By the end of today you can

• explain why graphs are needed alongside numerical summaries;
• tell exploratory graphs from explanatory ones;
• explain why position and length are read more accurately than angle, area, or colour;
• choose a graph from the question and the variables;
• build graphs with ggplot2 from data, mappings, and layers;
• judge whether a graph is honest, and improve a misleading one;
• export figures at the size and resolution a thesis needs.

Summaries can hide almost anything

anscombe_long |>
  summarise(mean_x = mean(x), mean_y = mean(y),
            sd_y = sd(y), correlation = cor(x, y), .by = set)

Anscombe’s four datasets share every summary.

Four identical summaries, four different stories

A line, a curve, an outlier, and one point making the whole trend.

Look first

Anyone who analysed these data without looking would draw the same, wrong, conclusion from all four.

Many errors in data, and in reasoning about data, are found only by looking.

Exploring and explaining

A thesis contains a few explanatory graphs, chosen from many exploratory ones.

A graph turns numbers into visual properties

flowchart LR
    A["Position on a<br>common scale"] --> B["Length"] --> C["Angle<br>and slope"] --> D["Area"] --> E["Colour<br>shade"]

Cleveland and McGill’s experiments: judged most accurately on the left, least on the right.

Put the most important comparison into position or length.

The same five numbers, two ways

In the pie the slices look equal. In the bars the decline from A to E is obvious.

Two more rules of thumb

• put values to be compared next to each other on the same scale, within one panel;
• use colour to separate a few categories, not to carry the main message.

Prefer bar charts and dot plots to pie charts, and scatter plots to bubble charts.

Choosing a graph

The grammar of graphics

flowchart LR
    D["Data<br>a data frame"] --> M["Mappings<br>aes(): variable → property"] --> G["Geoms<br>points, bars, lines"]

Every ggplot2 graph combines these three parts, joined with +.

Data and mappings give an empty canvas

pilot <- tibble(
  sleep  = c(6.5, 7.5, 5.5, 8, 6),
  stress = c(3.2, 2.1, 4.5, 1.8, 3.9)
)

ggplot(pilot, aes(x = sleep, y = stress))

A geom draws the data

ggplot(pilot, aes(x = sleep, y = stress)) +
  geom_point(size = 3)

One row per student

first_sem <- semesters |>
  filter(semester == 1) |>
  left_join(students, join_by(student_id))

Each student’s first-semester record, with their background information.

Most graphs are simplest with one row per case.

Histograms show a distribution

ggplot(first_sem, aes(x = sleep_hours)) +
  geom_histogram(binwidth = 0.5)

The binwidth changes the picture

Too narrow is noisy, too wide hides the shape. Try a few widths.

Bar charts count categories

ggplot(students, aes(x = faculty)) +
  geom_bar()

Box plots compare groups

ggplot(first_sem,
       aes(x = study_mode, y = wellbeing)) +
  geom_boxplot()

Reading a box plot

Whether the study-mode difference is larger than chance is a question for Chapter 8.

Scatter plots show relationships

ggplot(first_sem,
       aes(x = sleep_hours, y = gpa)) +
  geom_point(alpha = 0.4) +
  geom_smooth(method = "lm")

Line charts show change over time

wellbeing_by_sem <- semesters |>
  left_join(students, join_by(student_id)) |>
  summarise(mean_wellbeing = mean(wellbeing),
            .by = c(semester, workshop))

ggplot(wellbeing_by_sem,
       aes(x = semester, y = mean_wellbeing,
           colour = workshop)) +
  geom_line(linewidth = 1) +
  geom_point(size = 2.5)

Mapping and setting

aes(fill = workshop)                          # mapped: depends on the data
geom_histogram(fill = "steelblue")            # set: the same everywhere

The most common ggplot2 mistake

ggplot(first_sem,
       aes(x = sleep_hours,
           fill = "steelblue")) +
  geom_histogram(binwidth = 0.5)

fill and colour

A white colour on histogram bars separates them clearly.

From exploratory to explanatory

flowchart LR
    A["Labels"] --> B["Scales and<br>colours"] --> C["Theme"] --> D["Annotations"]

Each addition is a design decision with a reason behind it.

Labels say what was measured

p <- ggplot(wellbeing_by_sem,
            aes(x = semester, y = mean_wellbeing, colour = workshop)) +
  geom_line(linewidth = 1) +
  geom_point(size = 2.5) +
  labs(title    = "Wellbeing over the two years",
       subtitle = "Average score per semester, by workshop group",
       x = "Semester", y = "Average wellbeing (0 to 100)",
       colour = "Workshop")

Units in the axis labels, the message in the title. Storing the graph as p lets you add to it.

Scales and colour-blind-friendly palettes

p <- p +
  scale_x_continuous(breaks = 1:4) +
  scale_colour_viridis_d(end = 0.8)

Whole semesters only: there is no semester 2.5.

Viridis palettes work for colour vision deficiency, about one man in twelve, and print in greyscale.

Colour should never be the only cue

In a printed figure, groups should also differ by:

• shape or line type;
• labels placed directly on the lines.

Manual colours: scale_colour_manual(values = c("Invited" = "#1b9e77", "Not invited" = "#7570b3")).

