statisticall_significane_results.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "65289560-3567-4dfc-8442-f0ff011d198f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from inspect import getmembers\n",
    "from scipy.stats import wilcoxon, mannwhitneyu"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f47981a-7c70-427d-ba7c-49d7f23bdcd2",
   "metadata": {},
   "source": [
    "Gpa_Race Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "id": "7303e174-5038-4ff0-a027-3c54fa3298b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_fair_diff= np.array([0.18110897, 0.1490054  ,0.19448121 ,0.22011886, 0.21675262, 0.12836894, \n",
    "                      0.13689364, 0.15239729, 0.11294901, 0.14655845, 0.13851724, 0.18186689,\n",
    " 0.19133291, 0.10647815, 0.19887137 ,0.15841882 ,0.18772861, 0.17605858,\n",
    " 0.17077933, 0.1685073 , 0.21145288 ,0.18175574, 0.19185441, 0.15943925,\n",
    " 0.17413106, 0.20107437, 0.20754383 ,0.15580618, 0.15318213, 0.21145288,\n",
    " 0.20452196, 0.14681917, 0.23862156 ,0.19663896, 0.17352495, 0.16158863,\n",
    " 0.15988206, 0.15841882, 0.14718234 ,0.17529015, 0.12884181 ,0.17894623,\n",
    " 0.14440743, 0.13784277, 0.18469278 ,0.13669048, 0.17748085 ,0.1539392,\n",
    " 0.19736005 ,0.14929662, 0.15844699 ,0.22182865, 0.16835402 ,0.11590271,\n",
    " 0.16283391, 0.21145288, 0.13786294 ,0.20383239, 0.11383962 ,0.10801615,\n",
    " 0.16102788 ,0.16218828, 0.14150607 ,0.12740272, 0.14006936 ,0.13201345,\n",
    " 0.16834658 ,0.13377828 ,0.1666875  ,0.14061355, 0.18023479 ,0.18436701,\n",
    " 0.14913133 ,0.21525401 ,0.17023022 ,0.18430774 ,0.17092885 ,0.19765275,\n",
    " 0.18304344 ,0.15739805 ,0.16292723 ,0.13861935, 0.17201053 ,0.14061355,\n",
    " 0.1672823  ,0.1762323  ,0.16826181 ,0.18371578 ,0.14913133 ,0.14919094,\n",
    " 0.18577454 ,0.17643819 ,0.15818822 ,0.17378895, 0.15920622 ,0.19052756,\n",
    " 0.18186689 ,0.16635901, 0.21319444 ,0.18104184])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "id": "20342dee-cbf4-4b2d-a016-31bce9e07f1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_unfair_diff = np.array([0.22358242, 0.17815177, 0.25221285, 0.25957106, 0.22798538 ,0.18182101,\n",
    " 0.18045648 ,0.21528183, 0.1796425  ,0.19914106, 0.22846577, 0.24223537,\n",
    " 0.22459835 ,0.16217014, 0.26256182 ,0.17197253, 0.22113752, 0.19675115,\n",
    " 0.27170987 ,0.22112067, 0.25043859 ,0.22727413, 0.22565944, 0.1825326,\n",
    " 0.22639246 ,0.25323149, 0.24592962 ,0.21767811, 0.1959461 , 0.25043859,\n",
    " 0.25346937 ,0.20627261, 0.27257074 ,0.21396251 ,0.24123452, 0.26465735,\n",
    " 0.19694031 ,0.17197253, 0.18436205 ,0.19480432, 0.18368246, 0.23804661,\n",
    " 0.23497618 ,0.1728276 , 0.24165597 ,0.18835482, 0.20211323, 0.24832641,\n",
    " 0.2611978  ,0.2196947 , 0.24074189 ,0.25811568, 0.20894904 ,0.16715678,\n",
    " 0.21741584 ,0.25043859 ,0.22216653 ,0.28033797, 0.19395926, 0.22056387,\n",
    " 0.2568926  ,0.21431837, 0.21895242 ,0.20387798, 0.20021017, 0.23654297,\n",
    " 0.22019771 ,0.17841803 ,0.22565958 ,0.22574786, 0.22501857, 0.25109095,\n",
    " 0.2267903  ,0.26956247 ,0.2187941  ,0.2232612 , 0.19234407, 0.23366934,\n",
    " 0.22997664 ,0.20494617, 0.21047431, 0.19216076, 0.22198641, 0.22574786,\n",
    " 0.2125372  ,0.23241565, 0.20501062, 0.21031809, 0.2267903 , 0.21165049,\n",
    " 0.18882889 ,0.19274194, 0.22255979, 0.23163753, 0.22970738, 0.23756996,\n",
    " 0.24223537 ,0.21691553, 0.24513889, 0.20734388])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "id": "58d023fd-25ea-4a4e-bf93-56d1b06844c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.894801714589673e-18)"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_race_fair_diff,gpa_race_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "id": "e582598f-9e17-4800-9cd3-9b0a9659dee1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=861.0, pvalue=4.8863395525193486e-24)"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_race_fair_diff,gpa_race_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f7603038-d1c4-49dd-b6c5-5a6e25eea210",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_fair_ratio = np.array([1.26059568, 1.19830042, 1.2722737,  1.32755783, 1.32214609, 1.17380289,\n",
    " 1.18427989 ,1.20862945, 1.14880584 ,1.19811168, 1.18367501 ,1.26232414,\n",
    " 1.2749036  ,1.15185979, 1.28886344 ,1.20807249, 1.27140194 ,1.24377342,\n",
    " 1.23225989 ,1.23591022, 1.325217   ,1.25388104, 1.27631205 ,1.2237585,\n",
    " 1.24693162 ,1.29422746,1.30680393 ,1.21253561 ,1.21461881 ,1.325217,\n",
    " 1.302238  , 1.21134479, 1.36962947 ,1.27410279 ,1.24233657 ,1.2201959,\n",
    " 1.22289441, 1.20807249, 1.2005467  ,1.24199348 ,1.16889626 ,1.25359237,\n",
    " 1.18846394, 1.18272182, 1.26137808 ,1.19007256 ,1.25310312 ,1.21849435,\n",
    " 1.2825592 , 1.20518305, 1.21854758 ,1.33084158, 1.23744729 ,1.15010351,\n",
    " 1.22204625, 1.325217  , 1.18826444 ,1.30574858 ,1.15236995 ,1.13789295,\n",
    " 1.22739089, 1.22763267, 1.18867476, 1.16811906 ,1.19319911 ,1.18306838,\n",
    " 1.23568521, 1.17802802, 1.22997975, 1.18853214 ,1.2598477  ,1.26135543,\n",
    " 1.20465896, 1.33436123, 1.23849963, 1.26519836 ,1.23027915 ,1.28585263,\n",
    " 1.2626725  ,1.22174864, 1.23288468, 1.18677133 ,1.24260445 ,1.18853214,\n",
    " 1.23546801 ,1.23843193, 1.22918419, 1.25547975 ,1.20465896 ,1.20003254,\n",
    " 1.2583955  ,1.24122409, 1.22239403, 1.24742834 ,1.21619481 ,1.27935459,\n",
    " 1.26232414 ,1.23215071, 1.31979167, 1.26451622])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b8c4fbf9-ad3c-474d-a2d7-226cc8cd4217",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_unfair_ratio = np.array( [1.35309662, 1.26971581, 1.41809781, 1.42692608 ,1.37477049, 1.2738679,\n",
    " 1.26958438, 1.33401303 ,1.27442321, 1.304369   ,1.35607729 ,1.39696163,\n",
    " 1.35314205 ,1.23605831, 1.44328619 ,1.24607451 ,1.35187292 ,1.30104001,\n",
    " 1.44414113 ,1.34727284, 1.43619436 ,1.35466344 ,1.36463263 ,1.27830587,\n",
    " 1.36425966 ,1.42588933, 1.40089897 ,1.34060221 ,1.28935857 ,1.43619436,\n",
    " 1.41619045 ,1.32829303, 1.46474291 ,1.33580228 ,1.38565781 ,1.44334321,\n",
    " 1.29541047 ,1.24607451, 1.27536126 ,1.29210286 ,1.27176411 ,1.38334778,\n",
