MathPHP\Statistics\EffectSize::hedgesG PHP Method

hedgesG() public static method

The difference between two means divided by a standard deviation for the data. https://en.wikipedia.org/wiki/Effect_size#Hedges.27_g http://www.polyu.edu.hk/mm/effectsizefaqs/effect_size_equations2.html μ₁ - μ₂ g = ------- s* _________________________ (n₁ - 1)s₁² + (n₂ - 1)s₂² s* = / ------------------------- √ n₁ + n₂ - 2 Then, to remove bias 3 \ g* ≈ | 1 - -------------- | g \ 4(n₁ + n₂) - 9 / where μ₁ = mean of sample population 1 μ₂ = mean of sample population 2 s₁² = variance of sample population 1 s₂² = variance of sample population 1 n₁ = sample size of sample population 1 n₂ = sample size of sample population 2 s* = pooled standard deviation
public static hedgesG ( number $μ₁, number $μ₂, number $s₁, number $s₂, number $n₁, number $n₂ ) : number
$μ₁ number Mean of sample population 1
$μ₂ number Mean of sample population 2
$s₁ number Standard deviation of sample population 1
$s₂ number Standard deviation of sample population 2
$n₁ number Sample size of sample popluation 1
$n₂ number Sample size of sample popluation 2
return number
    public static function hedgesG($μ₁, $μ₂, $s₁, $s₂, $n₁, $n₂)
    {
        // Variance of each data set
        $s₁² = $s₁ * $s₁;
        $s₂² = $s₂ * $s₂;
        // Pooled standard deviation
        $⟮n₁ − 1⟯s₁² + ⟮n₂ − 1⟯s₂² = ($n₁ - 1) * $s₁² + ($n₂ - 1) * $s₂²;
        $⟮n₁ + n₂ − 2⟯ = $n₁ + $n₂ - 2;
        $s* = sqrt($⟮n₁ − 1⟯s₁² + ⟮n₂ − 1⟯s₂² / $⟮n₁ + n₂ − 2⟯);
        // g
        $g = ($μ₁ - $μ₂) / $s*;
        // Unbiased g
        return (1 - 3 / (4 * ($n₁ + $n₂) - 9)) * $g;
    }