phpOMS/Math/Stochastic/Distribution/ZTesting.php

<?php
/**
 * Orange Management
 *
 * PHP Version 7.4
 *
 * @package   phpOMS\Math\Stochastic\Distribution
 * @copyright Dennis Eichhorn
 * @license   OMS License 1.0
 * @version   1.0.0
 * @link      https://orange-management.org
 */
declare(strict_types=1);

namespace phpOMS\Math\Stochastic\Distribution;

use phpOMS\Math\Statistic\Average;
use phpOMS\Math\Statistic\MeasureOfDispersion;

/**
 * ZTest
 *
 * @package phpOMS\Math\Stochastic\Distribution
 * @license OMS License 1.0
 * @link    https://orange-management.org
 * @since   1.0.0
 *
 * @internal
 */
final class ZTesting
{
    public const TABLE = [
        '2.58' => 0.99,
        '2.33' => 0.98,
        '1.96' => 0.95,
        '1.64' => 0.90,
        '1.44' => 0.85,
        '1.28' => 0.80,
    ];

    /**
     * Test hypthesis.
     *
     * @param float $dataset      Value observed
     * @param float $expected     Expected value
     * @param float $total        Observed dataset size
     * @param float $significance Significance
     *
     * @return bool
     *
     * @since 1.0.0
     */
    public static function testHypothesis(float $dataset, float $expected, float $total, float $significance = 0.95) : bool
    {
        $z = ($dataset - $expected) / \sqrt($expected * (1 - $expected) / $total);

        $zSignificance = 0.0;
        foreach (self::TABLE as $key => $value) {
            if ($significance === $value) {
                $zSignificance = (float) $key;
            }
        }

        return $z > -$zSignificance && $z < $zSignificance;
    }

    /**
     * Z-TEST.
     *
     * @param float      $value Value to test
     * @param array      $data  Data
     * @param null|float $sigma Sigma / Significance
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function zTest(float $value, array $data, float $sigma = null) : float
    {
        $sigma ??= MeasureOfDispersion::standardDeviationSample($data);

        return 1 - NormalDistribution::getCdf((Average::arithmeticMean($data) - $value) / ($sigma / \sqrt(\count($data))), 0.0, 1.0);
    }

    /**
     * Z-TEST.
     *
     * @param float $value    Value to test
     * @param float $mean     Mean
     * @param int   $dataSize Data size
     * @param float $sigma    Sigma / Significance
     *
     * @return float
     *
     * @since 1.0.0
     */
    public static function zTestValues(float $value, float $mean, int $dataSize, float $sigma) : float
    {
        return 1 - NormalDistribution::getCdf(($mean - $value) / ($sigma / \sqrt($dataSize)), 0.0, 1.0);
    }
}