    " 1.38015255 ,1.25259418, 1.38987164 ,1.28742456 ,1.30691269 ,1.4235024,\n",
    " 1.43867836 ,1.35069279, 1.39039225 ,1.43184739 ,1.32681773 ,1.24823283,\n",
    " 1.34024167 ,1.43619436, 1.34833518 ,1.48754429 ,1.29778452 ,1.34849092,\n",
    " 1.43061852 ,1.33400266, 1.34859531 ,1.31631978, 1.31612132 ,1.38805416,\n",
    " 1.34959224 ,1.26384242, 1.35900387 ,1.3541143 , 1.36218742 ,1.41000927,\n",
    " 1.36569936 ,1.46524485, 1.34020585 ,1.35475246, 1.28056203 ,1.37638953,\n",
    " 1.36970929 ,1.32460418, 1.32469512 ,1.29281639, 1.34944957 ,1.3541143,\n",
    " 1.32962356 ,1.3597973  ,1.30558187 ,1.31725949, 1.36569936 ,1.32561613,\n",
    " 1.27779635 ,1.28969697 ,1.36184891 ,1.36653233, 1.36118463 ,1.38761415,\n",
    " 1.39696163 ,1.33910212 ,1.40113636 ,1.31308926])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "68761ecb-7342-4acb-886b-74252a716086",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.894801714589673e-18)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_race_fair_ratio,gpa_race_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "id": "739d4904-8957-4a4f-add2-9b3b1e11984f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=621.0, pvalue=1.0350334982420032e-26)"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_race_fair_ratio,gpa_race_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "dcd41d6b-7023-49cb-a88a-ba931467d7ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_fair_variation=np.array([0.23291168, 0.16241045 ,0.20836207, 0.23840662, 0.21675262, 0.18906181,\n",
    " 0.19947628, 0.16255765 ,0.15869274, 0.20053897 ,0.1935841  ,0.20749442,\n",
    " 0.21027154 ,0.19306782 ,0.19887137 ,0.19627253 ,0.2173913  ,0.17605858,\n",
    " 0.19122663 ,0.18204715 ,0.25158925 ,0.18175574 ,0.21144196, 0.18820341,\n",
    " 0.20326135 ,0.22177473 ,0.2296666  ,0.20436518 ,0.20023064, 0.25158925,\n",
    " 0.23419262 ,0.20803892 ,0.25126669 ,0.19663896 ,0.17962131, 0.1639876,\n",
    " 0.18512257 ,0.19627253 ,0.1647021  ,0.19854211 ,0.18816202, 0.20614939,\n",
    " 0.19542558 ,0.17681993 ,0.20410842 ,0.1856307  ,0.17748085, 0.19908583,\n",
    " 0.21626677 ,0.18268908 ,0.17803016 ,0.22182865 ,0.19782764, 0.15229511,\n",
    " 0.17002617 ,0.25158925 ,0.2159602  ,0.22463768 ,0.21889676, 0.20091188,\n",
    " 0.18440748 ,0.20682561, 0.15598181 ,0.18726    ,0.19547014, 0.18971628,\n",
    " 0.17732617 ,0.15199653,0.20060174 ,0.17133479 ,0.20305672 ,0.20489393,\n",
    " 0.21716465 ,0.27353766 ,0.19577001 ,0.21271161 ,0.17092885, 0.20464503,\n",
    " 0.19568275 ,0.18564416 ,0.20880264 ,0.1856625  ,0.19817132, 0.17133479,\n",
    " 0.20202559 ,0.19222224, 0.19239886 ,0.20075668 ,0.21716465, 0.19626917,\n",
    " 0.18577454 ,0.22138027, 0.18124229 ,0.18448266 ,0.20728252, 0.20342562,\n",
    " 0.20749442 ,0.17687412, 0.22490706 ,0.21515536])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "4f4e93bc-f228-4fd4-98d6-f5bcd657bf95",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_unfair_variation = np.array( [0.29809308, 0.26053603, 0.30765222, 0.29103846, 0.31284893, 0.27600343,\n",
    " 0.24217687, 0.27314429 ,0.26384675, 0.28871778 ,0.28927137, 0.31420961,\n",
    " 0.27416548 ,0.23705876 ,0.31720507, 0.22327748 ,0.30044058, 0.27565232,\n",
    " 0.30883083 ,0.28561825 ,0.32008628, 0.29699462, 0.29311252, 0.23301844,\n",
    " 0.2920663  ,0.33841976 ,0.30160317 ,0.30300752, 0.26565257, 0.32008628,\n",
    " 0.31423326 ,0.27071988 ,0.35752247, 0.27302603, 0.29177883, 0.32574714,\n",
    " 0.23148148 ,0.22327748 ,0.26207588, 0.28250779, 0.23224715, 0.27007342,\n",
    " 0.2855356  ,0.23849479, 0.287817  , 0.27225094, 0.25538747 ,0.32077922,\n",
    " 0.30167778 ,0.31756121, 0.27428461, 0.3448576 , 0.26430157 ,0.25316658,\n",
    " 0.28940232 ,0.32008628, 0.27016492, 0.36033487, 0.24429007 ,0.29220938,\n",
    " 0.32800769 ,0.2601901  ,0.30722421, 0.29072055, 0.28333333 ,0.32458459,\n",
    " 0.28711755 ,0.24219154 ,0.29892857, 0.28712312, 0.274458   ,0.3184611,\n",
    " 0.28364243 ,0.35017832 ,0.27668864, 0.28825103, 0.23790238 ,0.31545667,\n",
    " 0.30588068 ,0.2801107 , 0.25415961, 0.23104017, 0.30678308 ,0.28712312,\n",
    " 0.23688289 ,0.28386837, 0.24748127, 0.23812477, 0.28364243 ,0.26586538,\n",
    " 0.24414927 ,0.25991106, 0.29787256, 0.31476097, 0.28127442 ,0.29815447,\n",
    " 0.31420961 ,0.28526335, 0.29012346, 0.2798247 ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "786a6f94-fccc-4254-bd3b-66edef5c99e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.894801714589673e-18)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_race_unfair_variation, gpa_race_fair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "f1992933-0e5f-487f-a332-edb61a10a609",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=9876.0, pvalue=1.0149322645417814e-32)"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_race_unfair_variation, gpa_race_fair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "1cac326c-b36f-414e-bddd-7a718b39f149",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_fair_accuracy =  np.array([0.82612101, 0.83728216, 0.83121206, 0.83121206, 0.81965929, 0.82651263,\n",
    " 0.82455453, 0.8361073  ,0.82827492, 0.82847073 ,0.82886235 ,0.82807911,\n",
    " 0.8361073 , 0.82553358 ,0.81946348 ,0.83101625 ,0.82710006 ,0.82847073,\n",
    " 0.82964558, 0.83454083 ,0.82083415 ,0.83414921 ,0.82866654 ,0.81770119,\n",
    " 0.8300372 , 0.8259252  ,0.8319953  ,0.83140787 ,0.83277854 ,0.82083415,\n",
    " 0.82847073, 0.81339338 ,0.83708635 ,0.83277854 ,0.82690425 ,0.8339534,\n",
    " 0.82984139, 0.83101625 ,0.8339534  ,0.83082044 ,0.82827492 ,0.82455453,\n",
    " 0.8300372 , 0.82279225 ,0.82944977 ,0.82357548 ,0.82612101 ,0.82200901,\n",
    " 0.813785  , 0.83336597 ,0.82690425 ,0.82886235 ,0.81691796 ,0.83160368,\n",
    " 0.82572939, 0.82083415, 0.82847073 ,0.8239671  ,0.81926767 ,0.82083415,\n",
    " 0.8300372  ,0.82318387, 0.83042882 ,0.82651263 ,0.82670844 ,0.82083415,\n",
    " 0.81672215 ,0.82807911 ,0.82102996 ,0.83434502 ,0.82475034 ,0.82827492,\n",
    " 0.82122577 ,0.82670844 ,0.8339534  ,0.82142158 ,0.84021931 ,0.82240063,\n",
    " 0.81946348 ,0.82357548 ,0.81946348 ,0.81907186 ,0.83356178 ,0.83434502,\n",
