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275 changes: 253 additions & 22 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": 3,
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -51,7 +51,7 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 5,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -278,14 +278,14 @@
"[800 rows x 11 columns]"
]
},
"execution_count": 3,
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.read_csv(\"https://raw.githubusercontent.com/data-bootcamp-v4/data/main/pokemon.csv\")\n",
"df"
"df_pokemon = pd.read_csv(\"https://raw.githubusercontent.com/data-bootcamp-v4/data/main/pokemon.csv\")\n",
"df_pokemon"
]
},
{
Expand All @@ -297,11 +297,58 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 6,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"--- T-Test: Dragon HP vs. Grass HP (Unilateral) ---\n",
"Mean HP Dragon: 83.31\n",
"Mean HP Grass: 67.27\n",
"T-Statistic: 3.5904\n",
"P-Value (One-Tailed): 0.0003\n",
"\n",
"Finding: Since the p-value (0.0003) is less than alpha (0.05), we REJECT the Null Hypothesis (H₀).\n",
"Conclusion: There is statistically significant evidence to support the posit that Dragon-type Pokemons have, on average, more HP than Grass-type Pokemons.\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import ttest_ind\n",
"\n",
"# 1. Prepare data groups\n",
"hp_dragon = df_pokemon[df_pokemon['Type 1'] == 'Dragon']['HP']\n",
"hp_grass = df_pokemon[df_pokemon['Type 1'] == 'Grass']['HP']\n",
"\n",
"# 2. Perform Two-Sample T-Test (Two-tailed by default)\n",
"# We assume equal variances (equal_var=False if sample sizes/STDs are very different, but we'll start with True/default)\n",
"t_stat, p_value_two_tailed = ttest_ind(hp_dragon, hp_grass, nan_policy='omit')\n",
"\n",
"# 3. Adjust p-value for a one-tailed test (H_a: mu_Dragon > mu_Grass)\n",
"# Since we are testing for \">\" (right-sided) and the T-stat is positive, we divide p-value by 2.\n",
"if t_stat > 0:\n",
" p_value_one_tailed = p_value_two_tailed / 2\n",
"else:\n",
" # If T-stat is negative, it means Dragon HP is NOT greater, so P-value is close to 1\n",
" p_value_one_tailed = 1 - (p_value_two_tailed / 2)\n",
"\n",
"alpha = 0.05\n",
"\n",
"print(\"--- T-Test: Dragon HP vs. Grass HP (Unilateral) ---\")\n",
"print(f\"Mean HP Dragon: {hp_dragon.mean():.2f}\")\n",
"print(f\"Mean HP Grass: {hp_grass.mean():.2f}\")\n",
"print(f\"T-Statistic: {t_stat:.4f}\")\n",
"print(f\"P-Value (One-Tailed): {p_value_one_tailed:.4f}\")\n",
"\n",
"# Commentary:\n",
"if p_value_one_tailed < alpha:\n",
" print(f\"\\nFinding: Since the p-value ({p_value_one_tailed:.4f}) is less than alpha (0.05), we REJECT the Null Hypothesis (H₀).\")\n",
" print(\"Conclusion: There is statistically significant evidence to support the posit that Dragon-type Pokemons have, on average, more HP than Grass-type Pokemons.\")\n",
"else:\n",
" print(f\"\\nFinding: Since the p-value ({p_value_one_tailed:.4f}) is greater than alpha (0.05), we FAIL TO REJECT the Null Hypothesis (H₀).\")\n",
" print(\"Conclusion: There is no statistically significant evidence to support the posit that Dragon-type Pokemons have, on average, more HP than Grass-type Pokemons.\")"
]
},
{
Expand All @@ -313,11 +360,103 @@
},
{
"cell_type": "code",
"execution_count": 18,
"execution_count": 7,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"--- T-Test: Legendary vs. Non-Legendary Stats (Bilateral) ---\n",
"\n",
"Statistic: HP\n",
" P-Value: 0.000000\n",
" Finding: Reject H₀\n",
" Conclusion: Significant difference found\n",
