE","NG","NW","SC","SE"),
freion_first_long = c(
"Far West", "Great Lakes", "Midsouth", "Midwest",
"Mountain West", "Northeast", "New Englant", "Northwest",
"South Central", "Southeast")
),
by = "region_first"
)
# Colours used for sex throughout the chapter (colourblind-friendly)
sex_cols <- c("Female" = "#D55E00", "Male" = "#009E73")
# Applies a theme to every plot that follows
theme_set(theme_minimal(base_size = 14) + theme(plot.title.position = "plot"))Data Visualization with R
Chapter 5 – Comparing groups
September 28, 2026
Strategy 1: Superimpose the Distributions
- Groups are directly comparable: same axes, same panel.
- Transparency (
alpha) is needed, otherwise the front group hides the back one. - This strategy usually work well with two or three groups.
Strategy 2: Separate Into Panels
- Each panel stays readable even with many groups.
- Stack the panels vertically so the x-axes line up and shifts are easy to spot.
- The colour is redundant with the facet: we hide the legend with
guides().
Use after_stat(density) When Group Sizes Differ
With raw counts (default with geom_histogram()), a larger group would look “taller” even if its distribution had the same shape. Densities put every group on the same scale.
Boxplots and Violins: Many Groups Side by Side
When there are many groups, superimposing densities becomes unreadable.
In such cases, it may be better to use boxplots or violins that place one distribution per position on the categorical axis.
The default order is usually not the desired one
In the figure above, the order of the categories is alphabetical, which carries no information. Let us change this!
Order the Groups by What You Compare
fct_reorder() (from {forcats}, part of the tidyverse) reorders the levels of a factor according to a statistic computed on another variable.
Now the eye can follow a gradient from the lowest to the highest median.
Rule of Thumb
Unless the categories have a natural order (age groups, months…), never leave them in alphabetical order. Order them by the statistic you want the reader to compare. By default, the median of the variabled given as the second argument is used.
Showing More Than a Box
A boxplot summarises a distribution with five numbers and hides its shape. Combine layers to show more (using violins).
ggplot(
data = law,
mapping = aes(
x = fct_reorder(race, UGPA, .fun = median),
y = UGPA
)
) +
geom_violin(fill = "grey90", colour = "grey60") +
geom_boxplot(width = 0.15, outlier.shape = NA) +
stat_summary(
fun = mean, geom = "point",
colour = "#CC79A7", size = 2.5
) +
coord_flip() +
labs(x = NULL, y = "Undergraduate GPA")- Violin: full shape of the distribution.
- Box: median and quartiles.
- Red dot: the mean, via
stat_summary().
outlier.shape = NA: the outliers may densify the plot, they may be removed.
Solution 1: Two Versions
p_super <- ggplot(
data = law,
mapping = aes(x = LSAT, fill = first_pf_fct)
) +
geom_density(alpha = 0.4) +
labs(x = "LSAT score", y = "Density", fill = "First attempt")
p_facet <- ggplot(
data = law,
mapping = aes(x = LSAT, fill = first_pf_fct)
) +
geom_histogram(
mapping = aes(y = after_stat(density)),
binwidth = 2, colour = "white"
) +
facet_wrap(facets = vars(first_pf_fct), ncol = 1) +
guides(fill = "none") +
labs(x = "LSAT score", y = "Density")
With only two groups, superimposing is more direct: the shift between the two densities is visible at a glance.
Facets are more useful when a third or fourth group would make the overlay too busy.
Solution 1: Ordered Comparison of ZFYA
The summary table:
law |>
group_by(race) |>
summarise(
n = n(), mean = mean(ZFYA), median = median(ZFYA),
.groups = "drop"
) |>
arrange(median)# A tibble: 8 × 4
race n mean median
<chr> <int> <dbl> <dbl>
1 Black 1282 -0.829 -0.91
2 Puertorican 110 -0.626 -0.785
3 Amerindian 99 -0.600 -0.58
4 Mexican 389 -0.506 -0.55
5 Hispanic 488 -0.314 -0.4
6 Asian 845 -0.288 -0.34
7 Other 293 -0.0408 -0.08
8 White 18284 0.213 0.19 
Where the mean and the median of a group differ greatly, the distribution is skewed (or has outliers). In this kind of situation, the choice of the summary statistic matters, and the boxplot or violin shows why.
Stacked, Dodged, or Filled Bars?
The same data can be encoded in three ways. Each one answers a different question.
Question answered: how do the counts of each category compare within a group?
Proportions are still hidden by the differences in group sizes.
Question answered: how do the proportions differ between groups?
Group sizes are hidden, which is why the n should be reported elsewhere.
