Comparaison intra-sujets

from itertools import combinations

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.anova import AnovaRM
from statsmodels.stats.multitest import multipletests

# Data: fertility of the same countries in 1970, 1990 and 2010 (births per woman)
wb = sm.datasets.fertility.load_pandas().data
wb = wb[~wb["Country Name"].str.contains("classification|income levels|members|small states")]  # 5 aggregates
conditions = ["1970", "1990", "2010"]
wide = wb[conditions].dropna().reset_index(drop=True)
n = len(wide)
long = wide.rename_axis("id").reset_index().melt("id", var_name="condition", value_name="tfr")

# Repeated-measures ANOVA + partial eta squared
aov = AnovaRM(long, "tfr", "id", within=["condition"]).fit().anova_table.iloc[0]
eta_p = aov["F Value"] * aov["Num DF"] / (aov["F Value"] * aov["Num DF"] + aov["Den DF"])

# Pairwise paired t-tests (Holm) with Cohen's d_z
pairs = list(combinations(range(3), 2))
tests = [stats.ttest_rel(wide.iloc[:, j], wide.iloc[:, i]) for i, j in pairs]
adj_p = multipletests([t.pvalue for t in tests], method="holm")[1]
dz = [(wide.iloc[:, j] - wide.iloc[:, i]).mean() / (wide.iloc[:, j] - wide.iloc[:, i]).std()
      for i, j in pairs]

fig, ax = plt.subplots(figsize=(8, 5.6))
palette = ["#FF9500", "#AF52DE", "#007AFF"]
x = np.arange(3)
for _, row in wide.iterrows():                      # one line per subject
    ax.plot(x, row.values, color="#C7C7CC", lw=0.6, alpha=0.6, zorder=1)
for i, c in enumerate(palette):
    v = ax.violinplot(wide.iloc[:, i], positions=[i], widths=0.55, showextrema=False)
    v["bodies"][0].set(facecolor=c, alpha=0.15, edgecolor="none")
    ax.scatter(np.full(n, i), wide.iloc[:, i], s=12, color=c, alpha=0.6, lw=0, zorder=2)
means = wide.mean()
ax.plot(x, means, color="#1D1D1F", lw=2.5, zorder=3)
ax.scatter(x, means, s=110, color="#1D1D1F", edgecolor="white", lw=2, zorder=4)
for i, m in enumerate(means):
    ax.annotate(f"μ = {m:.1f}", (i, m), xytext=(14, 0), textcoords="offset points", va="center",
                fontsize=9.5, fontweight="semibold", color="#1D1D1F",
                bbox=dict(boxstyle="round,pad=0.2", fc="white", ec="none", alpha=0.9), zorder=5)

# Significance brackets
top, step = wide.values.max() + 0.4, 0.8
for h, ((i, j), p, d) in enumerate(sorted(zip(pairs, adj_p, dz), key=lambda t: t[0][1] - t[0][0])):
    y = top + h * step
    ax.plot([i, i, j, j], [y - 0.2, y, y, y - 0.2], color="#8E8E93", lw=1)
    label = "p < .001" if p < 0.001 else f"p = {p:.3f}"
    ax.text((i + j) / 2, y + 0.07, f"{label}, d_z = {d:.2f}", ha="center", va="bottom",
            fontsize=9, color="#3A3A3C")

ax.set_xticks(x, [f"{c}\n(n = {n})" for c in conditions])
ax.set_xlim(-0.5, 2.6)
ax.set_ylim(top=top + 3 * step)
ax.set_ylabel("Total fertility rate (births per woman)")
fell = (wide["2010"] < wide["1970"]).mean()
ax.set_title(f"Fertility fell between 1970 and 2010 in {fell:.0%} of countries", pad=26)
ax.text(0, 1.02, f"Repeated-measures ANOVA F({aov['Num DF']:.0f}, {aov['Den DF']:.0f}) = "
        f"{aov['F Value']:.1f}, p = {aov['Pr > F']:.1e}, η²p = {eta_p:.2f}  ·  "
        "pairwise: paired t-tests, Holm-adjusted", transform=ax.transAxes,
        fontsize=9.5, color="#6E6E73")
plt.show()