5. Axes — start at zero, or go logarithmic? · Dr. Seonggu Sohn's Data Visualization, First Steps

Here are the mutation counts of 407 lung adenocarcinoma samples. Real TCGA data.

fewest2

median223

mean336

most2,152

The largest is a thousand times the smallest. What happens if you put that on an ordinary axis?

On the left it is one spike against the wall. On the right a bell appears. Same data.

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

v = viz.meta()["n_mut"].dropna()
v = v[v > 0].values

fig, ax = plt.subplots(1, 2, figsize=(10, 3.2))
ax[0].hist(v, bins=40, color=viz.PAL[0])
ax[0].set_title("linear x", fontsize=9); ax[0].set_xlabel("mutations", fontsize=8)

ax[1].hist(np.log10(v), bins=40, color=viz.PAL[1])
ax[1].set_title("log10 x", fontsize=9); ax[1].set_xlabel("log10(mutations)", fontsize=8)
ax[1].set_xticks([0, 1, 2, 3]); ax[1].set_xticklabels(["1", "10", "100", "1000"])

for a in ax:
    viz.bare(a); a.set_ylabel("patients", fontsize=8)
fig.tight_layout()
print("Only %d of 407 patients are above 1,000 mutations." % (v > 1000).sum())

Change the axis. Truncate it, log it, flip it — and count how many different stories one dataset tells.

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An axis needs four decisions.

Decision	Default	When to break it
Start at zero?	bars: always	points and lines need not
Linear or log	linear	log when values differ by multiples
Tick spacing	multiples of 1·2·5·10	almost never
Matching ranges	identical across compared panels	if not, say so loudly

That last row matters most. When four conditions sit side by side the way they do in Fig. 5D, differing y-ranges make every height comparison wrong.

The two right-hand panels have cut the tail off. The fact that some patients reach 55% has simply vanished.

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import matplotlib.pyplot as plt
import viz

t = viz.til()
v = t["til_pct"].values
fig, ax = plt.subplots(1, 3, figsize=(11, 3))

# same data, only the y-axis differs
for a, (lo, hi, tag) in zip(ax, [(0, 60, "full range"),
                                 (0, 20, "clipped at 20"),
                                 (0, 6, "clipped at 6")]):
    a.hist(v, bins=40, range=(0, 60), color=viz.PAL[2])
    a.set_ylim(0, 120); a.set_xlim(lo, hi)
    a.set_title(tag, fontsize=9); a.set_xlabel("TIL %", fontsize=8)
    viz.bare(a)
ax[0].set_ylabel("patients", fontsize=8)
fig.tight_layout()
print("%d patients - median %.2f%% - max %.1f%%" % (len(v), viz.np.median(v), v.max()))

🤔 Check yourself

Why is gene expression usually plotted on a log2 scale?

🤔 Check yourself

Cell proportions for four conditions are drawn in four panels. What must you do?

🤔 Check yourself

When may a bar chart's y-axis start somewhere other than zero?