Racial Composition by Region
- Regions on the y-axis: horizontal bars leave room for long labels.
- Regions ordered by number of students with
fct_infreq(). - A qualitative palette, since the categories have no order.
Success Rate by Region: Compute First, Then Plot
When the quantity of interest is the rate of a single category (here the pass rate), a filled bar with two colours is wasteful. Compute the rate and plot it directly.
pass_region <- law |>
group_by(region_first) |>
summarise(
n = n(),
pass_rate = mean(first_pf),
.groups = "drop"
)
ggplot(
data = pass_region,
mapping = aes(
x = pass_rate,
y = fct_reorder(region_first, pass_rate)
)
) +
geom_col() +
scale_x_continuous(labels = scales::percent) +
labs(x = "First-attempt pass rate", y = NULL)
Stay Careful With the Bar Axis
Recall from the introduction of the class that a bar’s length encodes its value: the axis of a bar chart must start at zero.
Solution 2: Composition Within Groups
# Q1
sex_race <- law |>
count(race_grp, sex) |>
group_by(race_grp) |>
mutate(prop = n / sum(n)) |>
ungroup()
# Q2
p_col <- ggplot(
data = sex_race,
mapping = aes(x = race_grp, y = prop, fill = sex)
) +
geom_col(position = "stack") +
scale_y_continuous(labels = scales::percent) +
scale_fill_manual(values = sex_cols) +
labs(x = NULL, y = "Share within group", fill = "Sex")
# Q3
p_fill <- ggplot(
data = law,
mapping = aes(x = race_grp, fill = sex)
) +
geom_bar(position = "fill") +
scale_y_continuous(labels = scales::percent) +
scale_fill_manual(values = sex_cols) +
labs(x = NULL, y = "Share within group", fill = "Sex")
The two shares add up to a whole. Hence, stacking the proportions is natural.
Dodging would place two bars per group, which makes the comparison between groups harder.
Solution 2: Pass Rate by Race
pass_race <- law |>
group_by(race_grp) |>
summarise(
n = n(),
pass_rate = mean(first_pf),
.groups = "drop"
)
ggplot(
data = pass_race,
mapping = aes(
x = pass_rate,
y = fct_reorder(race_grp, pass_rate)
)
) +
geom_col() +
scale_x_continuous(labels = scales::percent) +
labs(x = "First-attempt pass rate", y = NULL)
The pass rate differences between racial groups are much larger than the differences in sex composition. That does not tell us why (this is a descriptive plot), but it is a striking pattern that deserves a careful presentation.
Dot Plots and Lollipops
Bars use a lot of ink for a single number. A dot on a light grid line carries the same information with less clutter, and the axis no longer has to start at zero (dots encode position, not length).
pass_region <- law |>
group_by(region_first) |>
summarise(
n = n(),
pass_rate = mean(first_pf),
.groups = "drop"
) |>
mutate(region_first = fct_reorder(region_first, pass_rate))
ggplot(
data = pass_region,
mapping = aes(x = pass_rate, y = region_first)
) +
geom_segment(
mapping = aes(
x = 0, xend = pass_rate,
y = region_first, yend = region_first
),
colour = "grey70"
) +
geom_point(colour = "dodgerblue", size = 3) +
scale_x_continuous(labels = scales::percent) +
labs(x = "First-attempt pass rate", y = NULL)
A Question to Keep in Mind
Some of these dots are computed on a small number of students, others on thousands. Should we trust them equally? We come back to this in Part 4.
Two Grouping Variables: Colour Inside a Dot Plot
To compare men and women within each region, put the two dots on the same line: the gap between them is the quantity of interest.
pass_rs <- law |>
group_by(region_first, sex) |>
summarise(
n = n(), pass_rate = mean(first_pf), .groups = "drop"
)
ggplot(
data = pass_rs,
mapping = aes(
x = pass_rate,
y = fct_reorder(region_first, pass_rate, .fun = mean),
colour = sex
)
) +
geom_point(size = 3) +
scale_colour_manual(values = sex_cols) +
scale_x_continuous(labels = scales::percent) +
labs(x = "First-attempt pass rate", y = NULL, colour = "Sex")
Heatmaps for Two Categorical Variables
When two categorical variables are crossed and the outcome is a number, geom_tile() draws one coloured cell per combination. Since the pass rate is a continuous variable without a meaningful midpoint, we use a sequential scale (Chapter 3).
pass_heat <- law |>
group_by(region_first, race_grp) |>
summarise(
n = n(), pass_rate = mean(first_pf), .groups = "drop"
)
ggplot(
data = pass_heat,
mapping = aes(x = race_grp, y = region_first, fill = pass_rate)
) +
geom_tile(colour = "white") +
geom_text(
mapping = aes(label = scales::percent(pass_rate, accuracy = 1)),
colour = "white", size = 3.5
) +
scale_fill_viridis_c(labels = scales::percent) +
labs(x = NULL, y = NULL, fill = "Pass rate")
Each Cell Is Not Equally Reliable
Some cells contain thousands of students, others only a handful. The heatmap treats them all the same. This is exactly the issue tackled in Part 4.
