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206 changes: 188 additions & 18 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 +297,46 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"T-statistic: 3.335, One-tailed p-value: 0.0008\n",
"Reject H0: Dragon-type Pokémon have significantly higher HP than Grass-type Pokémon.\n",
"Mean HP - Dragon: 83.31, Grass: 67.27\n"
]
}
],
"source": [
"#code here"
"# Filter HP stats by type\n",
"dragon_hp = df[df['Type 1'] == 'Dragon']['HP']\n",
"grass_hp = df[df['Type 1'] == 'Grass']['HP']\n",
"\n",
"# Two-sample t-test (assume unequal variance, one-tailed)\n",
"t_stat, p_value_two_tailed = st.ttest_ind(dragon_hp, grass_hp, equal_var=False)\n",
"\n",
"# Convert to one-tailed p-value for Dragon > Grass\n",
"if t_stat > 0:\n",
" p_value_one_tailed = p_value_two_tailed / 2\n",
"else:\n",
" p_value_one_tailed = 1 - p_value_two_tailed / 2\n",
"\n",
"print(f\"T-statistic: {t_stat:.3f}, One-tailed p-value: {p_value_one_tailed:.4f}\")\n",
"\n",
"# Significance check\n",
"alpha = 0.05\n",
"if p_value_one_tailed < alpha:\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 difference in HP between Dragon and Grass Pokémon.\")\n",
"\n",
"# Optional: mean HP for both types\n",
"mean_dragon = np.mean(dragon_hp)\n",
"mean_grass = np.mean(grass_hp)\n",
"print(f\"Mean HP - Dragon: {mean_dragon:.2f}, Grass: {mean_grass:.2f}\")"
]
},
{
Expand All @@ -313,11 +348,84 @@
},
{
"cell_type": "code",
"execution_count": 18,
"execution_count": 6,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Stat: HP\n",
"T-statistic: 8.981, Two-tailed p-value: 0.0000\n",
"Reject H0: Legendary and Non-Legendary Pokémon have significantly different HP.\n",
"\n",
"Stat: Attack\n",
"T-statistic: 10.438, Two-tailed p-value: 0.0000\n",
"Reject H0: Legendary and Non-Legendary Pokémon have significantly different Attack.\n",
"\n",
"Stat: Defense\n",
"T-statistic: 7.637, Two-tailed p-value: 0.0000\n",
"Reject H0: Legendary and Non-Legendary Pokémon have significantly different Defense.\n",
"\n",
"Stat: Sp. Atk\n",
"T-statistic: 13.417, Two-tailed p-value: 0.0000\n",
"Reject H0: Legendary and Non-Legendary Pokémon have significantly different Sp. Atk.\n",
"\n",
"Stat: Sp. Def\n",
"T-statistic: 10.016, Two-tailed p-value: 0.0000\n",
"Reject H0: Legendary and Non-Legendary Pokémon have significantly different Sp. Def.\n",
"\n",
"Stat: Speed\n",
"T-statistic: 11.475, Two-tailed p-value: 0.0000\n",
"Reject H0: Legendary and Non-Legendary Pokémon have significantly different Speed.\n",
"\n",
"Mean stats for Legendary Pokémon:\n",
"HP 92.738462\n",
"Attack 116.676923\n",
"Defense 99.661538\n",
"Sp. Atk 122.184615\n",
"Sp. Def 105.938462\n",
"Speed 100.184615\n",
"dtype: float64\n",
"\n",
"Mean stats for Non-Legendary Pokémon:\n",
"HP 67.182313\n",
"Attack 75.669388\n",
"Defense 71.559184\n",
"Sp. Atk 68.454422\n",
"Sp. Def 68.892517\n",
"Speed 65.455782\n",
"dtype: float64\n"
]
}
],
"source": [
"#code here"
"# Columns to test\n",
"stats_cols = ['HP', 'Attack', 'Defense', 'Sp. Atk', 'Sp. Def', 'Speed']\n",
"\n",
"# Split data\n",
"legendary = df[df['Legendary'] == True]\n",
"non_legendary = df[df['Legendary'] == False]\n",
"\n",
"# Significance level\n",
"alpha = 0.05\n",
"\n",
"# Perform independent t-tests for each stat\n",
"for col in stats_cols:\n",
" t_stat, p_value_two_tailed = st.ttest_ind(legendary[col], non_legendary[col], equal_var=False)\n",
