# Step 1: Import the tools we need
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

# Step 2: Create our data
# Coffee group: 25 people
np.random.seed(42)
coffee_group = np.random.normal(12, 3, 25)  # Average 12 tasks, std dev 3

# No coffee group: 25 people
no_coffee_group = np.random.normal(10, 2.5, 25)  # Average 10 tasks, std dev 2.5

print("☕ COFFEE PRODUCTIVITY EXPERIMENT")
print("="*60)
print(f"Coffee Group (n={len(coffee_group)}):")
print(f"  Average tasks: {np.mean(coffee_group):.2f}")
print(f"  Std deviation: {np.std(coffee_group, ddof=1):.2f}")
print(f"\nNo Coffee Group (n={len(no_coffee_group)}):")
print(f"  Average tasks: {np.mean(no_coffee_group):.2f}")
print(f"  Std deviation: {np.std(no_coffee_group, ddof=1):.2f}")
print(f"\nDifference: {np.mean(coffee_group) - np.mean(no_coffee_group):.2f} tasks")
print("="*60)

# Step 3: Perform Independent T-Test (ONE LINE!)
t_stat, p_value = stats.ttest_ind(coffee_group, no_coffee_group)

print(f"\n📊 TEST RESULTS:")
print(f"T-statistic: {t_stat:.4f}")
print(f"P-value: {p_value:.4f}")

# Step 4: Make a decision
print("\n🎯 DECISION:")
if p_value < 0.05:
    print(f"✅ REJECT H₀: Coffee DOES make a difference!")
    print(f"   (p-value {p_value:.4f} < 0.05)")
    print(f"   Coffee drinkers completed {np.mean(coffee_group) - np.mean(no_coffee_group):.1f} more tasks")
else:
    print(f"❌ FAIL TO REJECT H₀: No significant difference")
    print(f"   (p-value {p_value:.4f} > 0.05)")

# Step 5: Calculate Effect Size (Cohen's d)
# This tells us HOW BIG the difference is
pooled_std = np.sqrt((np.std(coffee_group, ddof=1)**2 + np.std(no_coffee_group, ddof=1)**2) / 2)
cohens_d = (np.mean(coffee_group) - np.mean(no_coffee_group)) / pooled_std

print(f"\n📏 EFFECT SIZE (Cohen's d): {cohens_d:.3f}")
if abs(cohens_d) < 0.2:
    print("   → Small effect (barely noticeable)")
elif abs(cohens_d) < 0.5:
    print("   → Medium effect (noticeable)")
else:
    print("   → Large effect (very noticeable!)")

# Step 6: Visualize the results
fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# Plot 1: Box plots comparing groups
axes[0].boxplot([coffee_group, no_coffee_group], labels=['Coffee', 'No Coffee'])
axes[0].set_ylabel('Tasks Completed per Day')
axes[0].set_title('Productivity Comparison')
axes[0].grid(True, alpha=0.3)

# Add mean markers
means = [np.mean(coffee_group), np.mean(no_coffee_group)]
axes[0].plot([1, 2], means, 'ro-', linewidth=2, markersize=10, label='Group Means')
axes[0].legend()

# Plot 2: Histograms overlaid
axes[1].hist(coffee_group, bins=10, alpha=0.6, color='brown', label='Coffee', edgecolor='black')
axes[1].hist(no_coffee_group, bins=10, alpha=0.6, color='blue', label='No Coffee', edgecolor='black')
axes[1].axvline(np.mean(coffee_group), color='brown', linestyle='--', linewidth=2)
axes[1].axvline(np.mean(no_coffee_group), color='blue', linestyle='--', linewidth=2)
axes[1].set_xlabel('Tasks Completed per Day')
axes[1].set_ylabel('Number of People')
axes[1].set_title('Distribution of Productivity')
axes[1].legend()
axes[1].grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

print("\n📊 The graphs show the coffee group is shifted to the right (higher productivity)!")

from scipy import stats

# Levene's Test for Equal Variances
stat, p_value_levene = stats.levene(coffee_group, no_coffee_group)

print("\n🔍 CHECKING ASSUMPTIONS:")
print("="*60)
print("Levene's Test for Equal Variances:")
print(f"  Test statistic: {stat:.4f}")
print(f"  P-value: {p_value_levene:.4f}")

if p_value_levene > 0.05:
    print("  ✅ Variances are equal (good!)")
    print("  → Use standard independent t-test")
else:
    print("  ⚠️  Variances are NOT equal")
    print("  → Use Welch's t-test instead")
    
