Pywayne Statistics

Comprehensive statistical testing library for hypothesis testing, A/B testing, and data analysis.

Quick Start

from pywayne.statistics import NormalityTests, LocationTests
import numpy as np

# Test data normality
nt = NormalityTests()
data = np.random.normal(0, 1, 100)
result = nt.shapiro_wilk(data)
print(f"p-value: {result.p_value:.4f}, is_normal: {not result.reject_null}")

# Compare two groups
lt = LocationTests()
group_a = np.random.normal(100, 15, 50)
group_b = np.random.normal(105, 15, 50)
result = lt.two_sample_ttest(group_a, group_b)
print(f"Significant difference: {result.reject_null}")

Test Categories

NormalityTests (NormalityTests)

Test if data follows a normal distribution or other specified distributions.

| Method | Description | Use Case | |---------|-------------|-----------| | shapiro_wilk | Shapiro-Wilk test | Small-medium samples (n ≤ 5000) | | ks_test_normal | K-S normality test | Medium-large samples | | ks_test_two_sample | Two-sample K-S test | Compare two sample distributions | | anderson_darling | Anderson-Darling test | Tail-sensitive normality test | | dagostino_pearson | D'Agostino-Pearson K² | Based on skewness and kurtosis | | jarque_bera | Jarque-Bera test | Large samples, regression residuals | | chi_square_goodness_of_fit | Chi-square goodness-of-fit | Categorical data | | lilliefors_test | Lilliefors test | Unknown parameters K-S test |

Example:

from pywayne.statistics import NormalityTests

nt = NormalityTests()
result = nt.shapiro_wilk(data)
if result.p_value < 0.05:
    print("Data is NOT normally distributed")
else:
    print("Data follows normal distribution")

LocationTests (LocationTests)

Compare means or medians across groups (parametric and non-parametric).

| Method | Description | Use Case | |---------|-------------|-----------| | one_sample_ttest | One-sample t-test | Compare sample mean to a value | | two_sample_ttest | Two-sample t-test | Compare two independent group means | | paired_ttest | Paired t-test | Compare before/after measurements | | one_way_anova | One-way ANOVA | Compare 3+ group means | | mann_whitney_u | Mann-Whitney U test | Non-parametric two-sample test | | wilcoxon_signed_rank | Wilcoxon signed-rank | Non-parametric paired test | | kruskal_wallis | Kruskal-Wallis H test | Non-parametric multi-group test |

Example (A/B Testing):

from pywayne.statistics import LocationTests, NormalityTests

lt = LocationTests()
nt = NormalityTests()

# Check normality first
if nt.shapiro_wilk(control).p_value > 0.05:
    result = lt.two_sample_ttest(control, treatment)
else:
    result = lt.mann_whitney_u(control, treatment)

print(f"Effect significant: {result.reject_null}")

CorrelationTests (CorrelationTests)

Test correlation between variables and independence of categorical variables.

| Method | Description | Use Case | |---------|-------------|-----------| | pearson_correlation | Pearson correlation | Linear relationship | | spearman_correlation | Spearman's rank | Monotonic relationship | | kendall_tau | Kendall's tau | Rank correlation, small samples | | chi_square_independence | Chi-square independence | Categorical variables | | fisher_exact_test | Fisher's exact test | 2×2 contingency table | | mcnemar_test | McNemar's test | Paired categorical data |

Example:

from pywayne.statistics import CorrelationTests

ct = CorrelationTests()
result = ct.pearson_correlation(x, y)
print(f"Correlation: {result.statistic:.3f}, p-value: {result.p_value:.4f}")

TimeSeriesTests (TimeSeriesTests)

Test time series properties: stationarity, autocorrelation, cointegration.

| Method | Description | Use Case | |---------|-------------|-----------| | adf_test | Augmented Dickey-Fuller | Unit root test for stationarity | | kpss_test | KPSS test | Stationarity test (complements ADF) | | ljung_box_test | Ljung-Box Q test | Overall autocorrelation | | runs_test | Runs test | Randomness testing | | arch_test | ARCH effect test | Heteroscedasticity | | granger_causality | Granger causality | Causal relationship | | engle_granger_cointegration | Engle-Granger cointegration | Long-term equilibrium | | breusch_godfrey_test | Breusch-Godfrey | Higher-order autocorrelation |

Example:

from pywayne.statistics import TimeSeriesTests

tst = TimeSeriesTests()
adf_result = tst.adf_test(time_series_data)
kpss_result = tst.kpss_test(time_series_data)

if adf_result.reject_null:
    print("Series is stationary")
else:
    print("Series has unit root (non-stationary)")

