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Lab OK #359

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179 changes: 164 additions & 15 deletions lab-hypothesis-testing.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -38,15 +38,14 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"#libraries\n",
"import pandas as pd\n",
"import scipy.stats as st\n",
"import numpy as np\n",
"\n"
"import numpy as np"
]
},
{
Expand Down Expand Up @@ -297,11 +296,73 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"# H0 : The average HP of Dragon = average of Grass\n",
"# H1 : The average HP of Dragon > average of Grass\n",
"\n",
"# one-sided two-sample t-test"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"69.25875"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df[\"HP\"].mean()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"dragon_hp = df[df['Type 1'] == 'Dragon']['HP']\n",
"grass_hp = df[df['Type 1'] == 'Grass']['HP']"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"t-statistic: 3.3349632905124063\n",
"p-value (bilateral): 0.0015987219490841195\n",
"✅ H0 rejected: Dragons have significantly more HP than Grass (5%).\n"
]
}
],
"source": [
"t_stat, p_val = st.ttest_ind(dragon_hp, grass_hp, equal_var=False)\n",
"\n",
"print(\"t-statistic:\", t_stat)\n",
"print(\"p-value (bilateral):\", p_val)\n",
"\n",
"# Unilateral hypothesis (Dragon > Grass),\n",
"# we divide p_val by 2 and check if the average of the Dragons is much greater\n",
"if (dragon_hp.mean() > grass_hp.mean()) and (p_val/2 < 0.05):\n",
" print(\"✅ H0 rejected: Dragons have significantly more HP than Grass (5%).\")\n",
"else:\n",
" print(\"❌ H0 cannot be rejected at the 5% threshold.\")"
]
},
{
Expand All @@ -313,11 +374,53 @@
},
{
"cell_type": "code",
"execution_count": 18,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"# H0 : Legendaries and non-legendaries have the same stats\n",
"# H1 : Legendaries and non-legendaries do not have the same stats"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"HP | mean Legendary=92.7, mean NonLegendary=67.2, F=64.58, p=0.0000\n",
"Attack | mean Legendary=116.7, mean NonLegendary=75.7, F=108.10, p=0.0000\n",
"Defense | mean Legendary=99.7, mean NonLegendary=71.6, F=51.57, p=0.0000\n",
"Sp. Atk | mean Legendary=122.2, mean NonLegendary=68.5, F=201.40, p=0.0000\n",
"Sp. Def | mean Legendary=105.9, mean NonLegendary=68.9, F=121.83, p=0.0000\n",
"Speed | mean Legendary=100.2, mean NonLegendary=65.5, F=95.36, p=0.0000\n"
]
}
],
"source": [
"legendary = df[df[\"Legendary\"] == True]\n",
"nonlegend = df[df[\"Legendary\"] == False]\n",
"\n",
"stats = [\"HP\", \"Attack\", \"Defense\", \"Sp. Atk\", \"Sp. Def\", \"Speed\"]\n",
"\n",
"for s in stats:\n",
" f, p = st.f_oneway(legendary[s], nonlegend[s])\n",
" print(f\"{s:7s} | mean Legendary={legendary[s].mean():.1f}, mean NonLegendary={nonlegend[s].mean():.1f}, F={f:.2f}, p={p:.4f}\")\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# We reject H0\n",
"\n",
"# This means that Legendary Pokémon have significantly different (and on average higher) stats than non-Legendaries in all dimensions tested \n",
"# (HP, Attack, Defense, Sp.Atk, Sp.Def, Speed)."
]
},
{
Expand All @@ -337,7 +440,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 11,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -453,7 +556,7 @@
"4 624.0 262.0 1.9250 65500.0 "
]
},
"execution_count": 5,
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
Expand Down Expand Up @@ -486,19 +589,65 @@
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
"source": [
"# H0 : The average price of nearby houses (≤ 0.5) is no different from that of distant houses (> 0.5).\n",
"# H1 : The average price of nearby houses is higher than that of distant houses."
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Close mean: 246934.639238653\n",
"Far mean: 180683.57168141592\n",
"t-stat: 37.97959304116918\n",
"p-value (bilateral): 4.642199519694926e-301\n",
"✅ H0 rejected : nearby houses are significantly more expensive (5%).\n"
]
}
],
"source": [
"school = (-118, 34)\n",
"hospital = (-122, 37)\n",
"\n",
"def euclidean_distance(x1, y1, x2, y2):\n",
" return np.sqrt((x1 - x2)**2 + (y1 - y2)**2)\n",
"\n",
"# Distance\n",
"df[\"dist_school\"] = df.apply(lambda row: euclidean_distance(row[\"longitude\"], row[\"latitude\"], *school), axis=1)\n",
"df[\"dist_hospital\"] = df.apply(lambda row: euclidean_distance(row[\"longitude\"], row[\"latitude\"], *hospital), axis=1)\n",
"\n",
"# Variable indicatrice \"close\"\n",
"df[\"close\"] = ((df[\"dist_school\"] <= 0.5) | (df[\"dist_hospital\"] <= 0.5))\n",
"\n",
"# Separate groups\n",
"close_prices = df[df[\"close\"] == True][\"median_house_value\"]\n",
"far_prices = df[df[\"close\"] == False][\"median_house_value\"]\n",
"\n",
"# T Test\n",
"t_stat, p_val = st.ttest_ind(close_prices, far_prices, equal_var=False)\n",
"\n",
"print(\"Close mean:\", close_prices.mean())\n",
"print(\"Far mean:\", far_prices.mean())\n",
"print(\"t-stat:\", t_stat)\n",
"print(\"p-value (bilateral):\", p_val)\n",
"\n",
"# Unilateral Test (close > far)\n",
"if (close_prices.mean() > far_prices.mean()) and (p_val/2 < 0.05):\n",
" print(\"✅ H0 rejected : nearby houses are significantly more expensive (5%).\")\n",
"else:\n",
" print(\"❌ H0 cannot be rejected at the 5% threshold.\")\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -512,7 +661,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.12.2"
}
},
"nbformat": 4,
Expand Down