Welch's Anova and Comparison with Traditional.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import f_oneway, f\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Welch's ANOVA Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Welch's anova\n",
    "def weight(arr):\n",
    "    n = len(arr)\n",
    "    sig2 = (np.var(arr, ddof=1))**2\n",
    "    return n/sig2\n",
    "\n",
    "def W_sum(*arrays):\n",
    "    s=0\n",
    "    for arr in arrays:\n",
    "        s+=weight(arr)\n",
    "    return s\n",
    "    \n",
    "def MS(*arrays):\n",
    "    s=0\n",
    "    W = W_sum(*arrays)\n",
    "    for arr in arrays:\n",
    "        s+=arr.mean()*weight(arr)\n",
    "    return s/W\n",
    "\n",
    "def Numerator(*arrays):\n",
    "    k=len(arrays)\n",
    "    s=0\n",
    "    for arr in arrays:\n",
    "        s+=(arr.mean() - MS(*arrays))**2*weight(arr)\n",
    "    return s/(k-1)\n",
    "\n",
    "def A(*arrays):\n",
    "    s=0\n",
    "    W = W_sum(*arrays)\n",
    "    for arr in arrays:\n",
    "        s+= ((1-weight(arr)/W)**2)/(len(arr)-1)\n",
    "    return s\n",
    "\n",
    "def Denominator(*arrays):\n",
    "    k=len(arrays)\n",
    "    return 3*A(*arrays)*(k-2)/(k**2-1)+1\n",
    "\n",
    "def DoF(*arrays):\n",
    "    k = len(arrays)\n",
    "    DF_Numerator = k-1\n",
    "    DF_Denominator = (k**2-1)/(3*A(*arrays))\n",
    "    return DF_Numerator, DF_Denominator\n",
    "        \n",
    "def Welch_anova(*arrays):\n",
    "    DFNum = DoF(*arrays)[0]\n",
    "    DFDen = DoF(*arrays)[1]\n",
    "    F = Numerator(*arrays)/Denominator(*arrays)\n",
    "    p = stats.f.sf(F, DFNum, DFDen)\n",
    "    return F,p\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Whelch's ANOVA VS traditional ANOVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def comparison_anova(*arrays):\n",
    "    F = f_oneway(*arrays)[0]\n",
    "    p = f_oneway(*arrays)[1]\n",
    "    Welch_F = Welch_anova(*arrays)[0]\n",
    "    Welch_p = Welch_anova(*arrays)[1]\n",
    "    print('statistic= %f'%F, 'pvalue= %f'%p)\n",
    "    if p > 0.05:\n",
    "        print('Accept Ho')\n",
    "    else:\n",
    "        print('Reject Ho')   \n",
    "    print('\\n')    \n",
    "    print('W_statistic= %f'%Welch_F, 'W_pvalue= %f'%Welch_p)    \n",
    "    if Welch_p > 0.05:\n",
    "        print('Accept Ho')\n",
    "    else:\n",
    "        print('Reject Ho')   \n",
    "    print('\\n')\n",
    "\n",
    "#'Accept Ho: All input samples are from populations with equal means (alpha = 5%)'\n",
    "#'Reject Ho: All input samples are not from populations with equal means (alpha = 5%)'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### == means <br> == variances <br> == sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 1.041478 pvalue= 0.352945\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 1.029274 W_pvalue= 0.357285\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 1, size=10000)\n",
    "b = np.random.normal(0, 1, size=10000)\n",
    "c = np.random.normal(0, 1, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 6.455091 pvalue= 0.001575\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.015804 W_pvalue= 0.984320\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(104, 20, size=10000)\n",
    "b = np.random.normal(104, 20, size=10000)\n",
    "c = np.random.normal(104, 20, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### == means <br>== variances <br> ! = sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.732989 pvalue= 0.480515\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.881429 W_pvalue= 0.416696\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 1, size=50)\n",
    "b = np.random.normal(0, 1, size=800)\n",
    "c = np.random.normal(0, 1, size=5000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.502194 pvalue= 0.605227\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.507834 W_pvalue= 0.603016\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 1, size=50)\n",
    "b = np.random.normal(0, 1, size=800)\n",
    "c = np.random.normal(0, 1, size=5000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.042891 pvalue= 0.958016\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.043178 W_pvalue= 0.957755\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 1.1, size=50)\n",
    "b = np.random.normal(0, 1.1, size=800)\n",
    "c = np.random.normal(0, 1.1, size=5000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.538719 pvalue= 0.583657\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.005160 W_pvalue= 0.994853\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(29, 10, size=50)\n",
    "b = np.random.normal(29, 10, size=800)\n",
    "c = np.random.normal(29, 10, size=200)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 1.063486 pvalue= 0.345623\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.010657 W_pvalue= 0.989401\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(100, 10, size=50)\n",
    "b = np.random.normal(100, 10, size=800)\n",
    "c = np.random.normal(100, 10, size=200)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.156953 pvalue= 0.854745\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 15.693940 W_pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(29, 0.1, size=5000)\n",
    "b = np.random.normal(29, 0.1, size=800)\n",
    "c = np.random.normal(29, 0.1, size=20000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.393815 pvalue= 0.674483\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 2.298113 W_pvalue= 0.100709\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(29, 0.41, size=5000)\n",
    "b = np.random.normal(29, 0.41, size=800)\n",
    "c = np.random.normal(29, 0.41, size=20000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Variances are all equal, though results highly depends on the value of the variance. Note that variances less then or equal to 1 behave them unstable and lead to rejecting the Ho hypothesis.  Weights get too big when variances get close to 0, as weights are inversely proptional to square of variances, so it's somewhat expected to have this kind of poor results on that. Maybe it can be controlled by appropriate sample size though it's not the thing we should manage."