ModelDiagnostics (ModelDiagnostics)

Regression model diagnostics: heteroscedasticity, autocorrelation, multicollinearity.

| Method | Description | Use Case | |---------|-------------|-----------| | breusch_pagan_test | Breusch-Pagan | Heteroscedasticity test | | white_test | White's test | General heteroscedasticity | | goldfeld_quandt_test | Goldfeld-Quandt | Structural break heteroscedasticity | | durbin_watson_test | Durbin-Watson | First-order autocorrelation | | variance_inflation_factor | VIF | Multicollinearity diagnosis | | levene_test | Levene's test | Homogeneity of variance | | bartlett_test | Bartlett's test | Homogeneity (normal assumption) | | residual_normality_test | Residual normality | Regression assumption check |

Example:

from pywayne.statistics import ModelDiagnostics

md = ModelDiagnostics()
residuals = y - model.predict(X)

# Check assumptions
bp_result = md.breusch_pagan_test(residuals, X)
dw_result = md.durbin_watson_test(residuals)

if bp_result.reject_null:
    print("Warning: Heteroscedasticity detected")

TestResult Object

All test methods return a unified TestResult object:

result = nt.shapiro_wilk(data)

# Access results
result.test_name        # Test method name
result.statistic        # Test statistic value
result.p_value          # P-value
result.reject_null      # True if null hypothesis is rejected
result.critical_value   # Critical value (if applicable)
result.confidence_interval # Tuple (lower, upper) if applicable
result.effect_size      # Effect size if applicable
result.additional_info  # Dict with additional information

Utility Functions

list_all_tests()

List all available test methods across all modules.

from pywayne.statistics import list_all_tests
print(list_all_tests())

show_test_usage(method_name)

Display usage and documentation for a specific test.

from pywayne.statistics import show_test_usage
show_test_usage('shapiro_wilk')

Method Selection Guide

Normality Tests

| Sample Size | Recommended Method | |-------------|-------------------| | n < 30 | Shapiro-Wilk | | 30 ≤ n ≤ 300 | Shapiro-Wilk, D'Agostino-Pearson | | n > 300 | Jarque-Bera, Kolmogorov-Smirnov |

Location Tests

| Condition | Parametric | Non-parametric | |-----------|-------------|----------------| | Normal data | t-test, ANOVA | - | | Non-normal data | - | Mann-Whitney U, Kruskal-Wallis | | Paired data | Paired t-test | Wilcoxon signed-rank |

Multiple Testing Correction

When performing multiple tests, apply p-value correction:

from statsmodels.stats.multitest import multipletests

p_values = [r.p_value for r in results]
rejected, p_corrected, _, _ = multipletests(
    p_values, alpha=0.05, method='fdr_bh'
)

Common Applications

Data Quality Check

def data_quality_check(data):
    nt = NormalityTests()
    lt = LocationTests()

    normality = nt.shapiro_wilk(data)

    # Outlier detection (IQR)
    Q1, Q3 = np.percentile(data, [25, 75])
    IQR = Q3 - Q1
    outliers = data[(data < Q1 - 1.5*IQR) | (data > Q3 + 1.5*IQR)]

    return {
        'size': len(data),
        'is_normal': not normality.reject_null,
        'p_value': normality.p_value,
        'outliers': len(outliers)
    }

A/B Testing Workflow

def ab_test_analysis(control, treatment):
    nt = NormalityTests()
    lt = LocationTests()

    # Check normality
    norm_c = nt.shapiro_wilk(control[:100])
    norm_t = nt.shapiro_wilk(treatment[:100])

    # Choose appropriate test
    if norm_c.p_value > 0.05 and norm_t.p_value > 0.05:
        result = lt.two_sample_ttest(control, treatment)
    else:
        result = lt.mann_whitney_u(control, treatment)

    return {
        'test_used': result.test_name,
        'p_value': result.p_value,
        'significant': result.reject_null,
        'effect_size': result.effect_size
    }

Regression Model Diagnostics

def diagnose_model(y, X, model):
    md = ModelDiagnostics()
    residuals = y - model.predict(X)

    return {
        'heteroscedasticity_bp': md.breusch_pagan_test(residuals, X).reject_null,
        'autocorrelation_dw': md.durbin_watson_test(residuals).statistic,
        'residuals_normal': md.residual_normality_test(residuals).p_value,
        'vif_max': max(md.variance_inflation_factor(X))
    }

Notes

• All methods accept np.ndarray or list as input
• All methods return TestResult with consistent interface
• Always validate test assumptions before applying parametric tests
• Apply multiple testing correction when performing several tests
• Report effect sizes alongside p-values for complete interpretation