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271 changes: 255 additions & 16 deletions lab-hypothesis-testing.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -38,7 +38,7 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -51,7 +51,7 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 14,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -278,7 +278,7 @@
"[800 rows x 11 columns]"
]
},
"execution_count": 3,
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -297,11 +297,67 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 15,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Dragon: n=32, mean=83.31, sd=23.80\n",
"Grass : n=70, mean=67.27, sd=19.52\n",
"Welch t = 3.335, df ≈ 50.8, one-sided p = 0.0007994\n",
"Mean difference (Dragon - Grass) = 16.04 [95% CI: 6.38, 25.70]\n",
"Hedges' g = 0.760\n"
]
}
],
"source": [
"#code here"
"#code here\n",
"type_col = \"Type 1\" if \"Type 1\" in df.columns else (\n",
" \"type\" if \"type\" in df.columns else [c for c in df.columns if \"type\" in c.lower()][0]\n",
")\n",
"\n",
"# Extract HP for Dragon vs Grass\n",
"dragon = df.loc[df[type_col].str.lower() == \"dragon\", \"HP\"].dropna().astype(float)\n",
"grass = df.loc[df[type_col].str.lower() == \"grass\", \"HP\"].dropna().astype(float)\n",
"\n",
"print(f\"Dragon: n={len(dragon)}, mean={dragon.mean():.2f}, sd={dragon.std(ddof=1):.2f}\")\n",
"print(f\"Grass : n={len(grass)}, mean={grass.mean():.2f}, sd={grass.std(ddof=1):.2f}\")\n",
"\n",
"# One-sided Welch's t-test: H0: mu_Dragon <= mu_Grass vs H1: mu_Dragon > mu_Grass\n",
"try:\n",
" # SciPy ≥ 1.9 supports 'alternative'\n",
" res = st.ttest_ind(dragon, grass, equal_var=False, alternative='greater')\n",
" tstat, p_one = res.statistic, res.pvalue\n",
" # compute Welch DOF for CI/effect size if you want\n",
" s1, s2 = dragon.var(ddof=1), grass.var(ddof=1)\n",
" n1, n2 = len(dragon), len(grass)\n",
" se = np.sqrt(s1/n1 + s2/n2)\n",
" dof = (s1/n1 + s2/n2)**2 / ((s1**2)/((n1**2)*(n1-1)) + (s2**2)/((n2**2)*(n2-1)))\n",
"except TypeError:\n",
" # Fallback for older SciPy: compute one-sided p manually\n",
" s1, s2 = dragon.var(ddof=1), grass.var(ddof=1)\n",
" n1, n2 = len(dragon), len(grass)\n",
" se = np.sqrt(s1/n1 + s2/n2)\n",
" tstat = (dragon.mean() - grass.mean()) / se\n",
" dof = (s1/n1 + s2/n2)**2 / ((s1**2)/((n1**2)*(n1-1)) + (s2**2)/((n2**2)*(n2-1)))\n",
" p_one = st.t.sf(tstat, dof) # one-sided tail\n",
"\n",
"print(f\"Welch t = {tstat:.3f}, df ≈ {dof:.1f}, one-sided p = {p_one:.4g}\")\n",
"\n",
"# (Optional) 95% CI for the mean difference (two-sided)\n",
"diff = dragon.mean() - grass.mean()\n",
"tcrit = st.t.ppf(0.975, dof)\n",
"ci_low, ci_high = diff - tcrit*se, diff + tcrit*se\n",
"print(f\"Mean difference (Dragon - Grass) = {diff:.2f} [95% CI: {ci_low:.2f}, {ci_high:.2f}]\")\n",
"\n",
"# (Optional) Effect size (Hedges' g)\n",
"sp2 = ((n1-1)*s1 + (n2-1)*s2) / (n1+n2-2) # pooled variance\n",
"d = diff / np.sqrt(sp2) # Cohen's d\n",
"J = 1 - 3/(4*(n1+n2)-9) # small-sample correction\n",
"g = J * d\n",
"print(f\"Hedges' g = {g:.3f}\")\n"
]
},
{
Expand All @@ -313,11 +369,117 @@
},
{
"cell_type": "code",
"execution_count": 18,
"execution_count": 16,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" stat mean_legendary mean_nonlegend diff(L-N) hedges_g p_raw p_holm reject_0.05\n",
"Sp. Atk 122.184615 68.454422 53.730194 1.834685 1.551461e-21 9.308768e-21 True\n",
" Speed 100.184615 65.455782 34.728833 1.262463 1.049016e-18 5.245082e-18 True\n",
" Attack 116.676923 75.669388 41.007535 1.344181 2.520372e-16 1.008149e-15 True\n",
"Sp. Def 105.938462 68.892517 37.045945 1.426976 2.294933e-15 6.884798e-15 True\n",
" HP 92.738462 67.182313 25.556149 1.038922 1.002691e-13 2.005382e-13 True\n",
"Defense 99.661538 71.559184 28.102355 0.928401 4.826998e-11 4.826998e-11 True\n",
"\n",
"MANOVA (Pillai’s trace):\n",