"\n",
"Statistic: Attack\n",
" P-Value: 0.000000\n",
" Finding: Reject H₀\n",
" Conclusion: Significant difference found\n",
"\n",
"Statistic: Defense\n",
" P-Value: 0.000000\n",
" Finding: Reject H₀\n",
" Conclusion: Significant difference found\n",
"\n",
"Statistic: Sp. Atk\n",
" P-Value: 0.000000\n",
" Finding: Reject H₀\n",
" Conclusion: Significant difference found\n",
"\n",
"Statistic: Sp. Def\n",
" P-Value: 0.000000\n",
" Finding: Reject H₀\n",
" Conclusion: Significant difference found\n",
"\n",
"Statistic: Speed\n",
" P-Value: 0.000000\n",
" Finding: Reject H₀\n",
" Conclusion: Significant difference found\n",
"\n",
"Detailed Results:\n",
" Legendary Mean Non-Legendary Mean T-Stat P-Value\n",
"HP 92.738462 67.182313 8.036124 3.330648e-15\n",
"Attack 116.676923 75.669388 10.397321 7.827253e-24\n",
"Defense 99.661538 71.559184 7.181240 1.584223e-12\n",
"Sp. Atk 122.184615 68.454422 14.191406 6.314916e-41\n",
"Sp. Def 105.938462 68.892517 11.037751 1.843981e-26\n",
"Speed 100.184615 65.455782 9.765234 2.354075e-21\n"
]
}
],
"source": [
"#code here"
"# 1. Define stats columns\n",
"stat_columns = ['HP', 'Attack', 'Defense', 'Sp. Atk', 'Sp. Def', 'Speed']\n",
"\n",
"# 2. Separate data groups\n",
"legendary_stats = df_pokemon[df_pokemon['Legendary'] == True]\n",
"non_legendary_stats = df_pokemon[df_pokemon['Legendary'] == False]\n",
"\n",
"results = {}\n",
"\n",
"print(\"--- T-Test: Legendary vs. Non-Legendary Stats (Bilateral) ---\")\n",
"\n",
"# 3. Perform T-test for each stat\n",
"for stat in stat_columns:\n",
" # Extract data for the current stat\n",
" legendary_group = legendary_stats[stat]\n",
" non_legendary_group = non_legendary_stats[stat]\n",
"\n",
" # Run T-test\n",
" t_stat, p_value = ttest_ind(legendary_group, non_legendary_group, nan_policy='omit')\n",
" \n",
" # Store results\n",
" results[stat] = {\n",
" 'T-Stat': t_stat,\n",
" 'P-Value': p_value,\n",
" 'Legendary Mean': legendary_group.mean(),\n",
" 'Non-Legendary Mean': non_legendary_group.mean()\n",
" }\n",
" \n",
" # Commentary\n",
" alpha = 0.05\n",
" if p_value < alpha:\n",
" finding = \"Reject H₀\"\n",
" conclusion = \"Significant difference found\"\n",
" else:\n",
" finding = \"Fail to Reject H₀\"\n",
" conclusion = \"No significant difference found\"\n",
" \n",
" print(f\"\\nStatistic: {stat}\")\n",
" print(f\" P-Value: {p_value:.6f}\")\n",
" print(f\" Finding: {finding}\")\n",
" print(f\" Conclusion: {conclusion}\")\n",
" \n",
"# Final Summary (Optional: display the table of results)\n",
"results_df = pd.DataFrame(results).T\n",
"print(\"\\nDetailed Results:\")\n",
"print(results_df[['Legendary Mean', 'Non-Legendary Mean', 'T-Stat', 'P-Value']])"
]
},
{
Expand All @@ -337,7 +476,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 9,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -453,14 +592,14 @@
"4 624.0 262.0 1.9250 65500.0 "
]
},
"execution_count": 5,
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.read_csv(\"https://raw.githubusercontent.com/data-bootcamp-v4/data/main/california_housing.csv\")\n",
"df.head()"
"df_housing = pd.read_csv(\"https://raw.githubusercontent.com/data-bootcamp-v4/data/main/california_housing.csv\")\n",
"df_housing.head()"
]
},
{
Expand All @@ -483,10 +622,102 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Proximity variable created.\n",
"is_close\n",
"False 10170\n",
"True 6830\n",
"Name: count, dtype: int64\n"
]
}
],
"source": [
"# School coordinates (-118, 34)\n",
"SCHOOL_COORD = (-118, 34)\n",
"# Hospital coordinates (-122, 37)\n",