    # Welch's t-test (doesn't assume equal variances)
    t_stat_welch, p_value_welch = stats.ttest_ind(coffee_group, no_coffee_group, equal_var=False)
    print(f"\n  Welch's T-test results:")
    print(f"    T-statistic: {t_stat_welch:.4f}")
    print(f"    P-value: {p_value_welch:.4f}")

# Step 1: Import tools
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

# Step 2: Create our data (30 students)
np.random.seed(42)
n_students = 30

# Before scores (average 70, std dev 8)
before_scores = np.random.normal(70, 8, n_students)

# After scores (average 76.5, std dev 8) - improved by ~6.5 points
after_scores = before_scores + np.random.normal(6.5, 3, n_students)

# Calculate differences
differences = after_scores - before_scores

print("📚 STUDY TECHNIQUE EFFECTIVENESS")
print("="*60)
print(f"Number of students: {n_students}")
print(f"\nBefore technique:")
print(f"  Average score: {np.mean(before_scores):.2f}")
print(f"  Std deviation: {np.std(before_scores, ddof=1):.2f}")
print(f"\nAfter technique:")
print(f"  Average score: {np.mean(after_scores):.2f}")
print(f"  Std deviation: {np.std(after_scores, ddof=1):.2f}")
print(f"\nAverage improvement: {np.mean(differences):.2f} points")
print(f"Std dev of improvements: {np.std(differences, ddof=1):.2f}")
print("="*60)

# Step 3: Perform Paired T-Test (ONE LINE!)
t_stat, p_value = stats.ttest_rel(after_scores, before_scores)

# For one-tailed test (we only care if it improved)
p_value_one_tailed = p_value / 2 if t_stat > 0 else 1 - p_value / 2

print(f"\n📊 TEST RESULTS:")
print(f"T-statistic: {t_stat:.4f}")
print(f"P-value (one-tailed): {p_value_one_tailed:.4f}")

# Step 4: Make a decision
print("\n🎯 DECISION:")
if p_value_one_tailed < 0.05:
    print(f"✅ REJECT H₀: The technique WORKS!")
    print(f"   (p-value {p_value_one_tailed:.4f} < 0.05)")
    print(f"   Students improved by {np.mean(differences):.1f} points on average")
else:
    print(f"❌ FAIL TO REJECT H₀: No significant improvement")
    print(f"   (p-value {p_value_one_tailed:.4f} > 0.05)")

# Step 5: Calculate Effect Size (Cohen's d for paired data)
cohens_d = np.mean(differences) / np.std(differences, ddof=1)

print(f"\n📏 EFFECT SIZE (Cohen's d): {cohens_d:.3f}")
if abs(cohens_d) < 0.2:
    print("   → Small effect (barely noticeable)")
elif abs(cohens_d) < 0.5:
    print("   → Medium effect (noticeable)")
else:
    print("   → Large effect (very noticeable!)")

# Step 6: Visualize the results
fig, axes = plt.subplots(1, 3, figsize=(16, 5))

# Plot 1: Before vs After (connected lines)
axes[0].plot([1, 2], [before_scores, after_scores], 'o-', alpha=0.3, color='gray')
axes[0].plot([1, 2], [np.mean(before_scores), np.mean(after_scores)], 
             'ro-', linewidth=3, markersize=12, label='Average')
axes[0].set_xticks([1, 2])
axes[0].set_xticklabels(['Before', 'After'])
axes[0].set_ylabel('Test Score')
axes[0].set_title('Individual Student Changes')
axes[0].legend()
axes[0].grid(True, alpha=0.3)

# Plot 2: Distribution of differences
axes[1].hist(differences, bins=12, color='green', alpha=0.7, edgecolor='black')
axes[1].axvline(0, color='red', linestyle='--', linewidth=2, label='No change')
axes[1].axvline(np.mean(differences), color='blue', linestyle='--', linewidth=2, 
                label=f'Avg change: {np.mean(differences):.1f}')
axes[1].set_xlabel('Score Improvement (After - Before)')
axes[1].set_ylabel('Number of Students')
axes[1].set_title('Distribution of Improvements')
axes[1].legend()
axes[1].grid(True, alpha=0.3)

# Plot 3: Box plot of differences
axes[2].boxplot(differences, vert=True)
axes[2].axhline(0, color='red', linestyle='--', linewidth=2, label='No change')
axes[2].set_ylabel('Score Improvement')
axes[2].set_title('Summary of Improvements')
axes[2].set_xticklabels(['Difference'])
axes[2].legend()
axes[2].grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

print("\n📊 The graphs show most students improved (differences are mostly positive)!")