" Multivariate linear model\n",
"================================================================\n",
" \n",
"----------------------------------------------------------------\n",
" Intercept Value Num DF Den DF F Value Pr > F\n",
"----------------------------------------------------------------\n",
" Wilks' lambda 0.0592 6.0000 793.0000 2100.8338 0.0000\n",
" Pillai's trace 0.9408 6.0000 793.0000 2100.8338 0.0000\n",
" Hotelling-Lawley trace 15.8953 6.0000 793.0000 2100.8338 0.0000\n",
" Roy's greatest root 15.8953 6.0000 793.0000 2100.8338 0.0000\n",
"----------------------------------------------------------------\n",
" \n",
"----------------------------------------------------------------\n",
" C(LegendaryFlag) Value Num DF Den DF F Value Pr > F\n",
"----------------------------------------------------------------\n",
" Wilks' lambda 0.7331 6.0000 793.0000 48.1098 0.0000\n",
" Pillai's trace 0.2669 6.0000 793.0000 48.1098 0.0000\n",
" Hotelling-Lawley trace 0.3640 6.0000 793.0000 48.1098 0.0000\n",
" Roy's greatest root 0.3640 6.0000 793.0000 48.1098 0.0000\n",
"================================================================\n",
"\n"
]
}
],
"source": [
"#code here"
"#code here\n",
"# Columns\n",
"flag_col = \"Legendary\" if \"Legendary\" in df.columns else [c for c in df.columns if \"legend\" in c.lower()][0]\n",
"stats_cols = [\"HP\",\"Attack\",\"Defense\",\"Sp. Atk\",\"Sp. Def\",\"Speed\"]\n",
"stats_cols = [c for c in stats_cols if c in df.columns] # keep only those present\n",
"\n",
"# Split groups\n",
"leg = df[df[flag_col] == True][stats_cols].astype(float)\n",
"non = df[df[flag_col] == False][stats_cols].astype(float)\n",
"\n",
"# Per-stat Welch t-tests (two-sided) + effect size\n",
"rows = []\n",
"for col in stats_cols:\n",
" x, y = leg[col].dropna().values, non[col].dropna().values\n",
" res = st.ttest_ind(x, y, equal_var=False) # two-sided\n",
" # Hedges' g\n",
" n1, n2 = len(x), len(y)\n",
" s1, s2 = np.var(x, ddof=1), np.var(y, ddof=1)\n",
" sp2 = ((n1-1)*s1 + (n2-1)*s2) / (n1+n2-2)\n",
" d = (x.mean() - y.mean()) / np.sqrt(sp2)\n",
" J = 1 - 3/(4*(n1+n2)-9) # small-sample correction\n",
" g = J*d\n",
" rows.append({\n",
" \"stat\": col,\n",
" \"mean_legendary\": x.mean(),\n",
" \"mean_nonlegend\": y.mean(),\n",
" \"diff(L-N)\": x.mean()-y.mean(),\n",
" \"t\": res.statistic,\n",
" \"p_raw\": res.pvalue,\n",
" \"hedges_g\": g\n",
" })\n",
"\n",
"out = pd.DataFrame(rows)\n",
"\n",
"# Multiple-comparison correction (Holm)\n",
"try:\n",
" from statsmodels.stats.multitest import multipletests\n",
" rej, p_holm, _, _ = multipletests(out[\"p_raw\"], method=\"holm\")\n",
" out[\"p_holm\"] = p_holm\n",
" out[\"reject_0.05\"] = rej\n",
"except Exception:\n",
" # simple Holm fallback\n",
" order = np.argsort(out[\"p_raw\"].values)\n",
" m = len(out)\n",
" holm = np.empty(m); holm[:] = np.nan\n",
" for rank, idx in enumerate(order, start=1):\n",
" holm[idx] = (m - rank + 1) * out.loc[idx, \"p_raw\"]\n",
" # monotone adjustment\n",
" for i in range(1, m):\n",
" holm[order[i]] = max(holm[order[i]], holm[order[i-1]])\n",
" out[\"p_holm\"] = np.clip(holm, 0, 1)\n",
" out[\"reject_0.05\"] = out[\"p_holm\"] < 0.05\n",
"\n",
"# Nicely sorted table\n",
"print(out.sort_values(\"p_holm\")[[\"stat\",\"mean_legendary\",\"mean_nonlegend\",\"diff(L-N)\",\"hedges_g\",\"p_raw\",\"p_holm\",\"reject_0.05\"]]\n",
" .to_string(index=False))\n",
"\n",
"# (Optional) Global multivariate test (MANOVA)\n",
"try:\n",
" from statsmodels.multivariate.manova import MANOVA\n",
" # make a temporary df with clean column names for formula\n",
" tmp = df[[flag_col]+stats_cols].dropna().copy()\n",
" tmp = tmp.rename(columns={flag_col:\"LegendaryFlag\",\n",
" \"Sp. Atk\":\"Sp_Atk\",\"Sp. Def\":\"Sp_Def\"})\n",
" formula = \"HP + Attack + Defense + Sp_Atk + Sp_Def + Speed ~ C(LegendaryFlag)\"\n",