Themes control everything that is not data

p <- p +
  theme_minimal(base_size = 13) +
  theme(legend.position = "bottom")

Annotations give a reference

ggplot(first_sem, aes(x = sleep_hours)) +
  geom_histogram(binwidth = 0.5) +
  geom_vline(xintercept = 7,
             linetype = "dashed") +
  annotate("text", x = 7.1, y = Inf,
           label = "Recommended: 7 hours",
           hjust = 0, vjust = 1.5)

A graph can be accurate and still mislead

Most misleading graphs are not deliberate. They come from defaults nobody questioned.

Bar axes start at zero

A bar represents its value by its length.

If the axis starts elsewhere, a bar twice as long no longer means twice as much.

Points and lines use position, so their axes may be zoomed, as long as the reader is told.

Zooming a line chart

The wellbeing line chart’s axis runs only from about 58 to 66, which makes a 5-point gap look large.

p + coord_cartesian(ylim = c(0, 100))

Either say so in the caption, or show the full scale and let readers judge the size.

Aspect ratio, clutter, and colour

• a graph somewhat wider than tall; the same shape for graphs that will be compared;
• no heavy grid lines, repeated legends, or three-dimensional effects;
• qualitative palettes for categories;
• sequential palettes for quantities in one direction;
• diverging palettes around a meaningful midpoint such as zero.

A rainbow palette is poor for all of these.

A misleading graph

The Education bar looks several times taller than Social Sciences. The averages differ by about 3 points out of 100.

What is wrong with it

• the axis starts at 58, so the bar lengths mean nothing;
• the colours repeat the axis labels, and the legend repeats them again;
• the faculties are alphabetical, not in a meaningful order;
• the axis titles are variable names;
• only averages are shown, hiding how much students differ.

The same data, redesigned

Differences between faculties are small compared with the differences within them.

How the redesign was built

ggplot(first_sem, aes(x = wellbeing, y = reorder(faculty, wellbeing))) +
  geom_jitter(height = 0.15, alpha = 0.25, colour = "grey45") +
  stat_summary(fun = mean, geom = "point", size = 3.5, colour = "#b2182b") +
  labs(x = "Wellbeing in semester 1 (0 to 100)", y = NULL)

Facets: small multiples

ggplot(first_sem,
       aes(x = sleep_hours, y = gpa)) +
  geom_point(alpha = 0.4) +
  geom_smooth(method = "lm") +
  facet_wrap(~ programme)

Density plots compare distributions

semesters |>
  filter(semester == 2) |>
  left_join(students, join_by(student_id)) |>
  ggplot(aes(x = wellbeing, fill = workshop)) +
  geom_density(alpha = 0.5) +
  scale_fill_viridis_d(end = 0.8)

Heat maps show a table of numbers

correlations |>
  as.data.frame() |>
  mutate(var1 = rownames(correlations)) |>
  pivot_longer(-var1, names_to = "var2", values_to = "r") |>
  ggplot(aes(x = var1, y = var2, fill = r)) +
  geom_tile() +
  geom_text(aes(label = round(r, 2))) +
  scale_fill_gradient2(limits = c(-1, 1))

The matrix becomes a long table with one row per pair (Chapter 3).

Reading the heat map

A diverging palette, white at zero. The numbers matter: colour alone is read imprecisely.

Exporting figures

ggsave("figures/wellbeing-lines.png", plot = p,
       width = 16, height = 10, units = "cm", dpi = 300)
ggsave("figures/wellbeing-lines.pdf", plot = p,
       width = 16, height = 10, units = "cm")

The file type follows from the file name.

Save at the printed size

The figure code lives in the script: a supervisor’s request is one changed line.

In your field: economics and business

ggplot(economics,
       aes(x = date, y = unemploy)) +
  geom_line()

Practical lab: the Chapter 4 playground

Work through the playground exercises in your browser, with hints and solutions.

Every exercise also runs in RStudio, from the downloadable chapter project.

Practical exercises 1–3: the basic graphs

1. A histogram of study hours with binwidths 1, 5, and 10: which shows the shape best?
2. A bar chart of employment in one colour, ordered from no job to full-time.
3. Box plots of GPA by faculty, with clear labels.

Practical exercises 4–6: relationships and honesty

4. Caffeine against sleep, with a trend line: what does it suggest?
5. Save a graph as a PNG, 16 by 10 cm, at 300 dpi.
6. Redraw the misleading graph from zero, and choose one of the three for a thesis.

Try this yourself

Pick one variable from your own research.

• make three exploratory graphs of it in five minutes;
• choose the one that answers your question;
• turn it into an explanatory graph: labels, scale, theme, one annotation;
• save it at 16 cm wide.

Then show it to someone for five seconds and ask what they saw.

Troubleshooting guide (Part 1)

Troubleshooting guide (Part 2)

Completion checklist

• every variable was graphed before it was analysed;
• the graph matches the question and the variable types;
• the key comparison uses position or length in one panel;
• axes are labelled with units;
• bar axes start at zero, and zoomed axes are stated;
• colours are colour-blind-friendly and not the only cue;
• the figure is saved at its printed size.

Misconceptions to leave behind (Part 1)

Misconceptions to leave behind (Part 2)

The chapter in one sentence

Look at the data first, then choose a graph that puts the key comparison in position or length and tells the truth about its size.

Next: Chapter 5

The next chapter moves from a topic to a plan:

• what data analysis is for;
• from a topic to a research question and a hypothesis;
• variables, measurement, reliability, and validity;
• study designs and randomisation;
• an analysis plan written before the data is seen.

Questions

Think of a graph that convinced you of something.

Would it still convince you with the axis starting at zero?