statscore 0.0.1

A production-quality Python library for Analysis of Variance (ANOVA) and Multiple Linear Regression with structured output, simultaneous inference, and FWER control.

statscore

A production-quality Python library for Analysis of Variance (ANOVA) and Multiple Linear Regression with structured output, simultaneous inference, and family-wise error rate (FWER) control.

Features

• One-Way & Two-Way ANOVA — sum-of-squares decomposition, F-tests, MLE estimation
• Multiple Comparison Procedures — Bonferroni, Šidák, Scheffé, and Tukey methods with automatic "best" selection
• OLS Multiple Linear Regression — matrix-based estimation, TSS partition, R²
• Simultaneous Inference — confidence intervals, confidence regions (ellipsoids), general hypothesis tests
• Prediction Intervals — Scheffé and Bonferroni simultaneous prediction CIs
• Structured Output — all functions return typed dataclass objects, not raw tuples
• Minimal Dependencies — only NumPy and SciPy required

Installation

# From PyPI (once published):
pip install statscore

# From source (development):
git clone https://github.com/furkankyildirim/statscore.git
cd statscore
pip install -e ".[dev]"

Requirements: Python >= 3.9, NumPy >= 1.21, SciPy >= 1.7

Quick Start

One-Way ANOVA

import numpy as np
from statscore import ANOVA1_partition_TSS, ANOVA1_test_equality

data = [
    np.array([28, 23, 14, 27, 31]),
    np.array([33, 36, 34, 29, 24]),
    np.array([18, 21, 20, 22]),
]

partition = ANOVA1_partition_TSS(data)
print(f"SS_total = {partition.SS_total}")
print(f"SS_within = {partition.SS_within}")
print(f"SS_between = {partition.SS_between}")

result = ANOVA1_test_equality(data, alpha=0.05)
print(f"F = {result.F_statistic:.4f}, p = {result.p_value:.4f}")
print(f"Reject H0: {result.reject_H0}")

Multiple Comparisons with FWER Control

from statscore import ANOVA1_CI_linear_combs, ANOVA1_test_linear_combs

C = np.array([[1, -1, 0], [0, 1, -1], [1, 0, -1]])
d = np.zeros(3)

# Automatic method selection (picks narrowest valid intervals)
ci_result = ANOVA1_CI_linear_combs(data, alpha=0.05, C=C, method="best")
for i, (lo, hi) in enumerate(ci_result.intervals):
    print(f"CI_{i+1}: [{lo:.2f}, {hi:.2f}]")

Multiple Linear Regression

from statscore import (
    Mult_LR_Least_squares, Mult_norm_LR_test_general, Mult_norm_LR_pred_CI
)

X = np.column_stack([np.ones(n), x1, x2])

ols = Mult_LR_Least_squares(X, y)
print(f"beta_hat = {ols.beta_hat}")
print(f"Se^2 = {ols.sigma2_unbiased:.4f}")

# General hypothesis test: H0: C*beta = c0
C = np.array([[0, 1, -1]])
c0 = np.array([0.0])
result = Mult_norm_LR_test_general(X, y, C, c0, alpha=0.05)
print(f"F = {result.test_statistic:.4f}, p = {result.p_value:.4f}")

# Simultaneous prediction intervals
D = np.array([[1, 0.5, 1.0], [1, 1.0, 0.0]])
pred = Mult_norm_LR_pred_CI(X, y, D, alpha=0.05, method="best")
for i, (lo, hi) in enumerate(pred.intervals):
    print(f"Prediction {i+1}: {pred.point_estimates[i]:.2f} [{lo:.2f}, {hi:.2f}]")

