PHP translation of the Wilson ConfidenceInterval Calculator. Ported from Ruby and uses a hardcoded (pre-calculated) confidence (z value) instead of a dynamic calculation with a translation of Ruby's Statistics2.pnormaldist method. Since z doesn't change once it's computed, nor is the computation dependant on the passed-in values, calculating it …

WilsonConfidenceIntervalCalculator.php

<?php

/*
 * (c) Mark Badolato <mbadolato@gmail.com>
 *
 * This content is released under the {@link http://www.opensource.org/licenses/MIT MIT License.}
 */
 
namespace Bado;

class WilsonConfidenceIntervalCalculator
{
    /**
     * Computed value for confidence (z)
     *
     * These values were computed using Ruby's Statistics2.pnormaldist function
     * 1.959964 = 95.0% confidence
     * 2.241403 = 97.5% confidence
     */
    private const CONFIDENCE = 2.241403;

    public function getScore(int $positiveVotes, int $totalVotes, float $confidence = self::CONFIDENCE) : float
    {
        return (float) $totalVotes ? $this->lowerBound($positiveVotes, $totalVotes, $confidence) : 0;
    }

    private function lowerBound(int $positiveVotes, int $totalVotes, float $confidence) : float
    {
        $phat        = 1.0 * $positiveVotes / $totalVotes;
        $numerator   = $this->calculationNumerator($totalVotes, $confidence, $phat);
        $denominator = $this->calculationDenominator($totalVotes, $confidence);

        return $numerator / $denominator;
    }

    private function calculationDenominator(int $total, float $z) : float
    {
        return 1 + $z * $z / $total;
    }

    private function calculationNumerator(int $total, float $z, float $phat) : float
    {
        return $phat + $z * $z / (2 * $total) - $z * sqrt(($phat * (1 - $phat) + $z * $z / (4 * $total)) / $total);
    }
}

WilsonConfidenceIntervalCalculatorTest.php

<?php

/*
 * (c) Mark Badolato <mbadolato@gmail.com>
 *
 * This content is released under the {@link http://www.opensource.org/licenses/MIT MIT License.}
 */
 
namespace Bado\Tests\ScoreCalculator;

use Bado\WilsonConfidenceIntervalCalculator;
use PHPUnit\Framework\TestCase;

class WilsonConfidenceIntervalCalculatorTest extends TestCase
{
    /**
     * @test
     * @dataProvider ratingsProvider
     *
     * @param int   $positiveVotes
     * @param int   $totalVotes
     * @param float $expectedScore
     */
    public function it_can_calculate_scores_properly(int $positiveVotes, int $totalVotes, float $expectedScore) : void
    {
        $calculator      = new WilsonConfidenceIntervalCalculator();
        $calculatedScore = $calculator->getScore($positiveVotes, $totalVotes);

        self::assertEquals($expectedScore, $calculatedScore, '', 0.000001);
    }

    public function ratingsProvider() : array
    {
        // Pre-calculated score results using the known Ruby implementation
        // Array format is [$positiveVotes, $totalVotes, $expectedScore]
        return [
            [0, 0, 0],
            [0, 10, 0],
            [1, 2, 0.077136],
            [10, 10, 0.665607],
            [10, 20, 0.275967],
            [52, 76, 0.556480],
        ];
    }
}

Updates to PHP 7