# Bonus: Show some individual students
print("\n👥 Sample of Individual Students:")
print("="*60)
print("Student | Before | After | Improvement")
print("-"*60)
for i in range(5):  # Show first 5 students
    print(f"   {i+1:2d}   |  {before_scores[i]:5.1f} | {after_scores[i]:5.1f} |    {differences[i]:+5.1f}")
print("  ...  |   ...  |  ...  |     ...")
print("="*60)

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

# Generate salary data
np.random.seed(42)
male_salaries = np.random.normal(75000, 15000, 40)    # Average $75k
female_salaries = np.random.normal(70000, 14000, 40)  # Average $70k

print("💰 GENDER PAY GAP ANALYSIS")
print("="*60)
print(f"Male employees (n={len(male_salaries)}):")
print(f"  Average salary: ${np.mean(male_salaries):,.2f}")
print(f"  Std deviation: ${np.std(male_salaries, ddof=1):,.2f}")
print(f"\nFemale employees (n={len(female_salaries)}):")
print(f"  Average salary: ${np.mean(female_salaries):,.2f}")
print(f"  Std deviation: ${np.std(female_salaries, ddof=1):,.2f}")
print(f"\nDifference: ${np.mean(male_salaries) - np.mean(female_salaries):,.2f}")
print("="*60)

# Perform independent t-test
t_stat, p_value = stats.ttest_ind(male_salaries, female_salaries)

print(f"\n📊 INDEPENDENT T-TEST RESULTS:")
print(f"T-statistic: {t_stat:.4f}")
print(f"P-value: {p_value:.4f}")

if p_value < 0.05:
    print(f"\n✅ Significant difference found!")
    print(f"   There IS a gender pay gap (p = {p_value:.4f})")
    diff = np.mean(male_salaries) - np.mean(female_salaries)
    print(f"   Men earn ${diff:,.2f} more on average")
else:
    print(f"\n❌ No significant difference")
    print(f"   No evidence of a pay gap (p = {p_value:.4f})")

# Visualize
plt.figure(figsize=(12, 5))

plt.subplot(1, 2, 1)
plt.boxplot([male_salaries, female_salaries], labels=['Male', 'Female'])
plt.ylabel('Salary ($)')
plt.title('Salary Distribution by Gender')
plt.grid(True, alpha=0.3)

plt.subplot(1, 2, 2)
plt.hist(male_salaries, bins=15, alpha=0.6, color='blue', label='Male', edgecolor='black')
plt.hist(female_salaries, bins=15, alpha=0.6, color='pink', label='Female', edgecolor='black')
plt.xlabel('Salary ($)')
plt.ylabel('Number of Employees')
plt.title('Salary Distributions')
plt.legend()
plt.grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

# Generate weight data
np.random.seed(123)
n_people = 25

# Before weights (average 180 lbs, std dev 20)
before_weight = np.random.normal(180, 20, n_people)

# After weights (lost 8 lbs on average, with some variation)
weight_loss = np.random.normal(8, 4, n_people)  # Average loss 8 lbs
after_weight = before_weight - weight_loss

print("🏋️ WEIGHT LOSS PROGRAM EVALUATION")
print("="*60)
print(f"Number of participants: {n_people}")
print(f"\nBefore program:")
print(f"  Average weight: {np.mean(before_weight):.1f} lbs")
print(f"\nAfter program:")
print(f"  Average weight: {np.mean(after_weight):.1f} lbs")
print(f"\nAverage weight loss: {np.mean(weight_loss):.1f} lbs")
print("="*60)

# Perform paired t-test
t_stat, p_value = stats.ttest_rel(before_weight, after_weight)

print(f"\n📊 PAIRED T-TEST RESULTS:")
print(f"T-statistic: {t_stat:.4f}")
print(f"P-value: {p_value:.4f}")

if p_value < 0.05:
    print(f"\n✅ Program WORKS!")
    print(f"   Significant weight loss detected (p = {p_value:.4f})")
    print(f"   Average loss: {np.mean(weight_loss):.1f} lbs")
else:
    print(f"\n❌ Program doesn't show significant results")
    print(f"   (p = {p_value:.4f})")

# Calculate percentage who lost weight
percent_lost = (weight_loss > 0).sum() / n_people * 100
print(f"\n📈 {percent_lost:.0f}% of participants lost weight")