" print(f\"\\nStat: {col}\")\n",
" print(f\"T-statistic: {t_stat:.3f}, Two-tailed p-value: {p_value_two_tailed:.4f}\")\n",
" if p_value_two_tailed < alpha:\n",
" print(f\"Reject H0: Legendary and Non-Legendary Pokémon have significantly different {col}.\")\n",
" else:\n",
" print(f\"Fail to reject H0: No significant difference in {col} between Legendary and Non-Legendary Pokémon.\")\n",
"\n",
"# Optional: print mean stats for each group\n",
"print(\"\\nMean stats for Legendary Pokémon:\")\n",
"print(legendary[stats_cols].mean())\n",
"print(\"\\nMean stats for Non-Legendary Pokémon:\")\n",
"print(non_legendary[stats_cols].mean())"
]
},
{
Expand All @@ -337,7 +445,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 17,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -453,7 +561,7 @@
"4 624.0 262.0 1.9250 65500.0 "
]
},
"execution_count": 5,
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
Expand Down Expand Up @@ -483,22 +591,84 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['longitude', 'latitude', 'housing_median_age', 'total_rooms', 'total_bedrooms', 'population', 'households', 'median_income', 'median_house_value']\n"
]
}
],
"source": [
"print(df.columns.tolist())"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"T-statistic: 37.992\n",
"One-tailed p-value: 0.0000\n",
"Reject H0: Houses close to a school or hospital are significantly more expensive.\n",
"Mean house value (close): 246951.98\n",
"Mean house value (far): 180678.44\n"
]
}
],
"source": [
"# Function to calculate Euclidean distance\n",
"def euclidean_distance(lon1, lat1, lon2, lat2):\n",
" return np.sqrt((lon1 - lon2)**2 + (lat1 - lat2)**2)\n",
"\n",
"# Calculate distance from each house to school and hospital\n",
"df['dist_school'] = euclidean_distance(df['longitude'], df['latitude'], school_coord[0], school_coord[1])\n",
"df['dist_hospital'] = euclidean_distance(df['longitude'], df['latitude'], hospital_coord[0], hospital_coord[1])\n",
"\n",
"# Minimum distance to either school or hospital\n",
"df['min_dist'] = df[['dist_school', 'dist_hospital']].min(axis=1)\n",
"\n",
"# Split dataset into houses close and far (distance < 0.50 is close)\n",
"close_houses = df[df['min_dist'] < 0.50]['median_house_value']\n",
"far_houses = df[df['min_dist'] >= 0.50]['median_house_value']\n",
"\n",
"# Two-sample t-test (unequal variance)\n",
"t_stat, p_value_two_tailed = stats.ttest_ind(close_houses, far_houses, equal_var=False)\n",
"\n",
"# Convert to one-tailed p-value for \"close houses > far houses\"\n",
"if t_stat > 0:\n",
" p_value_one_tailed = p_value_two_tailed / 2\n",
"else:\n",
" p_value_one_tailed = 1 - p_value_two_tailed / 2\n",
"\n",
"# Significance level\n",
"alpha = 0.05\n",
"\n",
"# Print results\n",
"print(f\"T-statistic: {t_stat:.3f}\")\n",
"print(f\"One-tailed p-value: {p_value_one_tailed:.4f}\")\n",
"\n",
"if p_value_one_tailed < alpha:\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 difference in house value based on proximity.\")\n",
"\n",
"# Optional: Mean house values for interpretation\n",
"print(f\"Mean house value (close): {close_houses.mean():.2f}\")\n",
"print(f\"Mean house value (far): {far_houses.mean():.2f}\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "tfdf_env",
"language": "python",
"name": "python3"
},
Expand All @@ -512,7 +682,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.11.13"
}
},
"nbformat": 4,
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