Sex Ratio Confidence Interval

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Figure 4.22 — 95% confidence interval for the sex ratio power plant study

Figure 4.22 The 95% confidence interval for the study that observed 52% girl births in a sample of 300 births near power plants.

Figure 4.22 — Resampling-based confidence interval

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt

np.random.seed(1)
n = 10000
sample_size = 300
obs = 0.52  # observed proportion of girl births in the study

# Parametric resampling: simulate n studies of size `sample_size`, assuming
# the true population rate equals the observed rate.
x = np.random.choice([0, 1], (n, sample_size), p=[1 - obs, obs])
z = np.sum(x, axis=1) / sample_size * 100  # % girl births per resample

q_low, q_high = np.percentile(z, [2.5, 97.5])
# Pivotal (reflected) CI: mirror the percentiles around the observed
# statistic instead of taking them at face value.
ci_low, ci_high = 2 * obs * 100 - q_high, 2 * obs * 100 - q_low

fig, ax = plt.subplots(figsize=(7, 3))

bins = np.arange(z.min() - 0.5, z.max() + 1.5, 1)
counts, _, _ = ax.hist(z, bins=bins, color="#c6e8b0", edgecolor="black", linewidth=0.5)

ax.axvspan(ci_low, ci_high, color="#a9d3f5", alpha=0.6, zorder=0,
           label="95% confidence interval")

peak_height = counts.max()
ax.annotate(
    "our study: 52%",
    xy=(obs * 100, peak_height * 1.02),
    xytext=(obs * 100, peak_height * 1.35),
    ha="center",
    arrowprops=dict(arrowstyle="->", color="black"),
)

ax.set_xlabel("% of girl birth")
ax.set_ylabel("Count")
ax.set_xticks(np.arange(40, 70, 5))
ax.set_xlim(35, 68)
ax.set_ylim(0, peak_height * 1.5)
ax.legend(loc="center left", bbox_to_anchor=(1.02, 0.5), borderaxespad=0, frameon=False)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)

plt.tight_layout()
plt.savefig("sex_ratio_power_plant_ci.png", dpi=150, bbox_inches="tight")
plt.show()

Resampling Statistics

Sex Ratio Near Power Plants: Confidence Interval