Package Structure

statscore/
├── __init__.py              # Top-level exports (20 public functions)
├── anova/
│   ├── one_way.py           # ANOVA1_partition_TSS, ANOVA1_test_equality
│   ├── two_way.py           # ANOVA2_partition_TSS, ANOVA2_MLE, ANOVA2_test_equality
│   └── multiple_tests.py    # Contrasts, orthogonality, corrections, CI, tests
├── regression/
│   ├── least_squares.py     # Mult_LR_Least_squares, Mult_LR_partition_TSS
│   ├── inference.py         # Simultaneous CI, CR, general/component/linear tests
│   └── prediction.py        # Mult_norm_LR_pred_CI
├── utils/
│   ├── distributions.py     # Critical values and p-values (F, t, chi2, q)
│   └── validation.py        # Input validation helpers
├── examples/
│   └── demo.py              # Full demonstration of all 20 functions
└── tests/                   # 58 unit tests (pytest)

API Reference

ANOVA Functions

Function	Description
ANOVA1_partition_TSS(data)	Partition SS_total into SS_within and SS_between
ANOVA1_test_equality(data, alpha)	F-test for equality of group means
ANOVA1_is_contrast(c)	Check if coefficients form a contrast
ANOVA1_is_orthogonal(n, c1, c2)	Check orthogonality of two contrasts
Bonferroni_correction(alpha, m)	Bonferroni-corrected significance level
Sidak_correction(alpha, m)	Šidák-corrected significance level
ANOVA1_CI_linear_combs(data, alpha, C, method)	Simultaneous CIs for linear combinations
ANOVA1_test_linear_combs(data, alpha, C, d, method)	Test multiple linear combinations (FWER)
ANOVA2_partition_TSS(data)	Two-way ANOVA sum of squares partition
ANOVA2_MLE(data)	MLE for μ, α_i, β_j, δ_{ij}
ANOVA2_test_equality(data, alpha, test)	Two-way ANOVA F-tests ("A", "B", "AB")

Regression Functions

Function	Description
Mult_LR_Least_squares(X, y)	OLS estimation: β̂, σ² MLE & unbiased
Mult_LR_partition_TSS(X, y)	TSS = RegSS + RSS decomposition
Mult_norm_LR_simul_CI(X, y, alpha)	Simultaneous CIs for all β_i
Mult_norm_LR_CR(X, y, C, alpha)	Confidence region (ellipsoid) for Cβ
Mult_norm_LR_is_in_CR(X, y, C, c0, alpha)	Test if c₀ is inside the CR
Mult_norm_LR_test_general(X, y, C, c0, alpha)	General test H₀: Cβ = c₀
Mult_norm_LR_test_comp(X, y, alpha, components)	Test H₀: β_{j₁}=...=β_{jᵣ}=0
Mult_norm_LR_test_linear_reg(X, y, alpha)	Test existence of linear regression
Mult_norm_LR_pred_CI(X, y, D, alpha, method)	Simultaneous prediction CIs

Mathematical Background

One-Way ANOVA

Model: X_{ij} = μ + α_i + ε_{ij}, where ε_{ij} ~ N(0, σ²).

Sum of squares decomposition:

• SS_total = Σ_i Σ_j (X_{ij} - X̄)²
• SS_within = Σ_i Σ_j (X_{ij} - X̄_i)²
• SS_between = Σ_i n_i (X̄_i - X̄)²
• Identity: SS_total = SS_within + SS_between

F-test: F = [SS_b/(I-1)] / [SS_w/(n-I)] ~ F_{I-1, n-I} under H₀.

Two-Way ANOVA

Model: X_{ijk} = μ + α_i + β_j + δ_{ij} + ε_{ijk}.

Decomposition: SS_total = SS_A + SS_B + SS_AB + SS_E

Multiple Linear Regression

Model: Y = Xβ + ε, where ε ~ N(0, σ²I).

OLS estimator: β̂ = (X^T X)^{-1} X^T Y

TSS partition: TSS = RegSS + RSS

General test: H₀: Cβ = c₀, using F = [(Cβ̂ - c₀)^T [C(X^TX)^{-1}C^T]^{-1} (Cβ̂ - c₀)] / (r · S_e²)

Development

# Install with dev dependencies
pip install -e ".[dev]"

# Run tests
pytest tests/ -v

# Run linter
ruff check .

# Type checking
mypy statscore/

Running the Demo

python examples/demo.py

This exercises all 20 functions with representative sample data.

License

MIT