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Solved lab #349

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227 changes: 213 additions & 14 deletions lab-hypothesis-testing.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -51,7 +51,7 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 2,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -278,7 +278,7 @@
"[800 rows x 11 columns]"
]
},
"execution_count": 3,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -297,11 +297,58 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.stats as st\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"#Two-Sample T-Test \n",
"\n",
"def is_type(df, t):\n",
" return (df['Type 1'].eq(t)) | (df['Type 2'].eq(t))\n",
"\n",
"dragons = df.loc[is_type(df, 'Dragon'), 'HP'].dropna().to_numpy()\n",
"grass = df.loc[is_type(df, 'Grass'), 'HP'].dropna().to_numpy()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"t=4.499135, one-sided p=0.000007\n",
"Decision: Reject H0 (Dragon > Grass)\n"
]
}
],
"source": [
"tstat, p_two = st.ttest_ind(dragons, grass, equal_var=True) \n",
"\n",
"p_one = p_two/2 if tstat > 0 else 1 - p_two/2\n",
"alpha = 0.05\n",
"print(f\"t={tstat:3f}, one-sided p={p_one:4f}\")\n",
"print(\"Decision:\", \"Reject H0 (Dragon > Grass)\" if p_one < alpha else \"Fail to reject H0\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fail to reject 𝐻0; the data do not provide sufficient evidence that Dragons have higher mean HP than Grass at 5%."
]
},
{
Expand All @@ -313,11 +360,125 @@
},
{
"cell_type": "code",
"execution_count": 18,
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"stats_cols = ['HP','Attack','Defense','Sp. Atk','Sp. Def','Speed']\n",
"leg = df[df['Legendary'] == True]\n",
"non = df[df['Legendary'] == False]"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>stat</th>\n",
" <th>t</th>\n",
" <th>p_two_sided</th>\n",
" <th>sig_5%</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>Sp. Atk</td>\n",
" <td>14.191406</td>\n",
" <td>6.314916e-41</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>Sp. Def</td>\n",
" <td>11.037751</td>\n",
" <td>1.843981e-26</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>Attack</td>\n",
" <td>10.397321</td>\n",
" <td>7.827253e-24</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>Speed</td>\n",
" <td>9.765234</td>\n",
" <td>2.354075e-21</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>HP</td>\n",
" <td>8.036124</td>\n",
" <td>3.330648e-15</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>Defense</td>\n",
" <td>7.181240</td>\n",
" <td>1.584223e-12</td>\n",
" <td>True</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" stat t p_two_sided sig_5%\n",
"3 Sp. Atk 14.191406 6.314916e-41 True\n",
"4 Sp. Def 11.037751 1.843981e-26 True\n",
"1 Attack 10.397321 7.827253e-24 True\n",
"5 Speed 9.765234 2.354075e-21 True\n",
"0 HP 8.036124 3.330648e-15 True\n",
"2 Defense 7.181240 1.584223e-12 True"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rows = []\n",
"for col in stats_cols:\n",
" x = leg[col].dropna().to_numpy()\n",
" y = non[col].dropna().to_numpy()\n",
" t, p = st.ttest_ind(x, y, equal_var=True)\n",
" rows.append({\"stat\": col, \"t\": t, \"p_two_sided\": p, \"sig_5%\": p < 0.05})\n",
"\n",
"pd.DataFrame(rows).sort_values(\"p_two_sided\")\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"“At the 5% level, Legendary Pokémon show significantly higher average values in [significant stats] compared with Non-Legendary, while differences in [non-significant stats] are not statistically significant."
]
},
{
Expand All @@ -337,7 +498,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 14,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -453,7 +614,7 @@
"4 624.0 262.0 1.9250 65500.0 "
]
},
"execution_count": 5,
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
Expand Down Expand Up @@ -483,22 +644,60 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": []
"source": [
"school_lon, school_lat = -118.0, 34.0\n",
"hospital_lon, hospital_lat = -122.0, 37.0"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": []
"source": [
"def euclidean(lon, lat, ref_lon, ref_lat):\n",
" return np.sqrt((lon - ref_lon)**2 + (lat - ref_lat)**2)\n",
"\n",
"df['dist_school'] = euclidean(df['longitude'], df['latitude'], school_lon, school_lat)\n",
"df['dist_hospital'] = euclidean(df['longitude'], df['latitude'], hospital_lon, hospital_lat)\n",
"df['near_either'] = (df['dist_school'] < 0.50) | (df['dist_hospital'] < 0.50)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Near n=6829, Far n=10171\n",
"Means: Near=246952, Far=180678\n",
"t=38.046, two-sided p=4.818e-304\n",
"Decision: Significant difference\n"
]
}
],
"source": [
"near_vals = df.loc[df['near_either'], 'median_house_value'].dropna().to_numpy()\n",
"far_vals = df.loc[~df['near_either'], 'median_house_value'].dropna().to_numpy()\n",
"\n",
"t, p = st.ttest_ind(near_vals, far_vals, equal_var=True) # pooled, as in lesson\n",
"alpha = 0.05\n",
"print(f\"Near n={len(near_vals)}, Far n={len(far_vals)}\")\n",
"print(f\"Means: Near={near_vals.mean():.0f}, Far={far_vals.mean():.0f}\")\n",
"print(f\"t={t:.3f}, two-sided p={p:.4g}\")\n",
"print(\"Decision:\", \"Significant difference\" if p < alpha else \"No significant difference\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -512,7 +711,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.12.7"
}
},
"nbformat": 4,
Expand Down