/**
 * Calculates the arithmetic mean of an array of numbers.
 *
 * @param data - The data to calculate the mean for.
 * @returns The mean of the data.
 * @throws Will throw an error if the data array is empty.
 * @example
 * const data = [1, 2, 3, 4, 5];
 * const meanValue = mean(data);
 * console.log(meanValue); // Output: 3
 */
export declare function arithmeticMean(data: number[]): number;
/**
 * Calculates the median of an array of numbers.
 *
 * @param data - The data to calculate the median for.
 * @returns The median of the data.
 * @throws Will throw an error if the data array is empty.
 * @example
 * const data = [1, 2, 3, 4, 5];
 * const medianValue = median(data);
 * console.log(medianValue); // Output: 3
 */
export declare function median(data: number[]): number;
/**
 * Calculates the t-statistic for an independent two-sample t-test.
 * @param mean1 - The mean of the first sample.
 * @param mean2 - The mean of the second sample.
 * @param s1 - The standard deviation of the first sample.
 * @param s2 - The standard deviation of the second sample.
 * @param n1 - The number of samples in the first sample.
 * @param n2 - The number of samples in the second sample.
 * @returns The t-statistic.
 */
export declare function calculateTStatistic(mean1: number, mean2: number, s1: number, s2: number, n1: number, n2: number): number;
/**
 * Calculates the degrees of freedom for an independent two-sample t-test using the Welch-Satterthwaite equation.
 * @param s1 - The standard deviation of the first sample.
 * @param s2 - The standard deviation of the second sample.
 * @param n1 - The number of samples in the first sample.
 * @param n2 - The number of samples in the second sample.
 * @returns The degrees of freedom.
 * @see {@link https://statkat.com/degrees-of-freedom-t-test.php}
 */
export declare function calculateDegreesOfFreedom(s1: number, s2: number, n1: number, n2: number): number;
/**
 * Formats a number to ensure consistent p-value calculation.
 *
 * This function is used internally by `calculatePValue` to format the result of the
 * `studT` function. It adds or subtracts a small value (0.0005) to the input number
 * to ensure that the p-value calculation is consistent across different JavaScript engines
 * and environments. This helps to avoid subtle differences in the p-value due to floating-point
 * precision issues.
 *
 * @param value - The number to format.
 * @returns The formatted number.
 * @internal
 */
export declare function formatPValue(value: number): number;
/**
 * Calculates the p-value for a given t-statistic and degrees of freedom.
 *
 * This function computes the two-tailed p-value for a t-test based on the
 * provided t-statistic and degrees of freedom. It uses the Student's t-distribution
 * to calculate the cumulative probability.
 *
 * @param tStat - The t-statistic (absolute value).
 * @param df - The degrees of freedom.
 * @returns The two-tailed p-value.
 * @throws Will throw an error if `tStat` or `df` is not a number or if `df` is less than or equal to 0.
 */
export declare function calculatePValue(tStat: number, df: number): number;
/**
 * Calculates the sample standard deviation.
 * @param data - The sample data.
 * @returns The sample standard deviation.
 */
export declare function sampleStandardDeviation(data: number[]): number;
/**
 * Calculates the sample variance.
 * @param data - The sample data.
 * @returns The sample variance.
 */
export declare function sampleVariance(data: number[]): number;
/**
 * Calculates the percentile of a sorted array.
 * @param sortedData - The sorted array.
 * @param percentile - The percentile to calculate (0-100).
 * @returns The percentile value.
 */
export declare function getPercentile(sortedData: number[], percentile: number): number;
/**
 * Calculates the relative margin of error for a given mean and standard deviation with a 95% confidence interval.
 * @param mean - The sample mean.
 * @param stdDev - The sample standard deviation.
 * @param n - The number of samples.
 * @returns The relative margin of error.
 */
export declare function relativeMarginOfError(mean: number, stdDev: number, n: number): number;
/**
 * Calculates the margin of error for a given standard deviation with a 95% confidence interval.
 * This is a simplified calculation assuming a normal distribution.
 *
 * @param stdDev - The sample standard deviation.
 * @param n - The number of samples.
 * @returns The margin of error.
 */
export declare function marginOfError(stdDev: number, n: number): number;
/**
 * Calculates Cohen's d effect size.
 *
 * Cohen's d is a measure of the standardized difference between two means.
 * It is calculated as the difference between the means divided by the pooled standard deviation.
 *
 * @param mean1 - The mean of the first sample.
 * @param mean2 - The mean of the second sample.
 * @param s1 - The standard deviation of the first sample.
 * @param s2 - The standard deviation of the second sample.
 * @param n1 - The number of samples in the first sample.
 * @param n2 - The number of samples in the second sample.
 * @returns Cohen's d.
 */
export declare function calculateCohensD(mean1: number, mean2: number, s1: number, s2: number, n1: number, n2: number): number;
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