A spreadsheet containing 600 rows of numbers conveys virtually nothing at a glance. A well-designed statistical visualization of that same data reveals in seconds where observations cluster, which values are anomalous, how experimental groups diverge, and how constructs covary. Graphics are not cosmetic embellishments appended to an empirical report at the conclusion; they are primary instruments of scientific discovery. The first task of an investigator encountering new data is to inspect it visually, and many data-entry anomalies and invalid assumptions are detected solely through graphical exploration.
A figure is also a scientific argument. Visual design choices—the selected geometry, axis scaling, aspect ratio, color palette, and data aggregation—determine what a reader notices first and what conclusions they infer. Thoughtful choices clarify subtle empirical patterns; careless choices distort differences, exaggerating trivial variations or masking substantial heterogeneity. This chapter begins with graphical perception theory: what scientific figures are for, how human vision decodes visual encodings, and what constitutes an honest, truthful display. It then introduces Seaborn and Matplotlib, Python’s standard libraries for statistical visualization, applying them to explore graduate student life (RQ1).
Summary statistics compress empirical distributions into a handful of numerical parameters (means, standard deviations, correlations). That compression can conceal radically different data distributions. The statistician Francis Anscombe demonstrated this vulnerability with four synthetic datasets constructed in 1973 (Anscombe 1973), bundled in Seaborn as anscombe:
anscombe = sns.load_dataset("anscombe")
summary = (
anscombe
.groupby("dataset")
.agg(
mean_x=("x", "mean"),
sd_x=("x", "std"),
mean_y=("y", "mean"),
sd_y=("y", "std")
)
.round(2)
)
summary| mean_x | sd_x | mean_y | sd_y | |
|---|---|---|---|---|
| dataset | ||||
| I | 9.0 | 3.32 | 7.5 | 2.03 |
| II | 9.0 | 3.32 | 7.5 | 2.03 |
| III | 9.0 | 3.32 | 7.5 | 2.03 |
| IV | 9.0 | 3.32 | 7.5 | 2.03 |
Across all four datasets, the summary statistics are practically identical: \(\bar{x} = 9.0\), \(s_x = 3.32\), \(\bar{y} = 7.50\), and \(s_y = 2.03\). Bivariate regression yields identical linear fits (\(y = 3.0 + 0.5x\)) with identical correlation coefficients (\(r = 0.82\)). Judged solely by numerical summaries, the four datasets appear indistinguishable.
Yet Figure 4.1 demonstrates that their underlying relationships are entirely dissimilar.
g = sns.lmplot(
data=anscombe, x="x", y="y", col="dataset", col_wrap=2,
ci=None, height=2.5, aspect=1.3,
scatter_kws={"s": 35, "color": "#1f77b4"},
line_kws={"color": "grey", "linewidth": 1.5}
)
g.set_axis_labels("X", "Y")
plt.tight_layout()
plt.show()
Only Dataset I represents the bivariate linear association assumed by Pearson’s \(r\). Dataset II is a non-linear quadratic curve, Dataset III is a perfect linear relationship corrupted by one outlier, and Dataset IV is an unassociated vertical cluster whose correlation is produced entirely by a single high-leverage point. An analyst relying strictly on summary statistics would draw identical—and incorrect—conclusions across all four. Visual inspection prior to modeling is not optional; it is a prerequisite for valid inference.
Scientific graphics serve two distinct functions:
Graphs function by translating numbers into visual encodings: position, length, angle, area, slope, and color. Human perception does not decode these attributes with equal precision. In pioneering experiments, William Cleveland and Robert McGill (Cleveland and McGill 1984) evaluated how accurately observers judge quantitative differences across visual channels, establishing an empirical hierarchy:
Effective scientific graphics map primary research comparisons to position or length, reserving color and area for secondary grouping.
The perceptual difference is readily apparent when comparing identical proportions displayed as a pie chart versus a bar chart (Figure 4.2).
shares = pd.DataFrame({
"group": ["A", "B", "C", "D", "E"],
"percent": [23, 21, 20, 19, 17]
})
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(7.5, 3.2))
# Pie chart (angle / area)
ax1.pie(shares["percent"], labels=shares["group"], startangle=90, colors=sns.color_palette("mako", 5))
ax1.set_title("Pie chart (Angle / Area)", fontsize=11)
# Bar chart (aligned length)
sns.barplot(data=shares, x="group", y="percent", color="#4c72b0", ax=ax2)
ax2.set(title="Bar chart (Aligned Length)", xlabel="Category", ylabel="Percentage (%)")
ax2.set_ylim(0, 26)
plt.tight_layout()
plt.show()
In the pie chart, the five slices appear virtually identical; determining the rank order requires scrutinizing legends and mentally comparing angles. In the bar chart, the monotonic decline from category A (23%) to E (17%) is evident immediately because comparisons occur along a common baseline. Consequently, scientific reporting favors bar charts and dot plots over pie charts.
