/**
 * LombokTableSheet — ANOVA Module
 * One-way & Two-way ANOVA with mathematical rigor.
 * Validated against R / SciPy / Excel to 4 decimal places.
 *
 * @module formulas/anova
 */
export interface AnovaGroupStats {
    n: number;
    mean: number;
    variance: number;
    std_dev: number;
}
export interface AnovaOneWayResult {
    f_statistic: number;
    p_value: number;
    df_between: number;
    df_within: number;
    ss_between: number;
    ss_within: number;
    ss_total: number;
    ms_between: number;
    ms_within: number;
    eta_squared: number;
    significant: boolean;
    alpha: number;
    groups: AnovaGroupStats[];
}
export interface AnovaTwoWayResult {
    factor_a: AnovaFactorResult;
    factor_b: AnovaFactorResult;
    interaction: AnovaFactorResult;
    ss_within: number;
    df_within: number;
    ms_within: number;
    ss_total: number;
    grand_mean: number;
    cell_means: number[][];
    n_per_cell: number;
}
export interface AnovaFactorResult {
    name: string;
    ss: number;
    df: number;
    ms: number;
    f_statistic: number;
    p_value: number;
    significant: boolean;
    eta_squared: number;
}
export declare function anovaOneWay(groups: number[][], alpha?: number): AnovaOneWayResult;
/**
 * data[i][j] = array of replicate values for factor A level i, factor B level j.
 * Requires a BALANCED design: same number of replicates (n) in every cell.
 */
export declare function anovaTwoWay(data: number[][][], factorAName?: string, factorBName?: string, alpha?: number): AnovaTwoWayResult;
export declare function round4(x: number): number;
/**
 * P-value from the F-distribution: P(F_{d1,d2} > f)
 * = regularized incomplete beta I_x(d2/2, d1/2), x = d2/(d2 + d1*f)
 */
export declare function fDistPValue(f: number, d1: number, d2: number): number;
/**
 * Regularized incomplete beta function I_x(a, b) via Lentz continued fraction.
 * Standard numerical recipe (Numerical Recipes in C, §6.4).
 */
export declare function incompleteBeta(x: number, a: number, b: number): number;
/** Lanczos approximation for log-gamma (high precision, g=7, n=9) */
export declare function logGamma(x: number): number;