PHP Класс MathPHP\Statistics\EffectSize

https://en.wikipedia.org/wiki/Effect_size - η² (Eta-squared) - η²p (Partial eta-squared) - ω² (omega-squared) - Cohen's ƒ² - Cohen's q - Cohen's d - Hedges' g - Glass' Δ (glass' delta)
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Открытые методы

Метод Описание
cohensD ( number $μ₁, number $μ₂, number $s₁, number $s₂ ) : number Cohen's d
cohensF ( number $measure_of_variance_explained ) : number Cohen's ƒ²
cohensQ ( number $r₁, number $r₂ ) : number Cohen's q
etaSquared ( number $SSt, number $SST ) : number η² (Eta-squared)
glassDelta ( number $μ₁, number $μ₂, number $s₂ ) : number Glass' Δ (glass' delta)
hedgesG ( number $μ₁, number $μ₂, number $s₁, number $s₂, number $n₁, number $n₂ ) : number Hedges' g
omegaSquared ( number $SSt, number $dft, number $SST, number $MSE ) : number ω² (omega-squared)
partialEtaSquared ( $SSt, number $SSE ) : number η²p (Partial eta-squared)

Описание методов

cohensD() публичный статический Метод

The difference between two means divided by a standard deviation for the data. https://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d μ₁ - μ₂ d = ------- s _________ s₁² + s₂² s = / --------- √ 2 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 s = pooled standard deviation This formula uses the common simplified version of the pooled standard deviation.
public static cohensD ( number $μ₁, number $μ₂, number $s₁, number $s₂ ) : 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
Результат number

cohensF() публичный статический Метод

One of several effect size measures to use in the context of an F-test for ANOVA or multiple regression. Its amount of bias (overestimation of the effect size for the ANOVA) depends on the bias of its underlying measurement of variance explained (R², η², ω²) https://en.wikipedia.org/wiki/Effect_size#Cohen.27s_.C6.922 R² ƒ² = ------ 1 - R² η² ƒ² = ------ 1 - η² ω² ƒ² = ------ 1 - ω²
public static cohensF ( number $measure_of_variance_explained ) : number
$measure_of_variance_explained number (R², η², ω²)
Результат number

cohensQ() публичный статический Метод

The difference between two Fisher transformed Pearson regression coefficients. hhttps://en.wikipedia.org/wiki/Effect_size#Cohen.27s_q 1 1 + r₁ 1 1 + r₂ q = - log ------ - - log ------ 2 1 - r₁ 2 1 - r₂ where r₁ and r₂ are the regressions being compared
public static cohensQ ( number $r₁, number $r₂ ) : number
$r₁ number
$r₂ number
Результат number

etaSquared() публичный статический Метод

Eta-squared describes the ratio of variance explained in the dependent variable by a predictor while controlling for other predictors, making it analogous to the r². https://en.wikipedia.org/wiki/Effect_size#Eta-squared_.28.CE.B72.29 SSt η² = --- SST where: SSt = sum of squares treatment SST = sum of squares total
public static etaSquared ( number $SSt, number $SST ) : number
$SSt number Sum of squares treatment
$SST number Sum of squares total
Результат number

glassDelta() публичный статический Метод

An estimator of the effect size that uses only the standard deviation of the second group. https://en.wikipedia.org/wiki/Effect_size#Glass.27_.CE.94 μ₁ - μ₂ Δ = ------- s₂ where μ₁ = mean of sample population 1 μ₂ = mean of sample population 2 s₂ = standard deviation of sample population 2
public static glassDelta ( number $μ₁, number $μ₂, number $s₂ ) : number
$μ₁ number Mean of sample population 1
$μ₂ number Mean of sample population 2
$s₂ number Standard deviation of sample population 2
Результат number

hedgesG() публичный статический Метод

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
Результат number

omegaSquared() публичный статический Метод

A less biased estimator of the variance explained in the population. https://en.wikipedia.org/wiki/Effect_size#Omega-squared_.28.CF.892.29 SSt - dft * MSE ω² = --------------- SST + MSE where: SSt = sum of squares treatment SST = sum of squares total dft = degrees of freedom treatment MSE = Mean squares error
public static omegaSquared ( number $SSt, number $dft, number $SST, number $MSE ) : number
$SSt number Sum of squares treatment
$dft number Degrees of freedom treatment
$SST number Sum of squares total
$MSE number Mean squares error
Результат number

partialEtaSquared() публичный статический Метод

https://en.wikipedia.org/wiki/Effect_size#Eta-squared_.28.CE.B72.29 SSt η²p = --------- SSt + SSE where: SSt = sum of squares treatment SSE = sum of squares error
public static partialEtaSquared ( $SSt, number $SSE ) : number
$SSE number Sum of squares error
Результат number