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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Math\Stochastic\Distribution |
| 8 | * @copyright Dennis Eichhorn |
| 9 | * @license OMS License 2.0 |
| 10 | * @version 1.0.0 |
| 11 | * @link https://jingga.app |
| 12 | */ |
| 13 | declare(strict_types=1); |
| 14 | |
| 15 | namespace phpOMS\Math\Stochastic\Distribution; |
| 16 | |
| 17 | use phpOMS\Math\Statistic\Average; |
| 18 | use phpOMS\Math\Statistic\MeasureOfDispersion; |
| 19 | |
| 20 | /** |
| 21 | * ZTest |
| 22 | * |
| 23 | * Test if the mean is the same as the population mean |
| 24 | * |
| 25 | * @package phpOMS\Math\Stochastic\Distribution |
| 26 | * @license OMS License 2.0 |
| 27 | * @link https://jingga.app |
| 28 | * @since 1.0.0 |
| 29 | * |
| 30 | * @internal |
| 31 | */ |
| 32 | final class ZTesting |
| 33 | { |
| 34 | public const TABLE = [ |
| 35 | '2.58' => 0.99, |
| 36 | '2.33' => 0.98, |
| 37 | '1.96' => 0.95, |
| 38 | '1.64' => 0.90, |
| 39 | '1.44' => 0.85, |
| 40 | '1.28' => 0.80, |
| 41 | ]; |
| 42 | |
| 43 | /** |
| 44 | * Test hypthesis. |
| 45 | * |
| 46 | * @param float $dataset Value observed |
| 47 | * @param float $expected Expected value |
| 48 | * @param float $total Observed dataset size |
| 49 | * @param float $significance Significance |
| 50 | * |
| 51 | * @return bool |
| 52 | * |
| 53 | * @since 1.0.0 |
| 54 | */ |
| 55 | public static function testHypothesis(float $dataset, float $expected, float $total, float $significance = 0.95) : bool |
| 56 | { |
| 57 | $z = ($dataset - $expected) / \sqrt($expected * (1 - $expected) / $total); |
| 58 | |
| 59 | $zSignificance = 0.0; |
| 60 | foreach (self::TABLE as $key => $value) { |
| 61 | if ($significance === $value) { |
| 62 | $zSignificance = (float) $key; |
| 63 | } |
| 64 | } |
| 65 | |
| 66 | return $z > -$zSignificance && $z < $zSignificance; |
| 67 | } |
| 68 | |
| 69 | /** |
| 70 | * Z-TEST. |
| 71 | * |
| 72 | * @param float $value Value to test |
| 73 | * @param array $data Data |
| 74 | * @param null|float $sigma Sigma / Significance |
| 75 | * |
| 76 | * @return float |
| 77 | * |
| 78 | * @since 1.0.0 |
| 79 | */ |
| 80 | public static function zTest(float $value, array $data, float $sigma = null) : float |
| 81 | { |
| 82 | $sigma ??= MeasureOfDispersion::standardDeviationSample($data); |
| 83 | |
| 84 | return 1 - NormalDistribution::getCdf((Average::arithmeticMean($data) - $value) / ($sigma / \sqrt(\count($data))), 0.0, 1.0); |
| 85 | } |
| 86 | |
| 87 | /** |
| 88 | * Z-TEST. |
| 89 | * |
| 90 | * @param float $value Value to test |
| 91 | * @param float $mean Mean |
| 92 | * @param int $dataSize Data size |
| 93 | * @param float $sigma Sigma / Significance |
| 94 | * |
| 95 | * @return float |
| 96 | * |
| 97 | * @since 1.0.0 |
| 98 | */ |
| 99 | public static function zTestValues(float $value, float $mean, int $dataSize, float $sigma) : float |
| 100 | { |
| 101 | return 1 - NormalDistribution::getCdf(($mean - $value) / ($sigma / \sqrt($dataSize)), 0.0, 1.0); |
| 102 | } |
| 103 | } |