8. Four ways to show a distribution — histogram, box, violin, points · Dr. Seonggu Sohn's Data Visualization, First Steps

TIL infiltration for 480 patients. Real TCGA lung adenocarcinoma data.

patients480

1st quartile2.60%

median5.67%

3rd quartile14.28%

max55.8%

mean9.90%

The mean is 1.7 times the median — the distribution has a long right tail. Write “mean 9.9%” on a single bar and all of that disappears.

The same 480 values drawn four ways. Compare what appears and what vanishes.

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Look only at the leftmost bar and every patient seems to sit near 10%. In fact some are at 0% and some at 55%.

Python Runs in your browser

import matplotlib.pyplot as plt
import viz, numpy as np

v = viz.til()["til_pct"].values
fig, ax = plt.subplots(1, 4, figsize=(12, 3.2))

ax[0].bar([0], [v.mean()], yerr=[v.std()/np.sqrt(len(v))], color=viz.PAL[0], width=.5)
ax[0].set_xticks([]); ax[0].set_title("bar (mean +- SEM)", fontsize=9)
ax[0].set_ylim(0, 60)

ax[1].hist(v, bins=30, color=viz.PAL[0]); ax[1].set_title("histogram", fontsize=9)
ax[1].set_xlabel("TIL %", fontsize=8)

ax[2].boxplot(v, widths=.5); ax[2].set_title("box", fontsize=9)
ax[2].set_xticks([]); ax[2].set_ylim(0, 60)

rng = np.random.default_rng(1)
ax[3].plot(rng.normal(0, .06, len(v)), v, ".", ms=2, alpha=.35, color=viz.PAL[0])
ax[3].violinplot(v, showextrema=False)
ax[3].set_xticks([]); ax[3].set_title("violin + points", fontsize=9); ax[3].set_ylim(0, 60)

for a in ax:
    viz.bare(a)
ax[0].set_ylabel("TIL %", fontsize=8)
fig.tight_layout()
print("mean %.2f%% - median %.2f%% - a factor of 1.7 apart." % (v.mean(), np.median(v)))

What each of the four shows and hides:

	Shows	Hides	Use when
Bar + error	the mean, one spread	shape · number of modes · outliers	only when n is very large
Histogram	the whole shape	individual values · group comparison	examining one group closely
Box	five numbers · outliers	bimodality	comparing several groups
Violin	shape + group comparison	exact counts	when every group has a large n

DDX54's two groups are slightly offset; CD8A's separate cleanly. Making the degree of overlap visible is what a violin is worth.

Python Runs in your browser

import matplotlib.pyplot as plt
import viz, numpy as np

e, m = viz.expr(), viz.meta()
des = list(m.index[m.group == "desert"])
inf = list(m.index[m.group == "inflamed"])

fig, ax = plt.subplots(1, 2, figsize=(9, 3.4))
for j, g in enumerate(["DDX54", "CD8A"]):
    a, b = e.loc[g, des].values, e.loc[g, inf].values
    parts = ax[j].violinplot([a, b], showextrema=False)
    for k, pc in enumerate(parts["bodies"]):
        pc.set_facecolor(viz.PAL[k]); pc.set_alpha(.45)
    rng = np.random.default_rng(2)
    for k, v in enumerate([a, b]):
        ax[j].plot(k + 1 + rng.normal(0, .05, len(v)), v, ".", ms=4,
                   color=viz.PAL[k], alpha=.8)
    ax[j].set_xticks([1, 2]); ax[j].set_xticklabels(["desert", "inflamed"], fontsize=8)
    ax[j].set_title(g, fontsize=10); ax[j].set_ylabel("log2 expression", fontsize=8)
    viz.bare(ax[j])
    print("%-6s desert %.2f  inflamed %.2f  (n=%d/%d)" % (g, a.mean(), b.mean(), len(a), len(b)))
fig.tight_layout()

🤔 Check yourself

You have four conditions with n = 6 each. What is the most honest chart?

🤔 Check yourself

A distribution has mean 9.9% and median 5.7%. What follows?

🤔 Check yourself

What does a box plot miss?