    " 0.81868024, 0.83219111 ,0.82729587 ,0.82044253 ,0.82122577 ,0.83238692,\n",
    " 0.83826121, 0.82631682, 0.8259252  ,0.83375759 ,0.82807911, 0.82122577,\n",
    " 0.82807911, 0.82357548, 0.82083415 ,0.82690425])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "22f3a5df-c51d-4e5f-a2bf-b704b925a077",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_unfair_accuracy = np.array( [0.84178578, 0.84550617, 0.83884864, 0.8441355,  0.83062463, 0.84158997,\n",
    " 0.84198159, 0.84433131 ,0.8400235,  0.84198159 ,0.83571568, 0.84139416,\n",
    " 0.84628941 ,0.83845702 ,0.83591149, 0.85157627 ,0.84061093, 0.84276483,\n",
    " 0.84237321 ,0.84158997, 0.82729587 ,0.84041512 ,0.8400235 , 0.82905816,\n",
    " 0.84276483 ,0.83551987, 0.84061093 ,0.84119836 ,0.84491874, 0.82729587,\n",
    " 0.84276483 ,0.82964558, 0.84687684 ,0.84883493 ,0.84021931, 0.84393969,\n",
    " 0.84276483 ,0.85157627 ,0.84531036 ,0.84119836 ,0.84237321, 0.83669473,\n",
    " 0.84276483 ,0.84785588 ,0.84628941 ,0.83963188 ,0.83023301, 0.84021931,\n",
    " 0.83591149 ,0.83591149 ,0.8421774  ,0.84041512 ,0.83317016, 0.84511455,\n",
    " 0.84021931 ,0.82729587 ,0.84511455 ,0.83924026 ,0.83551987, 0.83865283,\n",
    " 0.84021931 ,0.83689054 ,0.84452712 ,0.84315645 ,0.83786959, 0.83317016,\n",
    " 0.82827492 ,0.84315645 ,0.83747797 ,0.8521637  ,0.84315645, 0.84491874,\n",
    " 0.83630311 ,0.84158997 ,0.84452712 ,0.84041512 ,0.85314275, 0.84178578,\n",
    " 0.83767378 ,0.83571568 ,0.84198159 ,0.83747797, 0.84080674, 0.8521637,\n",
    " 0.83689054 ,0.84335226 ,0.84687684 ,0.84100255, 0.83630311, 0.8543176,\n",
    " 0.84589779 ,0.84178578 ,0.8319953  ,0.83982769, 0.85040141, 0.83708635,\n",
    " 0.84139416 ,0.84531036 ,0.8361073,  0.83297435])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "32dc49c2-42f0-4ef2-b2ff-79b458e7668f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.886241591437734e-18)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_race_fair_accuracy,gpa_race_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "id": "bfed0678-9ebf-4e69-8087-1610aef6a525",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=474.5, pvalue=2.02405335661332e-28)"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_race_fair_accuracy,gpa_race_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4084f62b-1c4f-49b0-b4d2-8c6ad72dd125",
   "metadata": {},
   "source": [
    "Gpa_Gender Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "3b4d50f3-594b-4f05-b754-75d43f2e91ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_gender_fair_diff = np.array( [0.03634252 ,0.02127014 ,0.03410368, 0.01860523, 0.051873 ,  0.02659822,\n",
    " 0.0672855  ,0.02933808, 0.02511171, 0.02625347 ,0.04364382 ,0.02635533,\n",
    " 0.01239205 ,0.03643697, 0.00977571, 0.01077515 ,0.03908552 ,0.0299325,\n",
    " 0.01860523 ,0.03585298, 0.06535389, 0.01720862 ,0.03380562 ,0.02689457,\n",
    " 0.03197443 ,0.02809444, 0.04724848, 0.02511171, 0.02883818 ,0.02689457,\n",
    " 0.03049972 ,0.02522435, 0.01860523, 0.03564116 ,0.03217576 ,0.023445,\n",
    " 0.02459063 ,0.02183528, 0.01615819, 0.01108047 ,0.04243378 ,0.04185916,\n",
    " 0.03696754 ,0.03933844, 0.05270607, 0.03896755 ,0.04670701, 0.02666907,\n",
    " 0.01775667 ,0.02811181, 0.03925546, 0.02106095 ,0.03675455, 0.0511259,\n",
    " 0.0430938  ,0.02458675, 0.04337064, 0.05351231 ,0.04672077, 0.03850854,\n",
    " 0.02130841 ,0.02114241, 0.03296072, 0.02175394 ,0.02768954, 0.03984948,\n",
    " 0.05456875 ,0.05492981, 0.03788059, 0.06533857 ,0.01135292, 0.05289707,\n",
    " 0.02100457 ,0.01240985, 0.02809444, 0.02202439 ,0.03114679, 0.04238096,\n",
    " 0.03224565 ,0.02442262, 0.02156086 ,0.01923229 ,0.02507399, 0.05337016,\n",
    " 0.01741017 ,0.02202439, 0.04539543, 0.02705621 ,0.02954139 ,0.02003404,\n",
    " 0.0298455  ,0.048787  , 0.01129002, 0.02437038 ,0.03514858 ,0.02965336,\n",
    " 0.0314733  ,0.03206975, 0.02061353, 0.06096782])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "965eaf20-8a18-4ad8-a77e-bfa55168d9b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_gender_unfair_diff = np.array([0.03608153, 0.02828322, 0.03147556, 0.02108418, 0.06614015 ,0.04370065,\n",
    " 0.06333615, 0.04604872, 0.03646442, 0.03114107 ,0.04279152 ,0.02357585,\n",
    " 0.01755574 ,0.07051897, 0.01450867, 0.01647759 ,0.04678576 ,0.03170506,\n",
    " 0.02108418, 0.03622261, 0.06689833 ,0.02999629 ,0.04785899 ,0.04351923,\n",
    " 0.04316986 ,0.02677068, 0.04133154 ,0.03646442 ,0.02717428 ,0.04351923,\n",
    " 0.03197247 ,0.03018402, 0.02108418 ,0.03071068 ,0.03961838, 0.01890351,\n",
    " 0.02557877 ,0.01669784, 0.02085865 ,0.01107307 ,0.04498155, 0.03812167,\n",
    " 0.04199118 ,0.03806856, 0.06197239 ,0.03142109 ,0.04444696, 0.02813552,\n",
    " 0.01645797 ,0.03003822, 0.03827698 ,0.05119219 ,0.05501283, 0.05738649,\n",
    " 0.04856637 ,0.02839386, 0.04243542 ,0.06699043 ,0.05182986, 0.04262383,\n",
    " 0.02049716 ,0.02226573, 0.02835079 ,0.04160516 ,0.02609662 ,0.04508864,\n",
    " 0.06043719 ,0.05359274, 0.04949738 ,0.05531037 ,0.00317967 ,0.04421992,\n",
    " 0.00667367 ,0.01629274, 0.02677068 ,0.02959686 ,0.03501969 ,0.06559272,\n",
    " 0.04036367 ,0.03465965, 0.0207664  ,0.02371331 ,0.01956404 ,0.05070612,\n",
    " 0.02145734 ,0.02959686, 0.03929533 ,0.0256643  ,0.03160238 ,0.03104606,\n",
    " 0.0222793  ,0.05139457, 0.01411349 ,0.03560176 ,0.03530084 ,0.02866814,\n",
    " 0.04943371 ,0.04528517, 0.04149709 ,0.05922967])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "dd4a3ea9-3eb8-4d06-8ea8-50b06273925b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1254.0, pvalue=1.2416877475160477e-05)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_gender_fair_diff, gpa_gender_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "id": "65a7ee24-7985-4c8f-8f42-68085ece89b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=4114.0, pvalue=0.030492462134964596)"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_gender_fair_diff, gpa_gender_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "db66ccc8-b8fd-4bfd-bd35-7b87c4376228",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_gender_fair_ratio = np.array( [1.04469229, 1.02665253 ,1.04172492, 1.02221178 ,1.06355515 ,1.03173771,\n",