# Visualize
fig, axes = plt.subplots(1, 3, figsize=(16, 5))

# Plot 1: Before vs After
axes[0].scatter(range(n_people), before_weight, color='red', label='Before', s=100, alpha=0.6)
axes[0].scatter(range(n_people), after_weight, color='green', label='After', s=100, alpha=0.6)
for i in range(n_people):
    axes[0].plot([i, i], [before_weight[i], after_weight[i]], 'k-', alpha=0.3)
axes[0].set_xlabel('Participant')
axes[0].set_ylabel('Weight (lbs)')
axes[0].set_title('Individual Weight Changes')
axes[0].legend()
axes[0].grid(True, alpha=0.3)

# Plot 2: Distribution of weight loss
axes[1].hist(weight_loss, bins=12, color='purple', alpha=0.7, edgecolor='black')
axes[1].axvline(0, color='red', linestyle='--', linewidth=2, label='No change')
axes[1].axvline(np.mean(weight_loss), color='blue', linestyle='--', linewidth=2,
                label=f'Avg: {np.mean(weight_loss):.1f} lbs')
axes[1].set_xlabel('Weight Loss (lbs)')
axes[1].set_ylabel('Number of People')
axes[1].set_title('Distribution of Weight Loss')
axes[1].legend()
axes[1].grid(True, alpha=0.3)

# Plot 3: Paired comparison
axes[2].boxplot([before_weight, after_weight], labels=['Before', 'After'])
axes[2].set_ylabel('Weight (lbs)')
axes[2].set_title('Weight Before and After Program')
axes[2].grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

def which_two_sample_test(same_subjects_measured_twice):
    """
    Simple function to help you decide which test to use!
    
    Parameters:
    - same_subjects_measured_twice: Are you measuring the same people/things twice? (True/False)
    """
    print("\n🔍 TWO-SAMPLE TEST SELECTION GUIDE")
    print("="*60)
    
    if same_subjects_measured_twice:
        print("✅ Use PAIRED T-TEST")
        print("\nReason: Same subjects measured twice")
        print("\nExamples:")
        print("  • Before/After treatment")
        print("  • Pre-test/Post-test")
        print("  • Repeated measurements on same subjects")
        print("\nPython code:")
        print("  t_stat, p_value = stats.ttest_rel(after, before)")
    else:
        print("✅ Use INDEPENDENT T-TEST")
        print("\nReason: Two different groups")
        print("\nExamples:")
        print("  • Men vs Women")
        print("  • Treatment group vs Control group")
        print("  • Product A vs Product B")
        print("\nPython code:")
        print("  t_stat, p_value = stats.ttest_ind(group1, group2)")
    
    print("="*60)

# Try it out!
which_two_sample_test(same_subjects_measured_twice=True)
which_two_sample_test(same_subjects_measured_twice=False)

# Write your code here!
# Hint: Same people measured twice = Paired test

# Write your code here!

import numpy as np
from scipy import stats

# Example: Compare two products, two groups, etc.
print("MY INDEPENDENT T-TEST")
print("="*60)
print("Scenario: [Describe your comparison]")
print("Group 1: [Description]")
print("Group 2: [Description]")
print("="*60)

# Generate or input your data
# group1 = np.array([...])
# group2 = np.array([...])

# Run independent t-test
# t_stat, p_value = stats.ttest_ind(group1, group2)

# Make conclusion

import numpy as np
from scipy import stats

# Example: Before/after comparison
print("MY PAIRED T-TEST")
print("="*60)
print("Scenario: [Describe your before/after situation]")
print("="*60)

# Generate or input your data
# before = np.array([...])
# after = np.array([...])

# Run paired t-test
# t_stat, p_value = stats.ttest_rel(after, before)

# Make conclusion

from scipy import stats
import numpy as np

# Independent T-Test (two different groups)
t_stat, p_value = stats.ttest_ind(group1, group2)

# Paired T-Test (same group, two measurements)
t_stat, p_value = stats.ttest_rel(after, before)

# Check equal variances (for independent t-test)
stat, p_val = stats.levene(group1, group2)
if p_val < 0.05:
    # Use Welch's t-test instead
    t_stat, p_value = stats.ttest_ind(group1, group2, equal_var=False)

# Calculate Effect Size (Cohen's d)
# For independent:
pooled_std = np.sqrt((std1**2 + std2**2) / 2)
cohens_d = (mean1 - mean2) / pooled_std

# For paired:
cohens_d = np.mean(differences) / np.std(differences, ddof=1)

# Decision
if p_value < 0.05:
    print("Significant difference found!")
else:
    print("No significant difference")