带置信区间的比例
按大小排序的各组比例点图，附 Wilson 95% 置信区间。
当问题是“每组中有多大比例……？”时，每组一个点加上其置信区间，胜过条形图：眼睛比较的是位置，而区间宽度能立刻显示哪些组样本较小。这里使用 Wilson 得分区间而非教科书中的 Wald 区间，因为前者在小样本组以及比例接近 0 或 1 时仍能保持 95% 的覆盖率。虚线为总体比例。
数据为 statsmodels 自带的 1974 年 Redbook 已婚女性调查（sm.datasets.fair）：按受访者职业划分的报告有过婚外情的比例。区间由 statsmodels.stats.proportion.proportion_confint(method="wilson") 计算，副标题用 scipy.stats.chi2_contingency 检验所有比例是否相等。
代码及图中文字均为英文。
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import statsmodels.api as sm
from scipy import stats
from statsmodels.stats.proportion import proportion_confint
# Data: share of women reporting any affair, by occupation
df = sm.datasets.fair.load_pandas().data
jobs = {1: "Student", 2: "Farming, semi- or unskilled", 3: "White-collar",
4: "Teacher, nurse, skilled", 5: "Managerial, business", 6: "Professional (advanced degree)"}
df["job"] = df.occupation.map(jobs)
df["affair"] = df.affairs > 0
# Proportion + Wilson 95% CI per group, sorted
g = df.groupby("job").affair.agg(k="sum", n="size")
g["p"] = g.k / g.n
g["low"], g["high"] = proportion_confint(g.k, g.n, alpha=0.05, method="wilson")
g = g.sort_values("p")
# Chi-squared test of homogeneity across the six groups
chi2, pval, dof, _ = stats.chi2_contingency(pd.crosstab(df.job, df.affair), correction=False)
overall = df.affair.mean()
fig, ax = plt.subplots(figsize=(8, 4.8))
y = np.arange(len(g))
ax.axvline(overall, color="#8E8E93", lw=1, ls="--", zorder=1)
ax.text(overall, len(g) - 0.45, f" overall {overall:.0%}", fontsize=9, color="#6E6E73", va="bottom")
ax.hlines(y, g.low, g.high, color="#007AFF", lw=2.5, alpha=0.45, zorder=2)
ax.scatter(g.p, y, s=80, color="#007AFF", edgecolor="white", lw=1.5, zorder=3)
for yi, (_, row) in zip(y, g.iterrows()):
ax.text(0.505, yi, f"{row.p:.0%}", va="center", fontsize=10, fontweight="semibold", color="#007AFF")
ax.text(0.545, yi, f"{row.k:.0f} / {row.n:.0f}", va="center", fontsize=9.5, color="#6E6E73")
ax.set_yticks(y, g.index)
ax.set_ylim(-0.6, len(g) - 0.2)
ax.set_xlim(0, 0.62)
ax.set_xticks(np.arange(0, 0.51, 0.1))
ax.xaxis.set_major_formatter(plt.matplotlib.ticker.PercentFormatter(1, decimals=0))
ax.grid(axis="x"); ax.grid(axis="y", visible=False)
ax.set_xlabel("Women reporting any extramarital affair (Wilson 95% CI)")
ax.set_title("Managers and professionals report the most affairs", pad=26)
ax.text(0, 1.02, f"χ²({dof}) = {chi2:.1f}, p < .001 for equal proportions · n = {len(df):,} · "
"Redbook survey, 1974", transform=ax.transAxes, fontsize=9.5, color="#6E6E73")
plt.show()
图表使用了可选的 PyStatlas 样式：添加 plt.style.use("pystatlas.mplstyle") 即可完全还原其外观。
数据来源
- Redbook survey of married women, 1974 (Fair's affairs data). Fair, R. C. (1978). A theory of extramarital affairs. Journal of Political Economy, 86(1), 45–61. https://doi.org/10.1086/260646
Data from the 1974 Redbook magazine survey; distributed with statsmodels (sm.datasets.fair) with the author's permission.
这些示例用于说明统计方法。图表标题描述的是该图在这些特定数据中呈现的内容——这些数据往往样本较小、年代较早或并不完整——而不是作者对实质问题的立场。关于解释、背景和数据质量，请以此处引用的原始来源为准。
如何引用
PyStatlas 由 Thierry Warin 创建并维护。如果它对你的工作有所帮助，敬请引用。
Warin, T. (2026). Proportions with confidence intervals. In PyStatlas: A Python Gallery of Statistical Graphics for the Social Sciences. https://warint.github.io/pystatlas/proportions-surveys/proportions-with-ci/
@misc{warin2026statlas,
author = {Warin, Thierry},
title = {PyStatlas: A Python Gallery of Statistical Graphics for the Social Sciences},
year = {2026},
howpublished = {\url{https://warint.github.io/pystatlas/}},
note = {Source code: https://github.com/warint/pystatlas}
}