    " 1.08256767, 1.03568527 ,1.03048445, 1.0311464  ,1.05281794 ,1.03333665,\n",
    " 1.01447859 ,1.04289691 ,1.01144661 ,1.01303498 ,1.04748766 ,1.03763789,\n",
    " 1.02221178 ,1.04359004 ,1.07920891 ,1.02061252 ,1.03992015 ,1.03203296,\n",
    " 1.03802916 ,1.03379977 ,1.05748063 ,1.03048445 ,1.03522712 ,1.03203296,\n",
    " 1.03760645 ,1.0303207  ,1.02221178 ,1.04384898 ,1.03872345 ,1.02742623,\n",
    " 1.02980325 ,1.02710764 ,1.01950735 ,1.01283567 ,1.05127145 ,1.05061738,\n",
    " 1.04463361 ,1.04761694 ,1.06360355 ,1.0469527  ,1.05840203 ,1.03258613,\n",
    " 1.02106723 ,1.03291269 ,1.04910536 ,1.02472372 ,1.04365995 ,1.06255023,\n",
    " 1.0517662  ,1.02968679 ,1.05187329 ,1.06597892 ,1.05659438 ,1.04887256,\n",
    " 1.02634685 ,1.02496332 ,1.03938609 ,1.02684529 ,1.03405814 ,1.04707365,\n",
    " 1.06629218 ,1.0660016  ,1.04624756 ,1.08224002 ,1.01319883 ,1.06585861,\n",
    " 1.02483801 ,1.01494479 ,1.03379977 ,1.02646142 ,1.03857448 ,1.05000284,\n",
    " 1.0388917  ,1.02843596 ,1.02597104 ,1.02291899 ,1.0306192 , 1.06550484,\n",
    " 1.02200829 ,1.02646142 ,1.05501191 ,1.03262778 ,1.03539058, 1.02337305,\n",
    " 1.03624423 ,1.05968043 ,1.01429614 ,1.02847626 ,1.04431778, 1.03657128,\n",
    " 1.03757328 ,1.03759464 ,1.0242209  ,1.07517765])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "4b0cd3f4-972f-495e-9a40-9583eb049512",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_gender_unfair_ratio = np.array([1.04422514, 1.03363256, 1.03838606, 1.02501731, 1.08257076 ,1.05397256,\n",
    " 1.07759453 ,1.05593649, 1.04433484 ,1.03724346, 1.05210548 ,1.02825205,\n",
    " 1.02072693 ,1.08737256 ,1.01715708 ,1.01971307 ,1.0563127  ,1.03778801,\n",
    " 1.02501731 ,1.04446784 ,1.08206557 ,1.03521832 ,1.05796142 ,1.05335203,\n",
    " 1.05257506 ,1.03205922 ,1.05049674 ,1.04433484 ,1.03312727 ,1.05335203,\n",
    " 1.03937458 ,1.03658105 ,1.02501731 ,1.03747209 ,1.04848459 ,1.0221331,\n",
    " 1.03103803 ,1.0198479  ,1.02503038 ,1.01307367 ,1.05434984 ,1.04567627,\n",
    " 1.05208274 ,1.04611436 ,1.07614826 ,1.03747586 ,1.05505911 ,1.03405414,\n",
    " 1.01949636 ,1.03571017 ,1.04782283 ,1.06243976 ,1.06810009 ,1.07009791,\n",
    " 1.05970261 ,1.0342836  ,1.05092251 ,1.08370074 ,1.06297607 ,1.0510579,\n",
    " 1.02476223 ,1.02655629 ,1.03397863 ,1.04955672 ,1.03189947 ,1.05399944,\n",
    " 1.07308251 ,1.06409459 ,1.06100334 ,1.06853676 ,1.00376971 ,1.05389527,\n",
    " 1.00793902 ,1.01963309 ,1.03205922 ,1.03499394 ,1.04242666 ,1.07975326,\n",
    " 1.04905738 ,1.04143468 ,1.0249625 , 1.02821645 ,1.02366318 ,1.06251597,\n",
    " 1.02566032 ,1.03499394 ,1.04747168, 1.03072167 ,1.03816497 ,1.03721589,\n",
    " 1.02680953 ,1.06307141 ,1.01674879, 1.04252432 ,1.04417858 ,1.0353133,\n",
    " 1.06051188, 1.05415924 ,1.05020737, 1.07201371])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "815e22c3-b4be-4ad6-8af4-eb25c99f2554",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1309.0, pvalue=2.9019447479229257e-05)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_gender_fair_ratio, gpa_gender_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "f22d18a6-65d2-4544-92f4-971bcf161905",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=4129.0, pvalue=0.03342151328757016)"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_gender_fair_ratio, gpa_gender_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "074435a5-e01a-4e20-82c4-1635a7802b15",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_gender_fair_variation = np.array( \n",
    "[0.07987636, 0.07598493 ,0.03410368, 0.04004253 ,0.05631899, 0.06786362,\n",
    " 0.0672855  ,0.08370822 ,0.03873047 ,0.06115888 ,0.07433758 ,0.07480345,\n",
    " 0.06209645 ,0.07292286 ,0.04674446 ,0.04401161 ,0.09559938, 0.0865342,\n",
    " 0.04004253 ,0.03585298 ,0.09522682 ,0.07356934 ,0.05693143, 0.05653476,\n",
    " 0.06185245 ,0.04234068 ,0.06467451 ,0.03873047 ,0.04153917, 0.05653476,\n",
    " 0.05481843 ,0.0381244  ,0.04004253 ,0.03564116 ,0.06367796, 0.06241393,\n",
    " 0.02459063 ,0.06865662 ,0.03394077 ,0.05276766 ,0.0714665  ,0.04185916,\n",
    " 0.07210836 ,0.07029727 ,0.07076558 ,0.06276698 ,0.06785843 ,0.04958236,\n",
    " 0.03583162 ,0.06776058 ,0.06162251 ,0.06086461 ,0.06845212 ,0.10576672,\n",
    " 0.06777768 ,0.03352492 ,0.0659419  ,0.05351231 ,0.06956199, 0.09692762,\n",
    " 0.04514646 ,0.05286379 ,0.06750313 ,0.07990592, 0.0759827 , 0.0837658,\n",
    " 0.07926688 ,0.07914815 ,0.07778843 ,0.10068243, 0.06404576, 0.0633533,\n",
    " 0.05105691 ,0.05089015 ,0.04234068 ,0.0815652 , 0.07729402, 0.07819917,\n",
    " 0.04076187 ,0.06554667 ,0.0498359  ,0.04896749, 0.05813672 ,0.06351222,\n",
    " 0.08392688 ,0.0815652  ,0.06732626 ,0.05397165, 0.04608411 ,0.06085037,\n",
    " 0.04329331 ,0.05478226 ,0.08286166 ,0.06639832, 0.09363688 ,0.05077706,\n",
    " 0.04790635, 0.07478616 ,0.05456822 ,0.06096782])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "acdcf3a0-6099-418d-bfb8-4077b6dadbae",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_gender_unfair_variation = np.array(\n",
    "[0.06751922, 0.07361033, 0.03147556 ,0.03892764 ,0.06707865, 0.04370065,\n",
    " 0.06333615, 0.0541794 , 0.04444575 ,0.06328972 ,0.05828461 ,0.05244739,\n",
    " 0.04886136, 0.07051897, 0.04185206 ,0.03532355 ,0.07711995, 0.0665956,\n",
    " 0.03892764, 0.04386153, 0.07848704 ,0.07058723 ,0.05481322, 0.04528854,\n",
    " 0.04316986, 0.04326861, 0.0436816  ,0.04444575 ,0.03363308, 0.04528854,\n",
    " 0.05668861, 0.04619318, 0.03892764 ,0.03754813 ,0.06330512, 0.07521384,\n",
    " 0.02886778, 0.07439661, 0.02859561 ,0.03157757 ,0.06238044, 0.04792412,\n",
    " 0.06667426, 0.07136548, 0.06197239 ,0.06372392 ,0.05505337, 0.03849758,\n",
    " 0.03873579 ,0.04596243, 0.05902181 ,0.05539486 ,0.06793079, 0.09373385,\n",
    " 0.04856637 ,0.02909316, 0.04823974 ,0.06699043 ,0.07389084, 0.08560853,\n",
    " 0.03894275 ,0.0406528 , 0.05380027 ,0.06370713 ,0.06447938, 0.07054833,\n",
    " 0.08220187 ,0.08269168 ,0.05987595, 0.08450479 ,0.02963094, 0.05155053,\n",
    " 0.0229004  ,0.04393032 ,0.04326861, 0.05799891 ,0.06818127 ,0.07429326,\n",
    " 0.04423102 ,0.05097835 ,0.05247757, 0.03616379 ,0.04574191 ,0.06957749,\n",
    " 0.05329576 ,0.05799891 ,0.04850633, 0.04166428 ,0.03940119 ,0.0369299,\n",
