feat(ch13): finalize fitness 2x2 example (LMM + paired & Welch tests); add docs and data

data/synthetic/fitness_meta.json

@@ -0,0 +1,11 @@
+{
+  "seed": 7,
+  "n": 80,
+  "design": "2x2 mixed (Group between \u00d7 Time within)",
+  "programs": [
+    "ProgramA",
+    "ProgramB"
+  ],
+  "dv": "strength_1RM_like",
+  "generated_utc": "2025-11-09T18:46:49Z"
+}

docs/ch13_fitness.md

@@ -0,0 +1,8 @@
+# Fitness 2×2 Mixed Example (Chapter 13)
+
+**Data**: `data/synthetic/fitness_subjects.csv`, `data/synthetic/fitness_long.csv`, and `data/synthetic/fitness_meta.json`
+
+**Run**
+```bash
+python scripts/sim_fitness_2x2.py
+python scripts/ch13_fitness_mixed.py --save-plots

scripts/ch13_fitness_mixed.py

@@ -0,0 +1,78 @@
+# SPDX-License-Identifier: MIT
+import argparse, os
+import numpy as np, pandas as pd
+import statsmodels.formula.api as smf
+import matplotlib; matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+
+def hedges_g(a, b):
+    na, nb = len(a), len(b)
+    sa, sb = a.var(ddof=1), b.var(ddof=1)
+    s_p = np.sqrt(((na-1)*sa + (nb-1)*sb)/(na+nb-2))
+    d = (a.mean()-b.mean())/s_p
+    J = 1 - 3/(4*(na+nb)-9)
+    return d*J
+
+def main():
+    ap = argparse.ArgumentParser()
+    ap.add_argument("--data", default="data/synthetic/fitness_long.csv")
+    ap.add_argument("--save-plots", action="store_true")
+    args = ap.parse_args()
+
+    df = pd.read_csv(args.data)
+    df["time"]  = pd.Categorical(df["time"],  categories=["pre","post"], ordered=True)
+    df["group"] = pd.Categorical(df["group"])
+
+    # Mixed model with random intercept per subject
+    import statsmodels.api as sm
+    md = sm.MixedLM.from_formula("strength ~ time*group + age + sex + bmi",
+                                 groups="id", re_formula="1", data=df)
+    m = md.fit(method="lbfgs")
+
+    print("=== LMM: strength ~ time*group + age + sex + bmi + (1|id) ===")
+    print(m.summary())
+
+    # Within-group pre→post paired tests
+    from scipy import stats
+    print("\n=== Within-group pre→post (paired) ===")
+    for g in df["group"].cat.categories:
+        wide = (df[df.group==g]
+                .pivot_table(index="id", columns="time", values="strength", observed=False))
+        pre, post = wide["pre"], wide["post"]
+        diff = (post - pre).dropna()
+        mean = diff.mean(); sd = diff.std(ddof=1); n = diff.shape[0]
+        t = mean / (sd/np.sqrt(n))
+        p = 2*stats.t.sf(abs(t), df=n-1)
+        d_paired = mean / sd
+        print(f"{g:8s} n={n:2d}  Δ={mean:6.2f}  t={t:6.2f}  p={p:.3g}  d_paired={d_paired:.2f}")
+
+    # Between-group at post (Welch t) + Hedges g
+    post = df[df.time=="post"]
+    cats = post.group.cat.categories
+    gA = post[post.group==cats[0]]["strength"]
+    gB = post[post.group==cats[1]]["strength"]
+    t2, p2 = stats.ttest_ind(gA, gB, equal_var=False)
+    g = hedges_g(gA, gB)
+    print("\n=== Between groups at post (Welch t) ===")
+    print(f"t={t2:.2f}  p={p2:.3g}  Hedges g={g:.2f}")
+
+    if args.save_plots:
+        os.makedirs("outputs", exist_ok=True)
+        fig, ax = plt.subplots(figsize=(6,4))
+        # spaghetti
+        for (grp, sid), sub in df.sort_values("time").groupby(["group","id"], observed=False):
+            ax.plot([0,1], sub["strength"].values, alpha=0.2)
+        # thick means per group
+        mean_pre  = df[df.time=="pre" ].groupby("group", observed=False)["strength"].mean()
+        mean_post = df[df.time=="post"].groupby("group", observed=False)["strength"].mean()
+        for gname in df["group"].cat.categories:
+            ax.plot([0,1], [mean_pre[gname], mean_post[gname]], linewidth=3, label=gname)
+        ax.set_xticks([0,1]); ax.set_xticklabels(["pre","post"])
+        ax.set_ylabel("Strength")
+        ax.legend()
+        fig.tight_layout()
+        fp = "outputs/ch13_fitness_spaghetti.png"; fig.savefig(fp, dpi=150)
+        print("Saved plot ->", fp)
+
+if __name__ == "__main__":
+    main()