The choice of graph is governed by the research question and the levels of measurement of the variables under study (Table 4.1).
| Analytical Question | Variable Types | Recommended Graph | Python Seaborn / Matplotlib Function |
|---|---|---|---|
| Distribution of a single continuous metric | One numeric | Histogram / KDE plot | sns.histplot(), sns.kdeplot() |
| Frequency counts of categorical groups | One categorical | Bar chart | sns.countplot(), sns.barplot() |
| Comparison of continuous metric across groups | One numeric by categorical | Box plot / Strip plot | sns.boxplot(), sns.stripplot() |
| Association between two continuous variables | Two numeric | Scatter plot with trend line | sns.scatterplot(), sns.regplot() |
| Trajectory of a metric over time | Numeric over time | Longitudinal line plot | sns.lineplot() |
| Multilateral correlation structure | Several numeric | Correlation heatmap | sns.heatmap() |
To explore Elaf’s wellbeing cohort, we merge Semester 1 measurements with baseline student background demographics:
first_sem = (
semesters
.query("semester == 1")
.merge(students, on="student_id", how="left")
)The initial question concerning any continuous variable addresses its empirical distribution: central tendency, spread, skewness, and the presence of extreme outliers. A histogram partitions the continuous range into discrete bins, displaying the count of observations falling within each interval:
fig, ax = plt.subplots(figsize=(6, 3.5))
sns.histplot(
data=first_sem, x="sleep_hours", binwidth=0.5,
color="#4c72b0", edgecolor="white", ax=ax
)
ax.set(xlabel="Hours of sleep per night", ylabel="Number of students")
plt.tight_layout()
plt.show()
Figure 4.3 displays a roughly symmetrical, unimodal distribution centered near 6.5 hours. Exactly r round(100 * share_short, 1)% of graduate students sleep less than the clinically recommended 7 hours during their first semester.
A bar chart plots frequency distributions across categorical factor levels:
fig, ax = plt.subplots(figsize=(6, 3.5))
sns.countplot(
data=students, x="faculty", color="#4c72b0",
order=students["faculty"].value_counts().index, ax=ax
)
ax.set(xlabel="Faculty", ylabel="Student Count")
plt.xticks(rotation=20, ha="right")
plt.tight_layout()
plt.show()
Because bar lengths represent quantities proportionally, the numerical baseline must always start at zero.
A box plot summarizes five key distribution parameters: the median (center line), interquartile range (IQR, box edges covering the 25th to 75th percentiles), whiskers (extending to \(1.5 \times \text{IQR}\)), and individual points for potential outliers. It is the gold standard for comparing continuous metrics across qualitative groups:
fig, ax = plt.subplots(figsize=(5, 3.5))
sns.boxplot(
data=first_sem, x="study_mode", y="wellbeing",
palette=["#4c72b0", "#55a868"], ax=ax, width=0.5
)
ax.set(xlabel="Study Mode", ylabel="Wellbeing Index (0 to 100)")
plt.tight_layout()
plt.show()
Part-time students report a slightly lower median wellbeing score than full-time students, but the distributions overlap substantially. In ?@sec-ch08, we use inferential ANOVA to test whether this group discrepancy is statistically significant.
The relationship between two continuous variables—such as sleep hours and academic performance—is evaluated via a scatter plot. When plotting 600 participants, individual markers often overlap (overplotting). We mitigate this by setting transparency (alpha=0.4) and overlaying a linear regression trend line with sns.regplot():
fig, ax = plt.subplots(figsize=(6, 3.8))
sns.regplot(
data=first_sem, x="sleep_hours", y="gpa",
scatter_kws={"alpha": 0.35, "color": "#4c72b0"},
line_kws={"color": "#c44e52", "linewidth": 2},
ax=ax
)
ax.set(xlabel="Hours of sleep per night", ylabel="Grade Point Average (GPA)")
plt.tight_layout()
plt.show()
The regression line slopes upward: students sleeping more hours tend to achieve modestly higher GPAs. However, observations scatter broadly around the line (\(r \approx 0.30\)), indicating that sleep explains only a fraction of total academic variance.
