Simple, Useful and Slow: Assorted Reference Statistics Functions (utf-8)
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// 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 | |
Ꝏ = 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, +Ꝏ ) | |
// Two tailed | |
p_value_2 = (score, distribution) => ʃ(distribution || N, score, +Ꝏ )+ʃ(distribution || N, -Ꝏ , -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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