Module hypothesis 

Hypothesis testing: t-test, chi-squared test, paired t-test. Statistical hypothesis tests — t-test (one-sample, two-sample, paired), chi-squared goodness-of-fit, ANOVA, F-test.

Determinism Contract

All tests are deterministic — same input => identical results. Uses Kahan summation for all reductions.

Structs

AnovaResult

Result of ANOVA.

ChiSquaredResult

Result of a chi-squared test.

KruskalWallisResult

Kruskal-Wallis H test result.

LmResult

Result of linear regression.

LogisticResult

Logistic regression result.

MannWhitneyResult

Mann-Whitney U test result.

NormalityResult

Result of a normality test.

TTestResult

Result of a t-test.

TukeyHsdPair

Tukey HSD pairwise comparison result.

WilcoxonResult

Wilcoxon signed-rank test result.

Functions

anderson_darling

Anderson-Darling test for normality. Compares the empirical CDF to a normal CDF.

anova_oneway

One-way ANOVA: compare means across groups.

bartlett_test

Bartlett’s test for equality of variances.

bonferroni

Bonferroni correction: adjusted_p[i] = min(p[i] * m, 1.0).

chi_squared_test

Chi-squared goodness-of-fit test.

cohens_d

Cohen’s d: standardized difference between two group means.

cramers_v

Cramér’s V: association between two categorical variables. Input: contingency table as flat row-major array with dimensions r x c.

eta_squared

Eta-squared: proportion of variance explained by group membership. Input: array of groups (each is a slice of f64).

f_test

F-test for equality of variances.

fdr_bh

Benjamini-Hochberg FDR correction.

jarque_bera

Jarque-Bera normality test. Tests whether data has skewness and kurtosis matching a normal distribution. JB = (n/6) * (S² + (K-3)²/4)

kruskal_wallis

Kruskal-Wallis H test: non-parametric one-way ANOVA on ranks.

ks_test_normal

Kolmogorov-Smirnov one-sample test for normality. Compares empirical distribution to a standard normal.

levene_test

Levene’s test for equality of variances across groups.

lm

Ordinary least squares regression: y = Xb + e. x_matrix: flattened row-major (n x p), y: (n). Adds intercept column automatically. Uses QR decomposition for numerical stability.

logistic_regression

Logistic regression via IRLS. x_flat: row-major n x p matrix (NO intercept column — auto-added). y: binary 0/1 response.

mann_whitney

Mann-Whitney U test (Wilcoxon rank-sum test).

t_test

One-sample t-test: is the mean significantly different from mu?

t_test_paired

Paired t-test.

t_test_two_sample

Two-sample independent t-test (Welch’s — unequal variance).

tukey_hsd

Tukey HSD post-hoc test after one-way ANOVA.

wilcoxon_signed_rank

Wilcoxon signed-rank test for paired data.

wls

Weighted least squares regression. Transforms to OLS: X_w = W^{1/2} * X, y_w = W^{1/2} * y. Then applies standard QR-based least squares via lm().