    " 0.04426513 ,0.05139457 ,0.05023226, 0.05388102 ,0.07387943, 0.04822519,\n",
    " 0.04943371 ,0.07591161 ,0.04893529, 0.05922967])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "8ad4a8a4-a36b-4812-857b-1b0814da9cde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=793.0, pvalue=2.5973200754317902e-09)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_gender_unfair_variation, gpa_gender_fair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "id": "62ec9e70-77aa-4e9a-a2a0-309a44fd0973",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=3708.0, pvalue=0.001601377796852779)"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_gender_unfair_variation, gpa_gender_fair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "0c65c3e9-026b-45c0-a172-25a137db6960",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_gender_fair_accuracy=np.array(\n",
    "[0.84276483, 0.83571568 ,0.83512826, 0.84531036 ,0.84080674, 0.83297435,\n",
    " 0.84374388, 0.83826121 ,0.82964558, 0.83963188 ,0.83689054, 0.83297435,\n",
    " 0.83963188, 0.84354807 ,0.83649892 ,0.8339534  ,0.83689054, 0.84452712,\n",
    " 0.84531036, 0.84158997 ,0.8339534  ,0.84433131 ,0.84550617, 0.83336597,\n",
    " 0.84276483, 0.83963188 ,0.8361073  ,0.82964558 ,0.84061093, 0.83336597,\n",
    " 0.84237321, 0.84707265 ,0.84531036 ,0.83336597 ,0.83454083, 0.8421774,\n",
    " 0.84315645, 0.84041512 ,0.84550617 ,0.84021931 ,0.83023301, 0.83826121,\n",
    " 0.8319953 , 0.83571568 ,0.84472293 ,0.84237321 ,0.83963188, 0.83865283,\n",
    " 0.83943607, 0.84021931 ,0.83728216 ,0.83884864 ,0.84061093, 0.83375759,\n",
    " 0.83904445, 0.8400235  ,0.84237321 ,0.83219111 ,0.83140787, 0.84041512,\n",
    " 0.83747797, 0.83689054 ,0.84354807 ,0.83982769 ,0.85294694, 0.83747797,\n",
    " 0.83845702, 0.84491874 ,0.8319953  ,0.84374388 ,0.83140787, 0.84256902,\n",
    " 0.83219111, 0.83434502 ,0.83963188 ,0.84119836, 0.83532407, 0.8441355,\n",
    " 0.84119836, 0.84178578 ,0.84178578 ,0.84452712 ,0.84726846, 0.83512826,\n",
    " 0.83258273, 0.84119836 ,0.83414921 ,0.85177208 ,0.84198159, 0.84178578,\n",
    " 0.84080674, 0.8380654  ,0.83630311 ,0.84256902 ,0.84374388, 0.83845702,\n",
    " 0.83904445, 0.83963188 ,0.83963188 ,0.84452712])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "0848088e-da99-44dc-84fc-4908a223ce99",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_gender_unfair_accuracy= np.array(\n",
    "[0.84139416, 0.83924026 ,0.83493245, 0.8441355  ,0.84041512, 0.83219111,\n",
    " 0.84491874, 0.83786959, 0.83062463, 0.84061093 ,0.8380654  ,0.8339534,\n",
    " 0.84256902, 0.8460936 , 0.83845702, 0.83493245 ,0.84021931 ,0.84511455,\n",
    " 0.8441355 , 0.8421774 , 0.8361073 , 0.84531036 ,0.84354807 ,0.83454083,\n",
    " 0.84433131, 0.83865283, 0.83845702, 0.83062463 ,0.83982769 ,0.83454083,\n",
    " 0.84374388, 0.8460936 , 0.8441355 , 0.83356178 ,0.83571568 ,0.84296064,\n",
    " 0.84256902, 0.84315645, 0.8460936  ,0.84393969 ,0.83317016 ,0.83767378,\n",
    " 0.83375759 ,0.83826121, 0.84942236, 0.8421774  ,0.83884864 ,0.83943607,\n",
    " 0.83924026 ,0.84315645, 0.83669473, 0.84041512 ,0.83924026 ,0.8380654,\n",
    " 0.8380654  ,0.83982769, 0.84472293, 0.83101625 ,0.83062463 ,0.84178578,\n",
    " 0.83884864 ,0.84021931, 0.84374388, 0.8421774  ,0.85275113 ,0.84021931,\n",
    " 0.84100255 ,0.84374388, 0.83375759 ,0.84531036 ,0.83649892 ,0.84393969,\n",
    " 0.83532407 ,0.83375759, 0.83865283 ,0.84531036 ,0.83591149 ,0.84628941,\n",
    " 0.84158997 ,0.84237321, 0.83865283 ,0.84550617 ,0.84844331 ,0.83532407,\n",
    " 0.83336597 ,0.84531036, 0.8380654  ,0.85177208, 0.84198159 ,0.84707265,\n",
    " 0.84061093 ,0.83689054, 0.83884864 ,0.84315645, 0.84491874 ,0.84119836,\n",
    " 0.8380654  ,0.84237321, 0.83845702 ,0.84550617])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "c0f287b6-3074-4ec5-9c80-8b9133416175",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1034.0, pvalue=8.086144174122965e-07)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_gender_fair_accuracy,gpa_gender_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "id": "afd6e696-3ad4-4fbc-9471-c49bf65761a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=4411.5, pvalue=0.15073011702556863)"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_gender_fair_accuracy,gpa_gender_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f69584b-6765-404f-88eb-1ff495ddb1ad",
   "metadata": {},
   "source": [
    "Synthetic Independent Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "8e8a4ee5-1851-43da-9d8a-8d92d45c4af6",
   "metadata": {},
   "outputs": [],
   "source": [
    "synthetic_independent_fair_diff=np.array(\n",
    "[0.01527957, 0.01864019 ,0.11540791, 0.03186891 ,0.15777128, 0.08759995,\n",
    " 0.05185665, 0.02337904 ,0.02895167, 0.03672441 ,0.03348422, 0.0534158,\n",
    " 0.01722145, 0.03647823 ,0.01486982 ,0.08463462 ,0.09695821, 0.05467452,\n",
    " 0.17687189, 0.05029189 ,0.04833293 ,0.00856198 ,0.08671962, 0.02570069,\n",
    " 0.02838369, 0.01153804 ,0.05207709 ,0.13534691 ,0.02098502, 0.04724193,\n",
    " 0.05431692, 0.03226766 ,0.07542624 ,0.01265838 ,0.02444225, 0.01820881,\n",
    " 0.05093484, 0.03532964 ,0.03880897 ,0.0094565  ,0.05484347, 0.05997417,\n",
    " 0.00735674, 0.02568208 ,0.02019836 ,0.02054642 ,0.08121609, 0.07108621,\n",
    " 0.01420596, 0.05675338 ,0.04282978 ,0.05428621 ,0.02783488, 0.01429442,\n",
    " 0.04229015, 0.0309054  ,0.07106916 ,0.0145741  ,0.05799035, 0.01964695,\n",
    " 0.06413412, 0.03556191 ,0.01133707 ,0.01703249 ,0.06863899, 0.01781206,\n",
    " 0.11637026, 0.01946728 ,0.03337258 ,0.06933972 ,0.02905685, 0.07001188,\n",
    " 0.13492146, 0.08640393 ,0.03050806 ,0.11143157 ,0.03901653, 0.05913286,\n",
    " 0.04153139, 0.02259536 ,0.08748979 ,0.05212466 ,0.02208618 ,0.01088007,\n",
    " 0.03029578, 0.02911958 ,0.03496004 ,0.0085722  ,0.06344029 ,0.10429263,\n",
    " 0.05283    ,0.06620107 ,0.04288871 ,0.06502203, 0.01238222 ,0.06750491,\n",
    " 0.04342307 ,0.02414716 ,0.02523524 ,0.06792869])\n",
    "\n",
    "synthetic_independent_fair_ratio= np.array(\n",
    "[1.02327994 ,1.02572222 ,1.16662067, 1.04118594 ,1.27289822, 1.12135827,\n",
