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Solved Lab #354

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170 changes: 155 additions & 15 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,
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"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -278,7 +278,7 @@
"[800 rows x 11 columns]"
]
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"execution_count": 3,
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"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -297,11 +297,65 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"# H0 = there is no difference\n",
"# H1 = Dragons have higher avg HP\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reject H0: Dragon-type Pokémon have significantly higher HP than Grass-type Pokémon.\n"
]
}
],
"source": [
"from scipy.stats import ttest_ind\n",
"\n",
"grass_hp = df[df['Type 1'] == 'Grass']['HP']\n",
"dragon_hp = df[df['Type 1'] == 'Dragon']['HP']\n",
"\n",
"# t-test\n",
"t_stat, p_value_two_tailed = ttest_ind(dragon_hp, grass_hp, equal_var=False)\n",
"\n",
"# Convert to one-tailed p-value (Dragon > Grass)\n",
"p_value_one_tailed = p_value_two_tailed / 2 if t_stat > 0 else 1 - (p_value_two_tailed / 2)\n",
"\n",
"t_stat, p_value_one_tailed\n",
"\n",
"if p_value_one_tailed < 0.05:\n",
" print(\"Reject H0: Dragon-type Pokémon have significantly higher HP than Grass-type Pokémon.\")\n",
"else:\n",
" print(\"Fail to reject H0: No significant evidence that Dragon-type Pokémon have higher HP.\")"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(3.3349632905124063, 0.0007993609745420598)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t_stat, p_value_one_tailed"
]
},
{
Expand All @@ -313,11 +367,57 @@
},
{
"cell_type": "code",
"execution_count": 18,
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"# H0 = No difference in stats\n",
"# H1 = Different stats"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 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",
" Legendary 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": [
"from statsmodels.multivariate.manova import MANOVA\n",
"\n",
"stats_cols = ['HP', 'Attack', 'Defense', 'Sp. Atk', 'Sp. Def', 'Speed']\n",
"df_manova = df[stats_cols + ['Legendary']]\n",
"\n",
"\n",
"maov = MANOVA.from_formula('HP + Attack + Defense + Q(\"Sp. Atk\") + Q(\"Sp. Def\") + Speed ~ Legendary', data=df_manova)\n",
"result = maov.mv_test()\n",
"print(result)"
]
},
{
Expand All @@ -337,7 +437,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 14,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -453,7 +553,7 @@
"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 +583,62 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": []
"source": [
"from scipy.stats import ttest_ind\n",
"\n",
"school_coords = (-118, 34)\n",
"hospital_coords = (-122, 37)\n",
"\n",
"def euclidean_distance(lat1, lon1, lat2, lon2):\n",
" return np.sqrt((lat1 - lat2)**2 + (lon1 - lon2)**2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Close to facility house values: [124700. 137500. 169100. ... 277700. 319400. 286100.]\n",
"Far from facility house values: [ 66900. 80100. 85700. ... 103600. 85800. 94600.]\n",
"t-statistic: 37.992, p-value: 0.000\n",
"Reject H0: Houses close to a school or hospital are significantly more expensive.\n"
]
}
],
"source": [
"df['dist_school'] = euclidean_distance(df['latitude'], df['longitude'], school_coords[1], school_coords[0])\n",
"df['dist_hospital'] = euclidean_distance(df['latitude'], df['longitude'], hospital_coords[1], hospital_coords[0])\n",
"\n",
"df['close_to_facility'] = (df['dist_school'] < 0.50) | (df['dist_hospital'] < 0.50)\n",
"\n",
"close_prices = df[df['close_to_facility']]['median_house_value']\n",
"far_prices = df[~df['close_to_facility']]['median_house_value']\n",
"\n",
"t_stat, p_value_two_tailed = ttest_ind(close_prices, far_prices, equal_var=False)\n",
"p_value_one_tailed = p_value_two_tailed / 2 if t_stat > 0 else 1 - (p_value_two_tailed / 2)\n",
"\n",
"\n",
"print(\"Close to facility house values:\", close_prices.values)\n",
"print(\"Far from facility house values:\", far_prices.values)\n",
"print(f\"t-statistic: {t_stat:.3f}, p-value: {p_value_one_tailed:.3f}\")\n",
"\n",
"if p_value_one_tailed < 0.05:\n",
" print(\"Reject H0: Houses close to a school or hospital are significantly more expensive.\")\n",
"else:\n",
" print(\"Fail to reject H0: No significant evidence that proximity to a school or hospital increases house prices.\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -512,7 +652,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.11.7"
}
},
"nbformat": 4,
Expand Down