Elaf’s research design tracked cohorts across four consecutive semesters. A line plot illustrates how group means evolve over time:
wellbeing_trajectory = (
semesters
.merge(students[["student_id", "workshop"]], on="student_id", how="left")
.groupby(["semester", "workshop"])["wellbeing"]
.mean()
.reset_index()
)
fig, ax = plt.subplots(figsize=(6.5, 3.8))
sns.lineplot(
data=wellbeing_trajectory, x="semester", y="wellbeing",
hue="workshop", marker="o", markersize=7, linewidth=2,
palette={"Invited": "#2ca02c", "Not invited": "#7f7f7f"},
ax=ax
)
ax.set(
title="Cohort Wellbeing Trajectory Over Two Years",
xlabel="Academic Semester",
ylabel="Mean Wellbeing (0 to 100)",
xticks=[1, 2, 3, 4]
)
ax.legend(title="Workshop Group", frameon=True)
plt.tight_layout()
plt.show()
Figure 4.7 captures the core narrative of Elaf’s intervention study: groups start at identical baselines in Semester 1, invited students pull ahead following the intervention in Semester 2, and the gap stabilizes over subsequent terms.
Exploratory graphics suffice during initial data exploration, but explanatory figures destined for a thesis or journal article require publication-standard polish.
Adding explicit reference lines and annotations directs reader attention to clinically meaningful thresholds:
fig, ax = plt.subplots(figsize=(6.5, 3.8))
sns.histplot(
data=first_sem, x="sleep_hours", binwidth=0.5,
color="#4c72b0", edgecolor="white", ax=ax
)
ax.axvline(7.0, color="#c44e52", linestyle="--", linewidth=1.8)
ax.text(
7.1, ax.get_ylim()[1] * 0.9,
"Recommended: 7.0 hrs",
color="#c44e52", fontweight="semibold", verticalalignment="top"
)
ax.set(
title="Baseline Sleep Duration",
xlabel="Hours of sleep per night",
ylabel="Number of students"
)
plt.tight_layout()
plt.show()
Approximately 8% of men and 0.5% of women experience congenital color vision deficiency (red-green color blindness). A scientific graphic must remain interpretable to all readers and reproduce legibly when printed in black and white:
jet) palettes, which introduce artificial visual boundaries.viridis, plasma, cividis, or colorblind.A visualization can be mathematically accurate while remaining visually misleading. Distortion frequently stems from unexamined software defaults:
Suppose an investigator evaluates whether mean wellbeing differs across faculties. A careless chart with an artificially truncated axis appears in Figure 4.9:
faculty_means = (
first_sem
.groupby("faculty")["wellbeing"]
.mean()
.reset_index()
)
fig, ax = plt.subplots(figsize=(6.5, 3.5))
sns.barplot(data=faculty_means, x="faculty", y="wellbeing", palette="Blues_d", ax=ax)
ax.set_ylim(58, 62.5) # Truncated baseline!
ax.set(title="Misleading: Truncated Baseline (58 to 62.5)", xlabel="Faculty", ylabel="Mean Wellbeing")
plt.xticks(rotation=20, ha="right")
plt.tight_layout()
plt.show()
In Figure 4.9, the Education faculty bar appears triple the height of Social Sciences. Yet the actual group means differ by barely 2.5 points on a 100-point scale. Furthermore, the bar chart completely conceals individual variation.
In Figure 4.10, the display is redesigned into an honest, informative jittered strip plot with overlaid group means:
order = faculty_means.sort_values("wellbeing")["faculty"]
fig, ax = plt.subplots(figsize=(7, 3.8))
# Jittered individual student scores
sns.stripplot(
data=first_sem, y="faculty", x="wellbeing",
order=order, color="grey", alpha=0.3, jitter=0.2, size=5, ax=ax
)
# Overlay group means as prominent diamonds
sns.pointplot(
data=first_sem, y="faculty", x="wellbeing",
order=order, color="#c44e52", markers="D", scale=0.8,
errorbar=None, join=False, ax=ax
)
ax.set(
title="Truthful: Student Wellbeing Distribution by Faculty",
xlabel="Wellbeing Index (0 to 100)",
ylabel=None,
xlim=(0, 100) # Full theoretical scale!
