{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "from scipy.stats import norm, t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "s1 = [95, 90, 91, 92]\n",
    "s2 = [97, 94, 89, 90]\n",
    "s3 = [85, 84, 79, 80]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m1 92.0\n",
      "m2 92.5\n",
      "m3 82.0\n"
     ]
    }
   ],
   "source": [
    "# calculate the means\n",
    "m1 = np.average(s1)\n",
    "m2 = np.average(s2)\n",
    "m3 = np.average(s3)\n",
    "print(\"m1\", m1)\n",
    "print(\"m2\", m2)\n",
    "print(\"m3\", m3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v1 4.666666666666667\n",
      "v2 13.666666666666666\n",
      "v3 8.666666666666666\n"
     ]
    }
   ],
   "source": [
    "# calculate the variances (w/ bessel's correction)\n",
    "# ddof = 1 has it use bessel's correction\n",
    "v1 = np.var(s1, ddof = 1)\n",
    "v2 = np.var(s2, ddof = 1)\n",
    "v3 = np.var(s3, ddof = 1)\n",
    "print(\"v1\", v1)\n",
    "print(\"v2\", v2)\n",
    "print(\"v3\", v3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample 1 vs 2 t value 0.2335496832484569\n"
     ]
    }
   ],
   "source": [
    "# calculate the t-value\n",
    "s1_n = len(s1)\n",
    "s2_n = len(s2)\n",
    "# numerator\n",
    "signal = abs(m1 - m2)\n",
    "# denominator\n",
    "noise = math.sqrt((v1/s1_n) + (v2/s2_n))\n",
    "t_val = signal / noise\n",
    "print(\"sample 1 vs 2 t value\", t_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.41154942928551863\n"
     ]
    }
   ],
   "source": [
    "# find the p-value via the scipy package:\n",
    "# use the cdf of t values to see how far through\n",
    "# the distribution this t value is\n",
    "# pass in the degrees of freedom\n",
    "# This is the one-tailed value\n",
    "print(1 - t.cdf(t_val, df = (s1_n + s2_n - 2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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