    " 1.06834424 ,1.02840307 ,1.03407853 ,1.04725314 ,1.05071302, 1.08029675,\n",
    " 1.02002876 ,1.04880791 ,1.01775064 ,1.12358779 ,1.13613647, 1.07628219,\n",
    " 1.35787309 ,1.06182859 ,1.06128283 ,1.01221613 ,1.10044537, 1.03720297,\n",
    " 1.03530738 ,1.01324714 ,1.06537803 ,1.17960156 ,1.02724371, 1.0575718,\n",
    " 1.07649813 ,1.03657691 ,1.10335816 ,1.01575348 ,1.02994994, 1.02284058,\n",
    " 1.07201015 ,1.04833853 ,1.04818323 ,1.01123232 ,1.08129418, 1.06882228,\n",
    " 1.00807465 ,1.03543303 ,1.02504124 ,1.02473595 ,1.11280012, 1.10044363,\n",
    " 1.01858598 ,1.07114588 ,1.04929466 ,1.06954046 ,1.04361579, 1.01738908,\n",
    " 1.0571541  ,1.03892076 ,1.09115204 ,1.0182547  ,1.08237729, 1.02385868,\n",
    " 1.07663918 ,1.04671593 ,1.01458884 ,1.02410977 ,1.09689418, 1.02113834,\n",
    " 1.15710734 ,1.02388462 ,1.03645072 ,1.09870321 ,1.03430689, 1.09549176,\n",
    " 1.18598487 ,1.10683592 ,1.0382878  ,1.16159492, 1.05379391, 1.09086792,\n",
    " 1.05974843 ,1.02806023 ,1.10949384 ,1.06647644, 1.02794146, 1.01154901,\n",
    " 1.03493374 ,1.03203001 ,1.0425139  ,1.01075707, 1.07643097, 1.14352878,\n",
    " 1.0656287  ,1.09071665 ,1.0626835  ,1.09169774, 1.01930249, 1.08360407,\n",
    " 1.0558836  ,1.03248237 ,1.03407666, 1.09314396])\n",
    "\n",
    "synthetic_independent_fair_variation=np.array(\n",
    "[0.278599 ,  0.18459268 ,0.26422964 ,0.13835847 ,0.3790816,  0.19507388,\n",
    " 0.14463383, 0.10045033 ,0.13147793 ,0.11569023 ,0.27822335, 0.28206554,\n",
    " 0.03709499 ,0.19023745 ,0.03354814 ,0.24330669 ,0.24834458 ,0.1830255,\n",
    " 0.4779114  ,0.16684855 ,0.09748859 ,0.19707373 ,0.26504241 ,0.25526426,\n",
    " 0.22665197 ,0.09997499 ,0.0808602  ,0.16717347 ,0.08049019 ,0.07967645,\n",
    " 0.30896075 ,0.23197513 ,0.18569029 ,0.1174978  ,0.0989638  ,0.08349054,\n",
    " 0.24250731 ,0.13885412 ,0.0710334  ,0.06931348 ,0.26669178 ,0.21489723,\n",
    " 0.18131517 ,0.2090781  ,0.0918782  ,0.0631813  ,0.1925239  ,0.23237423,\n",
    " 0.12056831 ,0.07080437, 0.18582101 ,0.35032346 ,0.32691578 ,0.1339839,\n",
    " 0.19924417 ,0.12103493, 0.15516882 ,0.10250859 ,0.20339395 ,0.08371154,\n",
    " 0.1529987  ,0.12125117, 0.0994195  ,0.25598973 ,0.22444799 ,0.18511973,\n",
    " 0.19623598 ,0.06320191, 0.26406011 ,0.23150538 ,0.18840825 ,0.19781529,\n",
    " 0.20085736 ,0.16912344, 0.10420991 ,0.24670804 ,0.18270547 ,0.30906747,\n",
    " 0.23346721 ,0.15437804, 0.15631589 ,0.07554189 ,0.13317628 ,0.25728499,\n",
    " 0.1600581  ,0.15478346, 0.13067957 ,0.05757667 ,0.07179078 ,0.16290835,\n",
    " 0.08856205 ,0.18306151, 0.25518341 ,0.23245198, 0.28896919 ,0.07657282,\n",
    " 0.14102989 ,0.17849022, 0.14993303 ,0.19450382])\n",
    "\n",
    "synthetic_independent_fair_accuracy=np.array(\n",
    "[0.83576, 0.83824 ,0.81152 ,0.82656 ,0.82304, 0.79768 ,0.84344, 0.8248  ,0.84296,\n",
    " 0.8472  ,0.8328  ,0.81568 ,0.85544 ,0.83824 ,0.8396  ,0.83856, 0.83928 ,0.82168,\n",
    " 0.82136 ,0.8452  ,0.84784 ,0.83112 ,0.79648 ,0.834   ,0.83352 ,0.84616 ,0.82952,\n",
    " 0.8512  ,0.82152 ,0.82984 ,0.79408 ,0.84752 ,0.84424 ,0.8504  ,0.85152 ,0.84064,\n",
    " 0.854   ,0.81288 ,0.83672 ,0.85216 ,0.84048 ,0.8424  ,0.84032 ,0.8356 , 0.85016,\n",
    " 0.83912 ,0.85088 ,0.82832 ,0.83944 ,0.83912 ,0.82824 ,0.79512 ,0.83056, 0.82952,\n",
    " 0.82936 ,0.84496 ,0.83008 ,0.85576 ,0.84112 ,0.82608 ,0.83192 ,0.84144, 0.828,\n",
    " 0.82272 ,0.80832 ,0.82896 ,0.85264 ,0.84272 ,0.82896 ,0.83312 ,0.82608, 0.84608,\n",
    " 0.84032 ,0.8112  ,0.8448  ,0.84376 ,0.84808 ,0.83176 ,0.8524  ,0.83536, 0.8172,\n",
    " 0.83408 ,0.8516  ,0.83008 ,0.84008 ,0.86416 ,0.83248 ,0.83264 ,0.84712, 0.83448,\n",
    " 0.85536 ,0.85144 ,0.81912 ,0.82952 ,0.81968 ,0.83144 ,0.83552 ,0.85848, 0.84184,\n",
    " 0.84536])\n",
    "\n",
    "synthetic_independent_unfair_diff=np.array(\n",
    "[0.0104625 , 0.02321431 ,0.15094388, 0.03222069 ,0.13601782, 0.08764839,\n",
    " 0.0472415 , 0.01540235, 0.01467121, 0.03821564 ,0.03242311, 0.06048871,\n",
    " 0.01222849 ,0.03776377 ,0.0139861  ,0.06472659 ,0.08465526 ,0.05205834,\n",
    " 0.16977186, 0.05264479, 0.04996426, 0.00979903 ,0.09351307, 0.02370795,\n",
    " 0.03132396, 0.01449094 ,0.05057107 ,0.13904095 ,0.0216174 , 0.0611464,\n",
    " 0.03482116, 0.03226766, 0.07659171 ,0.00319139 ,0.02142554, 0.01047295,\n",
    " 0.03105406, 0.03487063, 0.03086458 ,0.00987764 ,0.06126576, 0.06158854,\n",
    " 0.00828306, 0.01609436, 0.02241171 ,0.02350126 ,0.0755007 , 0.05589985,\n",
    " 0.01545596, 0.06092848, 0.05469007 ,0.06124588 ,0.02563106, 0.01800028,\n",
    " 0.04319155, 0.02744005, 0.04954503 ,0.0174738 , 0.03615463, 0.01662913,\n",
    " 0.06229764, 0.03266852, 0.01332032 ,0.02282201, 0.06150216, 0.01853781,\n",
    " 0.113051  , 0.01806374, 0.02335668 ,0.07115312, 0.02648314, 0.08176497,\n",
    " 0.10286901, 0.07668229, 0.02877133 ,0.08649265 ,0.05668241, 0.0723668,\n",
    " 0.05207589, 0.02008004, 0.08978708 ,0.03064453 ,0.03030237, 0.01318303,\n",
    " 0.02466463, 0.02809712, 0.0269139  ,0.00720225, 0.06624708, 0.09348537,\n",
    " 0.06023366, 0.06671434, 0.04244118 ,0.06415094, 0.01619686, 0.05556047,\n",
    " 0.03923811, 0.02165409, 0.01436035 ,0.04539909])\n",
    "\n",
    "synthetic_independent_unfair_ratio=np.array(\n",
    "[1.0158821 , 1.03124014, 1.25161323, 1.04281907, 1.20455468, 1.11384093,\n",
    " 1.06083769, 1.02064404, 1.01695525, 1.04944989, 1.04868138, 1.08844568,\n",
    " 1.01429706, 1.0516457 , 1.01677354, 1.08864453, 1.11160289, 1.07405226,\n",
    " 1.29525541, 1.06566745, 1.06418832, 1.01102587 ,1.12731836, 1.03484052,\n",
    " 1.03917884, 1.01874614, 1.06485142, 1.19838538, 1.02829517, 1.07306803,\n",
    " 1.04647934, 1.03657691, 1.09555596, 1.00401701, 1.02670891, 1.01328106,\n",
    " 1.04081997, 1.0478043 , 1.03564185, 1.01184857, 1.08652445, 1.06963207,\n",
    " 1.00912008, 1.02152868, 1.02806428, 1.0277694 , 1.09979138, 1.07369272,\n",
    " 1.01853336, 1.07844917, 1.06903447 ,1.08010276, 1.02938433, 1.02355177,\n",
    " 1.05875761, 1.03440652, 1.06010475, 1.02173064, 1.0483658 , 1.02036322,\n",
    " 1.07377166, 1.04264427, 1.01713068, 1.03275719, 1.08845154, 1.02225618,\n",
    " 1.15961037, 1.02217616, 1.02541008, 1.09753573, 1.03055076, 1.1189047,\n",