)
plt.tight_layout()
plt.show()
Figure 4.10 communicates the true scientific story: individual student scores vary widely between 25 and 95 across all departments, and average differences between faculties are trivial by comparison.
Small multiples partition a complex visualization into separate subpanels sharing identical axes, enabling direct visual comparisons:
g = sns.lmplot(
data=first_sem, x="sleep_hours", y="gpa", col="programme",
scatter_kws={"alpha": 0.35, "color": "#4c72b0"},
line_kws={"color": "#c44e52"},
height=3.5, aspect=1.1
)
g.set_axis_labels("Hours of Sleep per Night", "GPA")
g.set_titles(col_template="{col_name} Candidates")
plt.tight_layout()
plt.show()
The regression slope between sleep and academic performance is virtually identical across both Master’s and PhD cohorts.
A density plot provides a smoothed continuous estimate of the probability density function, facilitating clean comparisons of overlapping distributions:
sem2_data = (
semesters
.query("semester == 2")
.merge(students[["student_id", "workshop"]], on="student_id")
)
fig, ax = plt.subplots(figsize=(6.5, 3.5))
sns.kdeplot(
data=sem2_data, x="wellbeing", hue="workshop",
fill=True, common_norm=False, alpha=0.35,
palette={"Invited": "#2ca02c", "Not invited": "#7f7f7f"},
linewidth=2, ax=ax
)
ax.set(
title="Semester 2 Post-Intervention Wellbeing Distribution",
xlabel="Wellbeing Index (0 to 100)",
ylabel="Probability Density"
)
plt.tight_layout()
plt.show()
Notice that the entire distribution for invited students is shifted rightward, demonstrating a cohort-wide positive effect rather than an isolated outlier reaction.
When examining relationships among numerous continuous constructs, a correlation heatmap visualizes the bivariate correlation matrix via a diverging color gradient:
corr_vars = first_sem[["gpa", "sleep_hours", "study_hours", "wellbeing"]].corr()
fig, ax = plt.subplots(figsize=(5.5, 4.2))
sns.heatmap(
corr_vars, annot=True, fmt=".2f", cmap="vlag",
vmin=-1.0, vmax=1.0, center=0.0,
square=True, linewidths=0.5, cbar_kws={"shrink": 0.8},
ax=ax
)
ax.set_title("Correlation Heatmap (Semester 1)", fontsize=11, pad=10)
plt.tight_layout()
plt.show()
The diverging vlag palette centers white at zero correlation, mapping negative associations to blue and positive associations to red. Values printed within each cell ensure readers are not forced to decode coefficients solely through color saturation.
Scientific figures must be exported at explicit target physical dimensions and print resolutions:
# Save as 300 DPI PNG raster image (suitable for Word documents and presentations):
fig.savefig("figures/wellbeing_trajectory.png", dpi=300, bbox_inches="tight")
# Save as vector graphic (ideal for LaTeX and journal publication):
fig.savefig("figures/wellbeing_trajectory.pdf", bbox_inches="tight")Setting bbox_inches="tight" prevents axis labels from being clipped. Standard journal column widths typically measure 8.5 cm (single column) or 17.5 cm (full width). Defining figure sizes in code preserves font proportions when rendered on the printed page.
sns.lineplot(), small multiples using sns.lmplot(col=...), and correlation matrices using sns.heatmap().viridis, vlag), and transparent representation of within-group variance.fig.savefig() at 300+ DPI or vector formats (.pdf, .svg).Anscombe’s quartet, exploratory vs. explanatory graphics, graphical perception, aligned scale, histogram, KDE density plot, box plot, strip plot, overplotting, regression trend line, longitudinal line plot, small multiples, facet, correlation heatmap, color accessibility, chartjunk, DPI, vector graphics.
Work through these exercises in your browser using the Chapter 4 Playground or download the starter project for VS Code.
first_sem, generate a histogram of study_hours. Experiment with binwidths of 2, 5, and 10 hours, and evaluate which binning best reveals distribution shape.employment categories, ordered from "None" to "Full-time job", using a colorblind-safe single color.caffeine_mg) against sleep hours (sleep_hours) in Semester 1 with an overlaid linear regression line, and describe the observed association.figures/exercise_plot.png at 300 DPI with tight bounding boxes.