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://scholarscompass.vcu.edu/cgi/viewcontent.cgi?article=5026&context=etd\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### == means <br> ! = variances <br> = = sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.405246 pvalue= 0.666816\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.780858 W_pvalue= 0.458034\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 1, size=10000)\n",
    "b = np.random.normal(0, 1.5, size=10000)\n",
    "c = np.random.normal(0, 0.23, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.078067 pvalue= 0.924903\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.006051 W_pvalue= 0.993967\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 10, size=10000)\n",
    "b = np.random.normal(0, 3.5, size=10000)\n",
    "c = np.random.normal(0, 0.23, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.769692 pvalue= 0.463165\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.000346 W_pvalue= 0.999654\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(100, 89, size=10000)\n",
    "b = np.random.normal(100, 24, size=10000)\n",
    "c = np.random.normal(100, 0.1, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.541344 pvalue= 0.581971\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 7.246724 W_pvalue= 0.000715\n",
      "Reject Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(100, 0.4, size=10000)\n",
    "b = np.random.normal(100, 0.6, size=10000)\n",
    "c = np.random.normal(100, 0.1, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### == means <br>! = variances <br> ! = sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 1.495446 pvalue= 0.224165\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 1.135651 W_pvalue= 0.321239\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 1, size=10000)\n",
    "b = np.random.normal(0, 1.5, size=15000)\n",
    "c = np.random.normal(0, 0.23, size=6000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.043145 pvalue= 0.957773\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.002199 W_pvalue= 0.997803\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 10, size=1000)\n",
    "b = np.random.normal(0, 1.5, size=150)\n",
    "c = np.random.normal(0, 223, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 37.623700 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.000267 W_pvalue= 0.999733\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(111, 100, size=1000)\n",
    "b = np.random.normal(111, 1.5, size=15000)\n",
    "c = np.random.normal(111, 34, size=300)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 5.603438 pvalue= 0.003692\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 3.890922 W_pvalue= 0.020823\n",
      "Reject Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(111, 0.1, size=1000)\n",
    "b = np.random.normal(111, 0.4, size=15000)\n",
    "c = np.random.normal(111, 0.8, size=300)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ! = means <br>== variances <br> == sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 1.914376 pvalue= 0.147452\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 1.893702 W_pvalue= 0.150541\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 1, size=10000)\n",
    "b = np.random.normal(1e-1000, 1, size=10000)\n",
    "c = np.random.normal(1e-2, 1, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 1.561080 pvalue= 0.209926\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 1.549279 W_pvalue= 0.212427\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 1, size=10000)\n",
    "b = np.random.normal(1e-1000, 1, size=10000)\n",
    "c = np.random.normal(1e-2, 1, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.285180 pvalue= 0.751881\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.000028 W_pvalue= 0.999972\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 100, size=10000)\n",
    "b = np.random.normal(1e-1000, 100, size=10000)\n",
    "c = np.random.normal(1e-2, 100, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 30.740753 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.003035 W_pvalue= 0.996970\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 100, size=10000)\n",
    "b = np.random.normal(10, 100, size=10000)\n",
    "c = np.random.normal(2, 100, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 2863.819020 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 29.520666 W_pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 10, size=10000)\n",
    "b = np.random.normal(10, 10, size=10000)\n",
    "c = np.random.normal(2, 10, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 1.048135 pvalue= 0.350591\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.000000 W_pvalue= 1.000000\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#error 404 not found...\n",
    "a = np.random.normal(-9, 10000, size=1000000)\n",
    "b = np.random.normal(10, 10000, size=1000000)\n",
    "c = np.random.normal(2, 10000, size=1000000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ! = means <br>== variances <br> ! = sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.787125 pvalue= 0.455172\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.810606 W_pvalue= 0.444813\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 1, size=10000)\n",
    "b = np.random.normal(1e-1000, 1, size=3000)\n",
    "c = np.random.normal(1e-2, 1, size=500)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 26291.964026 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 22234.419072 W_pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 1, size=10000)\n",
