🔬 Hypothesis Testing Deep Dive

import pandas as pd
from scipy.stats import chi2_contingency

# Load hotel reservations data
data = pd.read_csv("Hotel Reservations.csv")

# Create contingency table
contingency_table = pd.crosstab(
    data['type_of_meal_plan'], 
    data['booking_status']
)
print("Contingency Table:")
print(contingency_table)

# Perform Chi-Square test
chi2, p_value, dof, expected = chi2_contingency(contingency_table)

print(f"\nChi-Square Statistic: {chi2:.2f}")
print(f"P-value: {p_value:.2e}")  # Scientific notation
print(f"Degrees of Freedom: {dof}")

# Interpret
if p_value < 0.05:
    print("✅ REJECT H₀: Meal plan and cancellation ARE related!")
else:
    print("❌ FAIL TO REJECT H₀: No significant relationship found.")

# Output:
# Chi-Square Statistic: 276.35
# P-value: 4.48e-61  ← Extremely small!
# ✅ REJECT H₀: Meal plan and cancellation ARE related!

# Test multiple categorical features against booking status
categorical_features = ['type_of_meal_plan', 'room_type_reserved', 
                        'no_of_weekend_nights', 'no_of_children']

for feature in categorical_features:
    # Create contingency table
    table = pd.crosstab(data[feature], data['booking_status'])
    
    # Chi-Square test
    chi2, p_value, dof, expected = chi2_contingency(table)
    
    print(f"\n{feature}:")
    print(f"  P-value: {p_value:.2e}")
    
    if p_value < 0.05:
        print(f"  ✅ SIGNIFICANT - Use this feature for prediction!")
    else:
        print(f"  ❌ Not significant - May not be useful alone")

# Output:
# type_of_meal_plan:
#   P-value: 4.48e-61
#   ✅ SIGNIFICANT - Use this feature for prediction!
# 
# room_type_reserved:
#   P-value: 4.43e-11
#   ✅ SIGNIFICANT - Use this feature for prediction!
# 
# no_of_weekend_nights:
#   P-value: 1.12e-40
#   ✅ SIGNIFICANT - Use this feature for prediction!

from scipy import stats
import pandas as pd

# Load data
data = pd.read_csv("Hotel Reservations.csv")

# Separate the two groups
canceled = data[data['booking_status'] == 'Canceled']['lead_time']
not_canceled = data[data['booking_status'] == 'Not_Canceled']['lead_time']

# Compare the means first
print("Descriptive Statistics:")
print(f"Canceled bookings - Mean lead time: {canceled.mean():.1f} days")
print(f"Not canceled bookings - Mean lead time: {not_canceled.mean():.1f} days")

# Perform Welch's T-Test (default in scipy)
t_stat, p_value = stats.ttest_ind(canceled, not_canceled)

print(f"\nT-statistic: {t_stat:.2f}")
print(f"P-value: {p_value}")

if p_value < 0.05:
    print("✅ SIGNIFICANT: Lead time differs between groups!")
else:
    print("❌ Not significant.")

# Output:
# Descriptive Statistics:
# Canceled bookings - Mean lead time: 135.2 days
# Not canceled bookings - Mean lead time: 72.8 days
# 
# T-statistic: 54.23
# P-value: 0.0  ← So small it's essentially zero!
# ✅ SIGNIFICANT: Lead time differs between groups!

# Test multiple numerical features
numerical_features = ['lead_time', 'avg_price_per_room']

for feature in numerical_features:
    canceled = data[data['booking_status'] == 'Canceled'][feature]
    not_canceled = data[data['booking_status'] == 'Not_Canceled'][feature]
    
    # T-Test
    t_stat, p_value = stats.ttest_ind(canceled, not_canceled)
    
    print(f"\n{feature}:")
    print(f"  Canceled mean: {canceled.mean():.2f}")
    print(f"  Not canceled mean: {not_canceled.mean():.2f}")
    print(f"  P-value: {p_value:.2e}")
    
    if p_value < 0.05:
        print(f"  ✅ SIGNIFICANT - Great predictor of cancellation!")
    else:
        print(f"  ❌ Not significant")

# Output:
# lead_time:
#   Canceled mean: 135.19
#   Not canceled mean: 72.84
#   P-value: 0.00e+00
#   ✅ SIGNIFICANT - Great predictor of cancellation!
# 
# avg_price_per_room:
#   Canceled mean: 108.71
#   Not canceled mean: 100.56
#   P-value: 5.23e-164
#   ✅ SIGNIFICANT - Great predictor of cancellation!

import pandas as pd
from scipy.stats import chi2_contingency, ttest_ind

# Load data
data = pd.read_csv("Hotel Reservations.csv")

# Define feature types
categorical_features = ['type_of_meal_plan', 'room_type_reserved']
numerical_features = ['lead_time', 'avg_price_per_room']

print("="*50)
print("FEATURE SELECTION USING HYPOTHESIS TESTS")
print("="*50)

selected_features = []

# Test categorical features with Chi-Square
print("\n📊 CATEGORICAL FEATURES (Chi-Square Test)")
for feature in categorical_features:
    table = pd.crosstab(data[feature], data['booking_status'])
    chi2, p_value, dof, expected = chi2_contingency(table)
    
    if p_value < 0.05:
        selected_features.append(feature)
        print(f"✅ {feature}: p={p_value:.2e} → SELECTED")
    else:
        print(f"❌ {feature}: p={p_value:.2f} → REJECTED")

# Test numerical features with T-Test
print("\n📈 NUMERICAL FEATURES (T-Test)")
for feature in numerical_features:
    canceled = data[data['booking_status'] == 'Canceled'][feature]
    not_canceled = data[data['booking_status'] == 'Not_Canceled'][feature]
    
    t_stat, p_value = ttest_ind(canceled, not_canceled)
    
    if p_value < 0.05:
        selected_features.append(feature)
        print(f"✅ {feature}: p={p_value:.2e} → SELECTED")
    else:
        print(f"❌ {feature}: p={p_value:.2f} → REJECTED")

print(f"\n🎯 FINAL SELECTED FEATURES: {selected_features}")

# Output:
# ==================================================
# FEATURE SELECTION USING HYPOTHESIS TESTS
# ==================================================
# 
# 📊 CATEGORICAL FEATURES (Chi-Square Test)
# ✅ type_of_meal_plan: p=4.48e-61 → SELECTED
# ✅ room_type_reserved: p=4.43e-11 → SELECTED
# 
# 📈 NUMERICAL FEATURES (T-Test)
# ✅ lead_time: p=0.00e+00 → SELECTED
# ✅ avg_price_per_room: p=5.23e-164 → SELECTED
# 
# 🎯 FINAL SELECTED FEATURES: ['type_of_meal_plan', 'room_type_reserved', 
#                              'lead_time', 'avg_price_per_room']