scripts/sim_fitness_2x2.py

@@ -1,10 +1,11 @@
 # SPDX-License-Identifier: MIT
 import os, json, time
 import numpy as np, pandas as pd
-rng = np.random.default_rng(7)
 
+rng = np.random.default_rng(7)
 N = 80
 GROUPS = ["ProgramA","ProgramB"]
+
 def simulate():
     os.makedirs("data/synthetic", exist_ok=True)
     subjects = pd.DataFrame({
@@ -14,25 +15,40 @@ def simulate():
         "sex": rng.choice(["F","M"], size=N, p=[0.5,0.5]),
         "bmi": rng.normal(24, 3.5, size=N).clip(17, 38),
     })
-    # baseline strength varies by covariates a bit
-    base = 80 + 0.8*(subjects["age"]-30) + 1.2*(subjects["bmi"]-24) + rng.normal(0, 8, N)
-    # program effects (post - pre), slightly larger for ProgramB
-    gain_A = rng.normal(8, 4, N)
-    gain_B = rng.normal(12, 4, N)
-    gain = np.where(subjects["group"]=="ProgramA", gain_A, gain_B)
+
+    # baseline strength with small covariate effects
+    base = (80
+            + 0.8*(subjects["age"]-30)
+            + 1.2*(subjects["bmi"]-24)
+            + rng.normal(0, 8, size=N))
+
+    # program gains
+    gain_A = rng.normal(8, 4, size=N)
+    gain_B = rng.normal(12, 4, size=N)
+    gain = np.where(subjects["group"].to_numpy()=="ProgramA", gain_A, gain_B)
 
     long = pd.concat([
-        pd.DataFrame({"id": subjects["id"], "time":"pre",  "strength": base + rng.normal(0, 3, N)}),
-        pd.DataFrame({"id": subjects["id"], "time":"post", "strength": base + gain + rng.normal(0, 3, N)})
+        pd.DataFrame({"id": subjects["id"], "time":"pre",
+                      "strength": base + rng.normal(0, 3, size=N)}),
+        pd.DataFrame({"id": subjects["id"], "time":"post",
+                      "strength": base + gain + rng.normal(0, 3, size=N)})
     ], ignore_index=True).merge(subjects, on="id")
 
     subjects.to_csv("data/synthetic/fitness_subjects.csv", index=False)
     long.to_csv("data/synthetic/fitness_long.csv", index=False)
+
     meta = dict(
-        seed=7, n= int(N), design="2x2 mixed (Group between × Time within)",
-        programs=GROUPS, dv="strength_1RM_like",
+        seed=7,
+        n=int(N),
+        design="2x2 mixed (Group between × Time within)",
+        programs=GROUPS,
+        dv="strength_1RM_like",
         generated_utc=time.strftime("%Y-%m-%dT%H:%M:%SZ", time.gmtime())
     )
-    with open("data/synthetic/fitness_meta.json","w") as f: json.dump(meta, f, indent=2)
+    with open("data/synthetic/fitness_meta.json","w") as f:
+        json.dump(meta, f, indent=2)
+
     print("Wrote fitness_subjects.csv, fitness_long.csv, fitness_meta.json")
-if __name__ == "__main__": simulate()
+
+if __name__ == "__main__":
+    simulate()