Ridgeline Plots for Many Distributions
{ggridges} stacks density curves vertically with slight overlap. It is a good alternative to superimposed densities when you have many groups (typically more than 4).
The groups are ordered by median: shifts in location are obvious, differences in shape too.
Solution 3: Three Encodings
p_b <-
ggplot(
data = pass_rs,
mapping = aes(
x = pass_rate,
y = fct_reorder(region_first, pass_rate, .fun = mean),
colour = sex
)
) +
geom_point(size = 3) +
scale_colour_manual(values = sex_cols) +
scale_x_continuous(labels = scales::percent) +
labs(x = "First-attempt pass rate", y = NULL, colour = "Sex")
- The facets (c) make the ranking of regions easy to compare across sexes, because the vertical order is shared by both panels.
- The dot plot with two colours (b) makes the within-region gap easy to read: the two dots are on the same line.
- The dodged bars (a) use the most ink and are the hardest to read with 10 regions.
Solution 3: Bonus, Plot the Gap Directly
gap_region <- pass_rs |>
select(region_first, sex, pass_rate) |>
pivot_wider(names_from = sex, values_from = pass_rate) |>
mutate(gap = Male - Female)
ggplot(
data = gap_region,
mapping = aes(
x = gap,
y = fct_reorder(region_first, gap)
)
) +
geom_vline(xintercept = 0, colour = "grey50") +
geom_point(size = 3, colour = "dodgerblue") +
labs(
x = "Pass rate gap (Male - Female)",
y = NULL
)
Plotting the gap directly makes the quantity of interest the position on the axis, compared against a meaningful reference (zero).
The price to pay is that the levels of the two groups are no longer shown, and that we cannot yet tell whether a small gap is a real difference or just noise: that question is the subject of Part 4!
Step 1: Show the Sample Size
A simple and honest fix: put the number of observations in the label of each group.
pass_race_all <- law |>
group_by(race) |>
summarise(
n = n(), pass_rate = mean(first_pf), .groups = "drop"
) |>
mutate(label = str_c(race, " (n = ", n, ")"))
ggplot(
data = pass_race_all,
mapping = aes(
x = pass_rate,
y = fct_reorder(label, pass_rate)
)
) +
geom_point(size = 3, colour = "dodgerblue") +
scale_x_continuous(labels = scales::percent) +
labs(x = "First-attempt pass rate", y = NULL)
Step 3: Plot the Intervals
geom_pointrange() draws a point with a vertical (or, after coord_flip(), horizontal) interval. It requires ymin and ymax.
ggplot(
data = pass_ci |>
mutate(label = str_c(race, " (n = ", n, ")")),
mapping = aes(
x = fct_reorder(label, pass_rate),
y = pass_rate, ymin = lower, ymax = upper
)
) +
geom_pointrange(colour = "dodgerblue") +
coord_flip() +
scale_y_continuous(labels = scales::percent) +
labs(
x = NULL, y = "First-attempt pass rate",
caption = "Points: observed rate. Bars: approximate 95% CI."
)
Small groups have wide intervals. Intervals that overlap heavily warn us against reading too much into the ranking.
Uncertainty on a Mean: stat_summary()
For a numerical variable, stat_summary() computes and draws an interval directly from the raw data, without a prior summarise().
mean_secomputes the mean and its standard error;mult = 1.96turns it into an approximate 95% interval.mean_cl_normal(also from{Hmisc}) is a closely related alternative, using a \(t\)-based interval instead of a normal one, more appropriate for smaller samples.
Showing Uncertainty is Important
An estimate without a measure of uncertainty is misleading, especially for small groups.
Whenever you compare group means or rates, show the interval or, at least, the number of observations.
Solution 4: Intervals by Region and Sex
pass_rs_counts <- law |>
group_by(region_first, sex) |>
summarise(
n = n(),
successes = sum(first_pf),
.groups = "drop"
)
pass_rs_ci <- pass_rs_counts |>
bind_cols(
Hmisc::binconf(pass_rs_counts$successes, pass_rs_counts$n, method = "wilson") |>
as_tibble() |>
rename(pass_rate = PointEst, lower = Lower, upper = Upper)
)
ggplot(
data = pass_rs_ci,
mapping = aes(
x = sex, y = pass_rate, ymin = lower, ymax = upper,
colour = sex
)
) +
geom_pointrange() +
scale_colour_manual(values = sex_cols) +
scale_y_continuous(labels = scales::percent) +
facet_wrap(facets = vars(region_first), ncol = 5) +
guides(colour = "none") +
labs(x = NULL, y = "First-attempt pass rate")
- The regions with the fewest students have the widest intervals.
