import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd
import numpy as np
from scipy.stats import mannwhitneyuSignificance Annotation (Python)
Reviewers expect pairwise significance marks โ brackets with p-values or stars โ directly on distribution plots. Neither matplotlib nor seaborn ships a bracket primitive, so this tutorial builds a small reusable helper from annotate, tests two groups with MannโWhitney U, and stacks brackets for several comparisons with Bonferroni-adjusted stars. The same helper attaches to bars, boxes, or violins.
Example
Setup
- System Requirements: Cross-platform (Linux/MacOS/Windows)
- Programming Language: Python
- Dependencies:
matplotlib,seaborn,pandas,numpy,scipy
Data Preparation
We reuse the drug-dose response experiment: raw replicate measurements for four groups, with the analysis comparing each dose against the vehicle control.
np.random.seed(41)
groups = ['Vehicle', 'Low dose', 'Mid dose', 'High dose']
raw = pd.DataFrame({
'Group': pd.Categorical(np.repeat(groups, 40), categories=groups, ordered=True),
'Response': np.concatenate([
np.random.normal(2.0, 0.9, 40),
np.random.normal(2.6, 0.9, 40),
np.random.normal(4.6, 0.9, 40),
np.random.normal(6.2, 0.9, 40),
])
})
def stars(p):
return '***' if p < 0.001 else '**' if p < 0.01 else '*' if p < 0.05 else 'ns'Visualization
Bracket Helper and a Pairwise Mark
The helper draws a bracket with annotate in axes coordinates; vertical space must be reserved by extending the y-limit before drawing.
def add_p_bracket(ax, x1, x2, y, h, text):
ax.annotate('', xy=(x1, y), xytext=(x2, y),
arrowprops=dict(arrowstyle='-', color='0.15', lw=1.1))
ax.plot([x1, x1], [y, y + h], color='0.15', lw=1.1)
ax.plot([x2, x2], [y, y + h], color='0.15', lw=1.1)
ax.text((x1 + x2) / 2, y + h, text, ha='center', va='bottom',
fontsize=10, color='0.1')
fig, ax = plt.subplots(figsize=(5.4, 4.4))
sns.boxplot(data=raw, x='Group', y='Response', color='#dddddd',
width=0.5, linewidth=1.0, showfliers=False, ax=ax)
sns.stripplot(data=raw, x='Group', y='Response', color='#2b2b2b',
size=3, alpha=0.5, jitter=0.12, ax=ax)
u, p = mannwhitneyu(raw.loc[raw.Group == 'Vehicle', 'Response'],
raw.loc[raw.Group == 'High dose', 'Response'])
add_p_bracket(ax, 0, 3, raw.Response.max() + 0.4, 0.15, stars(p))
ax.set_ylim(None, raw.Response.max() + 1.1)
ax.set_xlabel('Treatment group')
ax.set_ylabel('Response (a.u.)')
ax.spines[['top', 'right']].set_visible(False)
plt.tight_layout()
plt.show()
Multiple Comparisons vs Control
Loop over the dose arms, Bonferroni-adjust the raw p-values, and stack the brackets at increasing heights so they never overlap.
comparisons = [(0, 1), (0, 2), (0, 3)]
pvals = [mannwhitneyu(raw.loc[raw.Group == groups[a], 'Response'],
raw.loc[raw.Group == groups[b], 'Response']).pvalue
for a, b in comparisons]
padj = np.minimum(np.array(pvals) * len(comparisons), 1.0)
fig, ax = plt.subplots(figsize=(5.8, 4.6))
sns.boxplot(data=raw, x='Group', y='Response', color='#dddddd',
width=0.5, linewidth=1.0, showfliers=False, ax=ax)
sns.stripplot(data=raw, x='Group', y='Response', color='#2b2b2b',
size=3, alpha=0.5, jitter=0.12, ax=ax)
y_max = raw.Response.max()
for level, ((a, b), p) in enumerate(zip(comparisons, padj), start=1):
y = y_max + 0.5 + 0.55 * (level - 1)
add_p_bracket(ax, a, b, y, 0.15, stars(p))
ax.set_ylim(None, y_max + 2.3)
ax.set_xlabel('Treatment group')
ax.set_ylabel('Response (a.u.)')
ax.spines[['top', 'right']].set_visible(False)
plt.tight_layout()
plt.show()
References
- Mann, H. B., & Whitney, D. R. (1947). On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other. The Annals of Mathematical Statistics, 18(1), 50-60.
- Hunter, J. D. (2007). Matplotlib: A 2D graphics environment. Computing in Science & Engineering, 9(3), 90-95.
- Waskom, M. L. (2021). seaborn: statistical data visualization. Journal of Open Source Software, 6(60), 3021.