/**
 * vigiles — significance testing for eval A/B arms.
 *
 * The eval tier already reports mean ± se per arm; this answers the question that
 * `assertImproves(..., { by: se })` punted to the user: is the gap between two
 * arms real, or noise? A Welch's t-test over the per-arm summary stats (mean, se,
 * n) — no raw rows needed — yields a two-sided p-value and a significance verdict.
 * Pure + model-free, so it's fully unit-tested against known t-table values.
 *
 * For 0/1 (proportion) metrics this is the t approximation to the two-proportion
 * test — close at the trial counts evals use, and one code path for any metric.
 * The numerics (log-gamma, incomplete beta) are specialized to the argument range
 * these tests produce (a, b ≥ 0.5; x ∈ (0,1)); they are not a general library.
 */
import type { EvalReport } from "./eval.js";
/** Regularized incomplete beta I_x(a, b) ∈ [0, 1]. */
export declare function regularizedIncompleteBeta(a: number, b: number, x: number): number;
/** Two-sided p-value for Student's t with `df` degrees of freedom. */
export declare function tPValueTwoSided(t: number, df: number): number;
/** The verdict on one arm-vs-baseline comparison for a single metric. */
export interface Comparison {
    /** mean(arm) − mean(baseline). */
    readonly delta: number;
    /** Combined standard error of the difference. */
    readonly seDelta: number;
    /** Welch t statistic (delta / seDelta). */
    readonly t: number;
    /** Welch–Satterthwaite degrees of freedom. */
    readonly df: number;
    /** Two-sided p-value for the difference. */
    readonly pValue: number;
    /** p < alpha — the difference is unlikely to be noise. */
    readonly significant: boolean;
}
type Summary = {
    readonly mean: number;
    readonly se: number;
    readonly n: number;
};
/** Welch's unequal-variance t-test between two arms' summary stats. */
export declare function welchTTest(arm: Summary, baseline: Summary, alpha?: number): Comparison;
/**
 * Compare two arms on a metric using their reported summary stats, or null if
 * either arm/metric is absent. The grounded form of `assertImproves`'s `by`: it
 * computes the noise floor instead of asking the caller to supply it.
 */
export declare function compareArms(report: EvalReport, baseline: string, arm: string, metric: string, alpha?: number): Comparison | null;
export {};
//# sourceMappingURL=stats.d.ts.map