    " 1.12972062, 1.09173943, 1.034503  , 1.10895142, 1.08130772, 1.1072326,\n",
    " 1.07273701, 1.02507266, 1.11628712, 1.04033801, 1.03968972, 1.01397937,\n",
    " 1.02836298, 1.0359511 , 1.03196808, 1.00909339, 1.07871354, 1.12062445,\n",
    " 1.07232891, 1.09558431, 1.06211873, 1.08734558, 1.02616794, 1.06683822,\n",
    " 1.04948349, 1.02690095, 1.01930315 ,1.05249499])\n",
    "\n",
    "synthetic_independent_unfair_variation=np.array(\n",
    "[0.27457244, 0.15465106 ,0.37102856, 0.1653236  ,0.2763475 , 0.22512694,\n",
    " 0.12548019, 0.12993318 ,0.16251528, 0.11416235 ,0.27246519, 0.25968881,\n",
    " 0.03419083, 0.20883031 ,0.02596308, 0.17996909 ,0.18662594, 0.19911313,\n",
    " 0.38801633, 0.17461602 ,0.10630821, 0.2034905  ,0.27964594, 0.2660943,\n",
    " 0.23245528, 0.11046754 ,0.09839359, 0.23397067 ,0.09341831, 0.11260894,\n",
    " 0.3236098 , 0.18809209, 0.11085162, 0.12902628 ,0.10952137, 0.10259651,\n",
    " 0.17173295, 0.1422252 , 0.12145321, 0.084052   ,0.22239884, 0.22956137,\n",
    " 0.17537542, 0.17609774, 0.10519516, 0.06021101 ,0.1470466 , 0.17284769,\n",
    " 0.09372357, 0.0966111 , 0.18057653, 0.33477034 ,0.29281064 ,0.12641956,\n",
    " 0.20409619, 0.12181487, 0.12794759, 0.09910186 ,0.13404163 ,0.07890385,\n",
    " 0.17505597, 0.11687874, 0.10139439, 0.26718795 ,0.24492967 ,0.16992363,\n",
    " 0.24106091, 0.06038446, 0.28558943, 0.19431519 ,0.18487171 ,0.25110552,\n",
    " 0.12414869, 0.17732944, 0.0641224 , 0.16703671 ,0.21422163 ,0.28006583,\n",
    " 0.20365743, 0.14039716, 0.11920849, 0.10295459 ,0.16532561 ,0.26835105,\n",
    " 0.15615105, 0.1610583 , 0.12800098, 0.05782453 ,0.11091275 ,0.10573117,\n",
    " 0.06023366, 0.22098115, 0.25570804, 0.19559336 ,0.3239131  ,0.11102421,\n",
    " 0.12705895, 0.15664366, 0.15111455, 0.13897917])\n",
    "\n",
    "synthetic_independent_unfair_accuracy=np.array( \n",
    "[0.83744, 0.84136, 0.80712, 0.8248  ,0.8348,  0.80896 ,0.84184, 0.82624 ,0.8432,\n",
    " 0.84688, 0.83392, 0.82344, 0.85776 ,0.838 ,  0.84072 ,0.84544, 0.84912 ,0.824,\n",
    " 0.83816, 0.8428 , 0.84656, 0.826  , 0.78792, 0.83232, 0.83208, 0.84472, 0.82976,\n",
    " 0.85096, 0.82472, 0.83256, 0.80064, 0.84912, 0.83984, 0.84888, 0.84992, 0.83968,\n",
    " 0.8624 , 0.81344, 0.83816, 0.85024, 0.84456 ,0.8404 , 0.83888 ,0.83864, 0.84952,\n",
    " 0.83752 ,0.85072, 0.83656, 0.8364 , 0.84152 ,0.83264, 0.79592 ,0.83344, 0.82848,\n",
    " 0.82904, 0.84296, 0.83336, 0.85712 ,0.83952 ,0.8248 , 0.82752 ,0.84112, 0.82544,\n",
    " 0.8236 , 0.81144, 0.82704, 0.84936, 0.84336 ,0.82984, 0.83392 ,0.82296, 0.8428,\n",
    " 0.84088, 0.81136, 0.8484 , 0.84816, 0.846   ,0.83872, 0.8552  ,0.83576, 0.82464,\n",
    " 0.82688, 0.85016, 0.82944, 0.842 ,  0.86432 ,0.83368, 0.83088 ,0.84824, 0.83488,\n",
    " 0.85784, 0.8472,  0.82   , 0.8316,  0.8172  ,0.83112, 0.83624 ,0.85888, 0.84088,\n",
    " 0.85088])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "4e63d3b6-e016-4dfd-9e3e-74fcb88b86fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1854.0, pvalue=0.03019903843699843)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(synthetic_independent_fair_ratio, synthetic_independent_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "a168d1de-1ee9-4477-b704-8f7b5e47f8e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1876.0, pvalue=0.03655643813514655)"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(synthetic_independent_fair_diff, synthetic_independent_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "e43cc3f8-7b8b-4c4f-a925-32f4bb04d383",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=2305.0, pvalue=0.44939054842060555)"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(synthetic_independent_fair_variation, synthetic_independent_unfair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "a842c938-e84f-48fd-aa99-eb13fc5c81c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=2119.5, pvalue=0.16321631253956081)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(synthetic_independent_fair_accuracy, synthetic_independent_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "5476f601-59f7-4a31-9104-f9c64c06d628",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=5247.5, pvalue=0.5461646226079262)"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(synthetic_independent_fair_ratio, synthetic_independent_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "6bde429a-b254-4e92-914a-335052a16d23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=5215.5, pvalue=0.5993546345372709)"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(synthetic_independent_fair_diff, synthetic_independent_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "b6e57632-c7ca-4aa2-9f27-2921338af290",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=5164.0, pvalue=0.6895291826856957)"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(synthetic_independent_fair_variation, synthetic_independent_unfair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "a600c1ca-bbd3-49aa-9305-67dfe3d9b2e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=4853.5, pvalue=0.7212873627137555)"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(synthetic_independent_fair_accuracy, synthetic_independent_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8daea23-cd8c-48ee-a6c1-22ead8e34b13",
   "metadata": {},
   "source": [
    "Statisticall Dependent Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "518f6eef-1103-46df-a40b-1737e4bd1611",
   "metadata": {},
   "outputs": [],
   "source": [
    "statistical_dependent_fair_diff= np.array(\n",
    "[0.08917628, 0.10827341, 0.11147545, 0.06840991 ,0.07147954, 0.02770907,\n",
    " 0.07309991, 0.10819308, 0.0338156  ,0.02807876 ,0.02381059, 0.10396747,\n",
    " 0.08238889, 0.07167233, 0.06794366 ,0.10690208 ,0.07075014, 0.07873328,\n",
    " 0.06138999, 0.08749925, 0.06866898 ,0.08739389 ,0.14166069, 0.04720473,\n",
    " 0.09359454, 0.07413106, 0.08034184 ,0.03153216 ,0.1427046 , 0.07120384,\n",
    " 0.07885535, 0.0765667 , 0.07901723 ,0.02933336 ,0.09725162, 0.08034308,\n",
    " 0.07016964, 0.03721536, 0.05998569 ,0.07655062 ,0.06832908, 0.07938131,\n",
    " 0.21553742, 0.03571907 ,0.04561977 ,0.08187199 ,0.08376419, 0.02661763,\n",
