dist_paired_t_vs_wilcoxon.png

# --- 2) Paired t-Test vs. Wilcoxon Signed-Rank ---
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9.5, 4))
fig.subplots_adjust(wspace=0.35, bottom=0.18)

# Paired t-Test: Normal distribution of differences
x = np.linspace(-15, 15, 200)
ax1.plot(x, stats.norm.pdf(x, -2, 4), color=PRIMARY, linewidth=2, label="Differenzen (D3 - D0)")
ax1.fill_between(x, stats.norm.pdf(x, -2, 4), alpha=0.15, color=PRIMARY)
ax1.axvline(0, color=SECONDARY, linestyle="--", linewidth=1.2)
ax1.set_title("Gepaarter t-Test\n(Differenzen normalverteilt)")
ax1.set_xlabel("Differenz (z.B. Blutdruck-Änderung)")
ax1.set_ylabel("Dichte")
# Extra headroom above the curve so the legend never crosses the peak.
ax1.set_ylim(0, ax1.get_ylim()[1] * 1.32)
ax1.legend(loc="upper right")
ax1.grid(True, linestyle=":", alpha=0.6)

# Wilcoxon: Skewed/heavy-tailed distribution of differences
y_skew = stats.lognorm.pdf(x + 20, 0.6, scale=24) # Ensure domain fits bounds
ax2.plot(x, y_skew, color=PRIMARY, linewidth=2, label="Differenzen (D3 - D0)")
ax2.fill_between(x, y_skew, alpha=0.15, color=PRIMARY)
ax2.axvline(0, color=SECONDARY, linestyle="--", linewidth=1.2)
ax2.set_title("Wilcoxon-Vorzeichen-Rang-Test\n(Differenzen schief / mit Extremwerten)")
ax2.set_xlabel("Differenz (z.B. CRP-Änderung)")
ax2.set_ylabel("Dichte")
# Extra headroom above the curve so the legend never crosses the peak.
ax2.set_ylim(0, ax2.get_ylim()[1] * 1.32)
ax2.legend(loc="upper right")
ax2.grid(True, linestyle=":", alpha=0.6)

save(fig, M21_DIR / "dist_paired_t_vs_wilcoxon.png")