# =============================================================================
# COMPLETE HYPOTHESIS TESTING TOOLKIT
# =============================================================================

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

# -----------------------------------------------------------------------------
# Template 1: One-Sample t-test
# -----------------------------------------------------------------------------
def one_sample_ttest(data, null_value, alpha=0.05, alternative='two-sided'):
    """
    Perform one-sample t-test with complete analysis
    
    Parameters:
    -----------
    data : array-like
        Sample data
    null_value : float
        Hypothesized population mean
    alpha : float
        Significance level (default 0.05)
    alternative : str
        'two-sided', 'greater', or 'less'
    """
    
    # Calculate statistics
    n = len(data)
    x_bar = np.mean(data)
    s = np.std(data, ddof=1)
    se = s / np.sqrt(n)
    
    # Test statistic
    t_stat = (x_bar - null_value) / se
    df = n - 1
    
    # P-value calculation
    if alternative == 'two-sided':
        p_value = 2 * (1 - stats.t.cdf(abs(t_stat), df))
    elif alternative == 'greater':
        p_value = 1 - stats.t.cdf(t_stat, df)
    elif alternative == 'less':
        p_value = stats.t.cdf(t_stat, df)
    
    # Effect size (Cohen's d)
    cohens_d = (x_bar - null_value) / s
    
    # Confidence interval
    t_crit = stats.t.ppf(1 - alpha/2, df)
    ci_lower = x_bar - t_crit * se
    ci_upper = x_bar + t_crit * se
    
    # Results
    results = {
        'test_statistic': t_stat,
        'p_value': p_value,
        'degrees_of_freedom': df,
        'effect_size': cohens_d,
        'confidence_interval': (ci_lower, ci_upper),
        'reject_null': p_value <= alpha,
        'sample_mean': x_bar,
        'sample_std': s,
        'sample_size': n
    }
    
    return results

# -----------------------------------------------------------------------------
# Template 2: Two-Sample t-test
# -----------------------------------------------------------------------------
def two_sample_ttest(group1, group2, alpha=0.05, equal_var=True):
    """
    Perform two-sample t-test with complete analysis
    """
    
    # Calculate statistics
    n1, n2 = len(group1), len(group2)
    mean1, mean2 = np.mean(group1), np.mean(group2)
    s1, s2 = np.std(group1, ddof=1), np.std(group2, ddof=1)
    
    if equal_var:
        # Pooled variance
        pooled_var = ((n1-1)*s1**2 + (n2-1)*s2**2) / (n1+n2-2)
        se = np.sqrt(pooled_var * (1/n1 + 1/n2))
        df = n1 + n2 - 2
    else:
        # Welch's t-test
        se = np.sqrt(s1**2/n1 + s2**2/n2)
        df = (s1**2/n1 + s2**2/n2)**2 / ((s1**2/n1)**2/(n1-1) + (s2**2/n2)**2/(n2-1))
    
    # Test statistic
    t_stat = (mean1 - mean2) / se
    p_value = 2 * (1 - stats.t.cdf(abs(t_stat), df))
    
    # Effect size (Cohen's d)
    if equal_var:
        pooled_std = np.sqrt(pooled_var)
    else:
        pooled_std = np.sqrt(((n1-1)*s1**2 + (n2-1)*s2**2) / (n1+n2-2))
    
    cohens_d = (mean1 - mean2) / pooled_std
    
    results = {
        'test_statistic': t_stat,
        'p_value': p_value,
        'degrees_of_freedom': df,
        'effect_size': cohens_d,
        'reject_null': p_value <= alpha,
        'group1_stats': {'mean': mean1, 'std': s1, 'n': n1},
        'group2_stats': {'mean': mean2, 'std': s2, 'n': n2}
    }
    
    return results

# -----------------------------------------------------------------------------
# Template 3: Power Analysis
# -----------------------------------------------------------------------------
def power_analysis(effect_size, alpha=0.05, power=0.8):
    """
    Calculate required sample size for desired power
    """
    from scipy.stats import norm
    
    z_alpha = norm.ppf(1 - alpha/2)
    z_beta = norm.ppf(power)
    
    n = ((z_alpha + z_beta) / effect_size) ** 2
    
    return int(np.ceil(n))

# -----------------------------------------------------------------------------
# Example Usage
# -----------------------------------------------------------------------------

# Generate sample data
np.random.seed(42)
sample_data = np.random.normal(105, 15, 25)

# Perform one-sample t-test
results = one_sample_ttest(sample_data, null_value=100, alternative='greater')

print("One-Sample t-test Results:")
print(f"Test statistic: {results['test_statistic']:.3f}")
print(f"P-value: {results['p_value']:.4f}")
print(f"Effect size (d): {results['effect_size']:.3f}")
print(f"95% CI: ({results['confidence_interval'][0]:.2f}, {results['confidence_interval'][1]:.2f})")
print(f"Reject null: {results['reject_null']}")

# Power analysis
required_n = power_analysis(effect_size=0.5, power=0.8)
print(f"\nRequired sample size for d=0.5, power=0.8: {required_n}")