"HOSPITAL_COORD = (-122, 37)\n",
"DISTANCE_THRESHOLD = 0.50\n",
"\n",
"# 1. Function to calculate Euclidean distance\n",
"def euclidean_distance(lat1, lon1, lat2, lon2):\n",
" return np.sqrt((lon2 - lon1)**2 + (lat2 - lat1)**2)\n",
"\n",
"# 2. Calculate distances\n",
"df_housing['dist_to_school'] = euclidean_distance(\n",
" df_housing['latitude'], df_housing['longitude'], SCHOOL_COORD[1], SCHOOL_COORD[0]\n",
")\n",
"\n",
"df_housing['dist_to_hospital'] = euclidean_distance(\n",
" df_housing['latitude'], df_housing['longitude'], HOSPITAL_COORD[1], HOSPITAL_COORD[0]\n",
")\n",
"\n",
"# 3. Create the 'is_close' flag\n",
"# A house is considered close if dist_to_school OR dist_to_hospital is <= 0.50\n",
"df_housing['is_close'] = (df_housing['dist_to_school'] <= DISTANCE_THRESHOLD) | \\\n",
" (df_housing['dist_to_hospital'] <= DISTANCE_THRESHOLD)\n",
"\n",
"print(\"\\nProximity variable created.\")\n",
"print(df_housing['is_close'].value_counts())"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"--- T-Test: Close Houses vs. Far Houses (Unilateral) ---\n",
"Mean House Value (Close): $246,934.64\n",
"Mean House Value (Far): $180,683.57\n",
"T-Statistic: 38.0333\n",
"P-Value (One-Tailed): 0.000000\n",
"\n",
"Finding: Since the p-value (0.000000) is less than alpha (0.05), we REJECT the Null Hypothesis (H₀).\n",
"Conclusion: There is statistically significant evidence to support the posit that houses (neighborhoods) close to a school or a hospital are, on average, more expensive.\n"
]
}
],
"source": [
"# 1. Prepare data groups\n",
"close_houses = df_housing[df_housing['is_close'] == True]['median_house_value']\n",
"far_houses = df_housing[df_housing['is_close'] == False]['median_house_value']\n",
"\n",
"# 2. Perform Two-Sample T-Test (Two-tailed by default)\n",
"t_stat, p_value_two_tailed = ttest_ind(close_houses, far_houses, nan_policy='omit')\n",
"\n",
"# 3. Adjust p-value for a one-tailed test (H_a: mu_Close > mu_Far)\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",
"alpha = 0.05\n",
"\n",
"print(\"\\n--- T-Test: Close Houses vs. Far Houses (Unilateral) ---\")\n",
"print(f\"Mean House Value (Close): ${close_houses.mean():,.2f}\")\n",
"print(f\"Mean House Value (Far): ${far_houses.mean():,.2f}\")\n",
"print(f\"T-Statistic: {t_stat:.4f}\")\n",
"print(f\"P-Value (One-Tailed): {p_value_one_tailed:.6f}\")\n",
"\n",
"# Commentary:\n",
"if p_value_one_tailed < alpha:\n",
" print(f\"\\nFinding: Since the p-value ({p_value_one_tailed:.6f}) is less than alpha (0.05), we REJECT the Null Hypothesis (H₀).\")\n",
" print(\"Conclusion: There is statistically significant evidence to support the posit that houses (neighborhoods) close to a school or a hospital are, on average, more expensive.\")\n",
"else:\n",
" print(f\"\\nFinding: Since the p-value ({p_value_one_tailed:.6f}) is greater than alpha (0.05), we FAIL TO REJECT the Null Hypothesis (H₀).\")\n",
" print(\"Conclusion: There is no statistically significant evidence to support the posit that houses (neighborhoods) close to a school or a hospital are, on average, more expensive.\")"
]
},
{
"cell_type": "code",
Expand All @@ -498,9 +729,9 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python [conda env:base] *",
"language": "python",
"name": "python3"
"name": "conda-base-py"
},
"language_info": {
"codemirror_mode": {
Expand All @@ -512,9 +743,9 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.13.5"
}
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"nbformat": 4,
"nbformat_minor": 2
"nbformat_minor": 4
}