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Simple, Useful and Slow: Assorted Reference Statistics Functions (utf-8)
// Simple, Useful and Slow
// Assorted Reference Statistics Functions
// UTF-8 Edition
// Shorthands
pow = Math.pow
sqrt = Math.sqrt
pi = Math.PI
// Variables named:
// x, x1, x2, ..., xn: always a sample (array of numbers)
// v is always a number
// Length of a sample
n = x => x.length
// Mean
μ = x => x.reduce((acc, v) => acc+v, 0)/n(x)
// Variance
σ2 = x => x.reduce((acc, v) => acc+pow(v-μ(x), 2), 0)/(n(x)-1)
// Standard Deviation
σ = x => sqrt(σ2(x))
//
// Student's t-test
//
// Degrees of freedom
df = (x1, x2) => n(x1)+n(x2) - 2
// t-test
t = (x1, x2) => (μ(x1)-μ(x2))/sqrt(σ2(a)/n(a)+σ2(b)/n(b))
// z-test (same as t, just uses different distribution when applying the score)
z = t
//
// Normal Distribution
//
// Euler
e = 2.7182818284
// Normal Distribution
_N = (v, μ, σ2) => 1/sqrt(2*pi*σ2)*pow(e, -pow(v-μ, 2)/2*σ2)
// Standard Normal Distribution
N = v => 1/sqrt(2*pi)*pow(e, -0.5*v*v)
//
// Distribution Sampling
//
// Sample a distribution
sample = (distribution, from, to, delta) => {
let array = [];
for (;from<to;from+=delta) {
array.push(distribution(from))
}
return array;
}
ε = 0.0001
= 5
// Integral
ʃ = (f, a, b) => sample(f, a, b, ε).reduce((acc, v) => acc+v, 0)*ε
// p-value
// One tailed
p_value_1 = (score, distribution) => ʃ(distribution || N, score, + )
// Two tailed
p_value_2 = (score, distribution) => ʃ(distribution || N, score, + )+ʃ(distribution || N, - , -score)
p_value = p_value_2
// Example: statistical significance:
a = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
b = [ 10, 8, 7, 5, 3, 6, 1, 9, 4, 3 ]
p_value(z(a, b)) < 0.05
a = [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ]
b = [ 0, 0, 0, 1, 0, 0, 1, 0, 0, 1 ]
p_value(z(a, b)) < 0.05
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