    "b = np.random.normal(-1, 1, size=3000)\n",
    "c = np.random.normal(10, 1, size=500)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 6.859270 pvalue= 0.001065\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.000667 W_pvalue= 0.999333\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#error 404\n",
    "a = np.random.normal(0, 100, size=1000)\n",
    "b = np.random.normal(-1, 100, size=300)\n",
    "c = np.random.normal(10, 100, size=2000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 2749.401942 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.271983 W_pvalue= 0.761874\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#error 404\n",
    "a = np.random.normal(100, 100, size=10000)\n",
    "b = np.random.normal(20, 100, size=3000)\n",
    "c = np.random.normal(10, 100, size=20000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 2539.779194 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 19.949216 W_pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 11, size=1000)\n",
    "b = np.random.normal(10, 11, size=300)\n",
    "c = np.random.normal(30, 11, size=2000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 31.442666 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.002514 W_pvalue= 0.997490\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 110, size=1000)\n",
    "b = np.random.normal(10, 110, size=300)\n",
    "c = np.random.normal(30, 110, size=2000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ! = means <br>! = variances <br> == sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.458295 pvalue= 0.632365\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.443435 W_pvalue= 0.641837\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 2, size=10000)\n",
    "b = np.random.normal(1e-1000, 0.2, size=10000)\n",
    "c = np.random.normal(1e-2, 1.3, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 44.558765 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.593749 W_pvalue= 0.552268\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(10, 2, size=10000)\n",
    "b = np.random.normal(11, 20, size=10000)\n",
    "c = np.random.normal(12, 13, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 1743.723903 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 4.492042 W_pvalue= 0.011215\n",
      "Reject Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(10, 2, size=10000)\n",
    "b = np.random.normal(21, 20, size=10000)\n",
    "c = np.random.normal(12, 13, size=10000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 27.911283 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.062204 W_pvalue= 0.939719\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#error 404\n",
    "a = np.random.normal(10, 2, size=100)\n",
    "b = np.random.normal(21, 20, size=100)\n",
    "c = np.random.normal(12, 13, size=100)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 3.184600 pvalue= 0.041675\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.078648 W_pvalue= 0.924373\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#error 404\n",
    "a = np.random.normal(10, 100, size=500)\n",
    "b = np.random.normal(21, 20, size=500)\n",
    "c = np.random.normal(12, 13, size=500)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 1517.021883 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 22.901735 W_pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(100, 2, size=100)\n",
    "b = np.random.normal(21, 20, size=100)\n",
    "c = np.random.normal(3, 13, size=100)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ! = means <br>! = variances <br> ! = sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.675045 pvalue= 0.509161\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.009315 W_pvalue= 0.990728\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(0, 3, size=300)\n",
    "b = np.random.normal(1e-1000, 1.5, size=2000)\n",
    "c = np.random.normal(1e-2, 0.4, size=6000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 1540445.911576 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 58878.719432 W_pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(100, 3, size=300)\n",
    "b = np.random.normal(13, 1.5, size=2000)\n",
    "c = np.random.normal(-2, 0.4, size=6000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 0.373177 pvalue= 0.688546\n",
      "Accept Ho\n",
      "\n",
      "\n",
      "W_statistic= 0.000108 W_pvalue= 0.999892\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(111, 300, size=30000)\n",
    "b = np.random.normal(115, 15, size=2000)\n",
    "c = np.random.normal(110, 190, size=6000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 20983.204044 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 1.148756 W_pvalue= 0.317062\n",
      "Accept Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(111, 300, size=30000)\n",
    "b = np.random.normal(215, 15, size=2000)\n",
    "c = np.random.normal(910, 190, size=6000)\n",
    "comparison_anova(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistic= 22048.317560 pvalue= 0.000000\n",
      "Reject Ho\n",
      "\n",
      "\n",
      "W_statistic= 3.874123 W_pvalue= 0.020806\n",
      "Reject Ho\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.normal(111, 300, size=30000)\n",
    "b = np.random.normal(215, 100, size=2000)\n",
    "c = np.random.normal(910, 109, size=6000)\n",
    "comparison_anova(a,b,c)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
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 },
 "nbformat": 4,
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