Simple, Useful and Slow: Assorted Reference Statistics Functions (utf-8)

simple_useful_slow.js

// 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