- For those regions, the point estimates differ the most between sexes.
- Consequently, a large part of the visible gap is compatible with noise.
Solution 4: Removing Small Cells from the Heatmap
pass_heat |>
mutate(pass_rate = if_else(n < 30, NA_real_, pass_rate)) |>
ggplot(mapping = aes(x = race_grp, y = region_first, fill = pass_rate)) +
geom_tile(colour = "white") +
scale_fill_viridis_c(labels = scales::percent, na.value = "grey90") +
labs(
x = NULL, y = NULL, fill = "Pass rate",
caption = "Cells with less than 30 students are removed."
)
- Cells with too few students are now shown in grey rather than as a misleading colour.
- A threshold like 30 is a convention, not a rule. What matters is being explicit about it (state it in a caption).
- Another possibility is to keep all cells and map the size of the tile or the transparency (
alpha) ton.
Overplotting: Three Fixes
geom_hex() and geom_bin2d() count the observations in each cell (this is a stat at work, a seen in Chapter 3): the fill encodes a count rather than a raw observation.
Adding a Trend: Linear or Flexible?
ggplot(
data = law,
mapping = aes(x = LSAT, y = ZFYA)
) +
geom_point(alpha = 0.1) +
geom_smooth(
method = "lm", colour = "#D81B60", fill = "#D81B60"
) +
geom_smooth(colour = "#1E88E5", fill = "#1E88E5") +
labs(
x = "LSAT score", y = "Standardized first-year average",
caption = "Red: linear fit; Blue: GAM fit"
)- Red: linear fit (
method = "lm"). - Blue: flexible fit. For large datasets, the default method of
geom_smooth()is a generalized additive model (GAM). - The band is a confidence interval around the fitted curve, not a range containing most of the observations.
The Band Is Not the Spread of the Data
With a large sample, the confidence band is very narrow, while the observations are widely scattered around the line.
Do not confuse uncertainty on the trend with variability of the outcome.
The Same Relationship, Group by Group
Mapping a discrete variable to colour creates one trend per group (the groups mechanism from Chapter 3).
Both lines are nearly parallel: the relationship between LSAT and ZFYA looks similar for women and men.
More Groups: Facets
With more groups, colours become confusing. Use facets and keep the trend line in each panel.
The slopes can be compared across panels because the scales are shared (default scales = "fixed").
Solution 5: A Possible Answer
Solution 5: A Possible Answer
Since there are only two groups, the two trends on the same graph makes the comparison easier.
Solution 5: A Possible Answer
# Q4
ggplot(
data = law,
mapping = aes(x = UGPA, y = ZFYA)
) +
geom_point(alpha = 0.05) +
geom_smooth(method = "lm", colour = "#D81B60") +
facet_wrap(facets = vars(race_grp), ncol = 2) +
labs(
x = "Undergraduate GPA",
y = "Standardized first-year average",
caption = "Each panel is a group. Line: linear fit with 95% CI."
)
Possible caption: “Students with a higher undergraduate GPA tend to have a higher first-year average, in each of the four groups. This is a descriptive association, not a causal effect.”
Trap 1: The Truncated Bar Axis
The Rule
For bars, the axis must start at zero because the length of the bar is the encoding.
For dots or intervals (position encodings), a non-zero axis can be acceptable, as long as it is clearly labelled.
Solution 6: Problems and a Fix
Problems: (1) the axis is truncated on a bar chart; (2) the categories are in alphabetical order; (3) the sample sizes are not shown; (4) no uncertainty interval, although some groups are very small; (5) the title is a conclusion, not a description.
pass_ci |>
mutate(label = str_c(race, " (n = ", n, ")")) |>
ggplot(
mapping = aes(
x = fct_reorder(label, pass_rate),
y = pass_rate, ymin = lower, ymax = upper
)
) +
geom_pointrange(colour = "dodgerblue") +
coord_flip() +
scale_y_continuous(labels = scales::percent) +
labs(
title = "First-attempt bar exam pass rate, by racial group",
subtitle = "Points: observed rate. Bars: approximate 95% CI.",
x = NULL, y = "Pass rate",
caption = "Source: LSAC National Longitudinal Bar Passage Study (Wightman, 1998)."
)
The new version conveys the same ranking, but a reader can now judge how much each gap is worth, and how many students stand behind each point.
