PHP Класс MathPHP\Statistics\Significance

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Открытые методы

Метод Описание
chiSquaredTest ( array $observed, array $expected ) : array χ² test (chi-squared goodness of fit test) Tests the hypothesis that data were generated according to a particular chance model (Statistics [Freedman, Pisani, Purves]).
sem ( number $σ, integer $n ) : float Standard error of the mean (SEM) Can be considered true standard deviation of the sample mean.
tScore ( number $Hₐ, number $s, integer $n, number $H₀ ) : number T-score
tTestOneSample ( number $Hₐ, number $s, integer $n, number $H₀ ) : array One-sample Student's t-test Compares sample mean to the population mean.
tTestTwoSample ( number $μ₁, number $μ₂, number $n₁, number $n₂, number $σ₁, number $σ₂, number $Δ ) : array Two-sample t-test Test the means of two samples.
zScore ( number $M, number $μ, number $σ, boolean $table_value = false ) : float Z score - standard score https://en.wikipedia.org/wiki/Standard_score
zTest ( number $Hₐ, integer $n, number $H₀, number $σ ) : array One-sample Z-test When the population mean and standard deviation are known.

Описание методов

chiSquaredTest() публичный статический Метод

https://en.wikipedia.org/wiki/Chi-squared_test#Example_chi-squared_test_for_categorical_data (Oᵢ - Eᵢ)² χ² = ∑ ---------- Eᵢ where: O = observed value E = expected value k (degrees of freedom) = number of terms - 1 p = χ² distribution CDF(χ², k)
public static chiSquaredTest ( array $observed, array $expected ) : array
$observed array
$expected array
Результат array [chi-square, p]

sem() публичный статический Метод

Used in the Z test. https://en.wikipedia.org/wiki/Standard_error σ SEM = -- √n
public static sem ( number $σ, integer $n ) : float
$σ number Population standard deviation
$n integer Sample size (number of observations of the sample)
Результат float

tScore() публичный статический Метод

Hₐ - H₀ X - μ t = ------- = ----- s/√n s/√n
public static tScore ( number $Hₐ, number $s, integer $n, number $H₀ ) : number
$Hₐ number Alternate hypothesis (M Sample mean)
$s number SD of sample
$n integer Sample size
$H₀ number Null hypothesis (μ₀ Population mean)
Результат number

tTestOneSample() публичный статический Метод

https://en.wikipedia.org/wiki/Student%27s_t-test Hₐ - H₀ M - μ M - μ M - μ z = ------- = ----- = ----- = ----- σ σ SEM σ/√n p1 = CDF below if left tailed = CDF above if right tailed p2 = CDF outside
public static tTestOneSample ( number $Hₐ, number $s, integer $n, number $H₀ ) : array
$Hₐ number Alternate hypothesis (M Sample mean)
$s number SD of sample
$n integer Sample size
$H₀ number Null hypothesis (μ₀ Population mean)
Результат array [ z => z score p1 => one-tailed p value (left or right tail depends on how Hₐ differs from H₀) p2 => two-tailed p value ]

tTestTwoSample() публичный статический Метод

https://en.wikipedia.org/wiki/Student%27s_t-test μ₁ - μ₂ - Δ z = -------------- _________ σ₁² σ₂² --- + --- √ n₁ n₂ where μ₁ is sample mean 1 μ₂ is sample mean 2 Δ is the hypothesized difference between the population means (0 if testing for equal means) σ₁ is standard deviation of sample mean 1 σ₂ is standard deviation of sample mean 2 n₁ is sample size of mean 1 n₂ is sample size of mean 2 For Student's t distribution CDF, degrees of freedom: ν = (n₁ - 1) + (n₂ - 1) p1 = CDF above p2 = CDF outside
public static tTestTwoSample ( number $μ₁, number $μ₂, number $n₁, number $n₂, number $σ₁, number $σ₂, number $Δ ) : array
$μ₁ number Sample mean of population 1
$μ₂ number Sample mean of population 2
$n₁ number Sample size of population 1
$n₂ number Sample size of population 1
$σ₁ number Standard deviation of sample mean 1
$σ₂ number Standard deviation of sample mean 2
$Δ number (Optional) hypothesized difference between the population means (0 if testing for equal means)
Результат array [ t => t score p1 => one-tailed p value p2 => two-tailed p value ]

zScore() публичный статический Метод

M - μ z = ----- σ
public static zScore ( number $M, number $μ, number $σ, boolean $table_value = false ) : float
$M number Sample mean
$μ number Population mean
$σ number Population standard deviation
$table_value boolean Whether to return a rouned z score for looking up in a standard normal table, or the raw z score value
Результат float

zTest() публичный статический Метод

https://en.wikipedia.org/wiki/Z-test Hₐ - H₀ M - μ M - μ M - μ z = ------- = ----- = ----- = ----- σ σ SEM σ/√n p1 = CDF below if left tailed = CDF above if right tailed p2 = CDF outside
public static zTest ( number $Hₐ, integer $n, number $H₀, number $σ ) : array
$Hₐ number Alternate hypothesis (M Sample mean)
$n integer Sample size
$H₀ number Null hypothesis (μ Population mean)
$σ number SD of population (Standard error of the mean)
Результат array [ z => z score p1 => one-tailed p value (left or right tail depends on how Hₐ differs from H₀) p2 => two-tailed p value ]