" manova = MANOVA.from_formula(formula, data=tmp)\n",
" print(\"\\nMANOVA (Pillai’s trace):\")\n",
" print(manova.mv_test()) # look at Pillai/ Wilks p-values\n",
"except Exception as e:\n",
" print(\"\\nMANOVA skipped (statsmodels not available or column names differ).\")\n"
]
},
{
Expand All @@ -337,7 +499,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 17,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -453,7 +615,7 @@
"4 624.0 262.0 1.9250 65500.0 "
]
},
"execution_count": 5,
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
Expand Down Expand Up @@ -483,10 +645,87 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Close: n=6829, mean=$246,952\n",
"Far : n=10171, mean=$180,678\n",
"Welch t = 37.992, df ≈ 14571.2, one-sided p = 1.503e-301, diff = $66,274\n",
"Hedges' g = 0.595\n",
"Mann–Whitney U one-sided p = 0\n"
]
}
],
"source": [
"# 0) Load\n",
"df = pd.read_csv(\"https://raw.githubusercontent.com/data-bootcamp-v4/data/main/california_housing.csv\")\n",
"\n",
"# 1) Columns\n",
"lon_col = next(c for c in df.columns if \"long\" in c.lower()) # 'longitude'\n",
"lat_col = next(c for c in df.columns if \"lat\" in c.lower()) # 'latitude'\n",
"price_col = next(c for c in df.columns if \"median_house_value\" in c.lower())\n",
"\n",
"# 2) Distances (euclidean on lon/lat degrees, as hinted)\n",
"school = (-118.0, 34.0)\n",
"hospital = (-122.0, 37.0)\n",
"\n",
"def euclid_xy(x1, y1, x2, y2):\n",
" return np.sqrt((x1 - x2)**2 + (y1 - y2)**2)\n",
"\n",
"df[\"dist_school\"] = euclid_xy(df[lon_col], df[lat_col], school[0], school[1])\n",
"df[\"dist_hospital\"] = euclid_xy(df[lon_col], df[lat_col], hospital[0], hospital[1])\n",
"df[\"dist_min\"] = df[[\"dist_school\",\"dist_hospital\"]].min(axis=1)\n",
"\n",
"# 3) Close vs Far\n",
"threshold = 0.50 # per instructions\n",
"df[\"close\"] = df[\"dist_min\"] < threshold\n",
"\n",
"# 4) Prepare groups\n",
"close_vals = df.loc[df[\"close\"], price_col].dropna().astype(float)\n",
"far_vals = df.loc[~df[\"close\"], price_col].dropna().astype(float)\n",
"\n",
"print(f\"Close: n={len(close_vals)}, mean=${close_vals.mean():,.0f}\")\n",
"print(f\"Far : n={len(far_vals)}, mean=${far_vals.mean():,.0f}\")\n",
"\n",
"# 5) Hypothesis test (one-sided Welch t-test)\n",
"# H0: mu_close <= mu_far vs H1: mu_close > mu_far\n",
"try:\n",
" # SciPy >= 1.9 supports 'alternative'\n",
" res = st.ttest_ind(close_vals, far_vals, equal_var=False, alternative=\"greater\")\n",
" tstat, p_one = res.statistic, res.pvalue\n",
"except TypeError:\n",
" # manual one-sided from two-sided\n",
" res = st.ttest_ind(close_vals, far_vals, equal_var=False)\n",
" tstat = res.statistic\n",
" p_one = st.t.sf(tstat, df=min(len(close_vals)-1, len(far_vals)-1)) # conservative df\n",
"\n",
"# Welch SE & dof (for reporting)\n",
"s1, s2 = close_vals.var(ddof=1), far_vals.var(ddof=1)\n",
"n1, n2 = len(close_vals), len(far_vals)\n",
"se = np.sqrt(s1/n1 + s2/n2)\n",
"dof = (s1/n1 + s2/n2)**2 / ((s1**2)/((n1**2)*(n1-1)) + (s2**2)/((n2**2)*(n2-1)))\n",
"\n",
"diff = close_vals.mean() - far_vals.mean()\n",
"print(f\"Welch t = {tstat:.3f}, df ≈ {dof:.1f}, one-sided p = {p_one:.4g}, diff = ${diff:,.0f}\")\n",
"\n",
"# 6) Effect size (Hedges' g)\n",
"sp2 = ((n1-1)*s1 + (n2-1)*s2) / (n1+n2-2)\n",
"d = diff / np.sqrt(sp2)\n",
"J = 1 - 3/(4*(n1+n2)-9)\n",
"g = J*d\n",
"print(f\"Hedges' g = {g:.3f}\")\n",
"\n",
"# 7) (Optional) Robustness: one-sided Mann–Whitney U (close > far)\n",
"try:\n",
" u_stat, p_mwu = st.mannwhitneyu(close_vals, far_vals, alternative=\"greater\")\n",
" print(f\"Mann–Whitney U one-sided p = {p_mwu:.4g}\")\n",
"except TypeError:\n",
" pass\n"
]
},
{
"cell_type": "code",
Expand All @@ -498,7 +737,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -512,7 +751,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.12.7"
}
},
"nbformat": 4,
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