    " 0.05770148 ,0.09734525 ,0.05404322 ,0.06981023 ,0.06157606, 0.07922325,\n",
    " 0.05843917 ,0.04875499 ,0.11820203 ,0.06952471 ,0.01775934, 0.17320718,\n",
    " 0.09360937, 0.05746203, 0.04245548 ,0.11767008 ,0.05262975, 0.08314064,\n",
    " 0.04944108, 0.03738753, 0.08288047 ,0.05933883 ,0.0689684 , 0.05047722,\n",
    " 0.0891928 , 0.09282509, 0.10301271 ,0.0489604  ,0.05953054, 0.08539741,\n",
    " 0.06668372, 0.01604507 ,0.03396551 ,0.04508235, 0.04167383 ,0.06554995,\n",
    " 0.06406517 ,0.06121452, 0.10063384, 0.07856664, 0.02709777 ,0.06985664,\n",
    " 0.07661166, 0.01636472, 0.05397498, 0.06086478, 0.03435942 ,0.05023507,\n",
    " 0.01477143, 0.10274852, 0.06619149 ,0.0441946 ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "59271018-91c1-459e-ac52-2318745d6743",
   "metadata": {},
   "outputs": [],
   "source": [
    "statistical_dependent_fair_ratio=np.array( \n",
    "[1.1125233,  1.1386743 , 1.13746551, 1.09931954 ,1.086228,   1.0368708,\n",
    " 1.10234941, 1.14503795, 1.04508006, 1.03003507, 1.02576509, 1.13073753,\n",
    " 1.12008097, 1.0846672 , 1.07847786, 1.14532211, 1.0874988 , 1.09494436,\n",
    " 1.08075461 ,1.11838133, 1.09122908, 1.11199483, 1.22918717, 1.05974651,\n",
    " 1.11477003 ,1.09931543, 1.12227545, 1.03828216, 1.19208   , 1.10371654,\n",
    " 1.10529358 ,1.09973628, 1.10339996, 1.03695402, 1.12289279, 1.09388357,\n",
    " 1.08598136 ,1.04622393, 1.07995584, 1.11323438, 1.0934914 , 1.09395217,\n",
    " 1.32436863 ,1.04632826, 1.05705194, 1.12006713, 1.10395427, 1.0309759,\n",
    " 1.07014493 ,1.13061359, 1.07170701, 1.0833887 , 1.07408922, 1.1152888,\n",
    " 1.08144315 ,1.06012561, 1.16295891, 1.08980449, 1.02195522, 1.24462703,\n",
    " 1.1192908  ,1.07679915, 1.04864691, 1.14881607, 1.066154  , 1.12373713,\n",
    " 1.05730931 ,1.04433597, 1.11413525, 1.07030821, 1.09939118 ,1.06699315,\n",
    " 1.10698068 ,1.13080199, 1.12314026, 1.06482345, 1.07934968 ,1.11722388,\n",
    " 1.08742228 ,1.01986532, 1.04269419, 1.05797428, 1.05089281 ,1.0922947,\n",
    " 1.07709411 ,1.07259255, 1.12133897, 1.1123481 , 1.03126665 ,1.08598982,\n",
    " 1.09804498 ,1.01860561, 1.05924285, 1.07252876, 1.04045545 ,1.06412988,\n",
    " 1.01752668 ,1.13810285, 1.08858484, 1.06008996])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "d72ee099-6dd2-4a79-8af4-fd0b859a3070",
   "metadata": {},
   "outputs": [],
   "source": [
    "statistical_dependent_fair_variation=np.array(\n",
    "[0.09652268, 0.32673599 ,0.22906967, 0.26197157 ,0.10528185, 0.1885324,\n",
    " 0.23558595, 0.10819308, 0.13990954, 0.23594617 ,0.16687574, 0.10508493,\n",
    " 0.25776891 ,0.13646217 ,0.19479587, 0.15962581 ,0.10312496, 0.12401979,\n",
    " 0.28530345 ,0.17226781 ,0.1759287 , 0.12206374 ,0.31915445, 0.09713189,\n",
    " 0.12593754 ,0.16149335 ,0.28923064 ,0.03153216 ,0.1427046 , 0.27750534,\n",
    " 0.19075001 ,0.12564821, 0.14230458, 0.15366805 ,0.09725162, 0.1390937,\n",
    " 0.16228206 ,0.123598  , 0.21745497, 0.27747451 ,0.19284097, 0.31804904,\n",
    " 0.24090282 ,0.16016682, 0.24037397, 0.2403371  ,0.18192838, 0.04012015,\n",
    " 0.07827942 ,0.37996579, 0.1548517 , 0.08347509 ,0.15621262, 0.28324492,\n",
    " 0.24005322 ,0.12717921, 0.19596744, 0.15906134 ,0.20875193, 0.21164195,\n",
    " 0.0979711  ,0.20894458, 0.26103253, 0.11767008 ,0.11116145, 0.30776325,\n",
    " 0.23536047 ,0.27904988, 0.19042844, 0.15087276, 0.2373083 , 0.21811151,\n",
    " 0.19155594 ,0.23441473, 0.13765222, 0.14503457, 0.17764005, 0.18349769,\n",
    " 0.18145166 ,0.03463327, 0.21563306, 0.18131039, 0.05857057 ,0.19572098,\n",
    " 0.09587195 ,0.17072947, 0.21639218, 0.2486681 , 0.21442365 ,0.11966849,\n",
    " 0.09731199 ,0.21508241, 0.21709147, 0.08277699, 0.07894636 ,0.125,\n",
    " 0.06908919 ,0.19802204, 0.13050473, 0.18625275])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "48e0cfb3-953f-409a-9e84-86de648a505e",
   "metadata": {},
   "outputs": [],
   "source": [
    "statistical_dependent_fair_accuracy=np.array(\n",
    "[0.83184, 0.81432, 0.81728, 0.8392  ,0.84,    0.82176 ,0.83072, 0.82032, 0.83376,\n",
    " 0.85896, 0.85368, 0.85432, 0.8404  ,0.84224, 0.82864 ,0.84888, 0.83496, 0.85048,\n",
    " 0.81176, 0.84904, 0.85048, 0.84272 ,0.8188 , 0.82224 ,0.85992, 0.83336, 0.8408,\n",
    " 0.84392, 0.82584, 0.83248, 0.83048 ,0.8512 , 0.82936 ,0.84544, 0.84912, 0.85936,\n",
    " 0.83136, 0.83464, 0.84392, 0.84776 ,0.81808, 0.83376, 0.83304, 0.84392, 0.8264,\n",
    " 0.82096, 0.84304 ,0.86272, 0.84056 ,0.8     ,0.84888 ,0.85184 ,0.8464  ,0.82456,\n",
    " 0.86424, 0.83992 ,0.83872, 0.84544 ,0.82488, 0.84192, 0.84448, 0.8356,  0.83384,\n",
    " 0.8488 , 0.84872 ,0.82896 ,0.82704 ,0.79912 ,0.85032 ,0.82776 ,0.8324 , 0.80512,\n",
    " 0.83768, 0.85464 ,0.84904 ,0.818  , 0.85648 ,0.83496, 0.83952 ,0.82872, 0.83384,\n",
    " 0.85128, 0.85048, 0.84072 ,0.83896, 0.84592 ,0.84216, 0.80672 ,0.8472 , 0.84032,\n",
    " 0.83072, 0.85072, 0.81952 ,0.84664, 0.82968 ,0.85096, 0.83568 ,0.84648, 0.82752,\n",
    " 0.8416 ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "51b91997-f6cc-424b-b231-eb1f09b37fa1",
   "metadata": {},
   "outputs": [],
   "source": [
    "statistical_dependent_unfair_diff=np.array(\n",
    "[0.10434468, 0.10586486 ,0.13151031, 0.05032359, 0.08719617 ,0.02556596,\n",
    " 0.06972525, 0.1001273  ,0.03132165, 0.03789434, 0.02549354 ,0.11260321,\n",
    " 0.10753704, 0.06040863 ,0.085318   ,0.10654724, 0.1079737  ,0.08824778,\n",
    " 0.09735725, 0.08887572 ,0.0830152 , 0.10259513, 0.1188299  ,0.04875546,\n",
    " 0.0846634 , 0.10914816 ,0.07456295, 0.02849912, 0.13715278 ,0.09463423,\n",
    " 0.07472932, 0.08360135 ,0.08379005, 0.02953874, 0.09620228 ,0.11733821,\n",
    " 0.06479347, 0.05167544 ,0.0654241 , 0.07573048, 0.07792372 ,0.10191574,\n",
    " 0.27508761, 0.04264675 ,0.04181843, 0.08154246, 0.0915926  ,0.03727477,\n",
    " 0.05674773, 0.0550852  ,0.05436426, 0.08584593, 0.08223655 ,0.1411764,\n",
    " 0.07895299, 0.06115197 ,0.14929722, 0.09660162, 0.0217079  ,0.20252676,\n",
    " 0.09778991 ,0.06316251 ,0.04815725, 0.11401585, 0.06252935 ,0.09240503,\n",
    " 0.04543991, 0.03890957, 0.0999443 , 0.06467014, 0.07628817 ,0.08045377,\n",
    " 0.13062458, 0.09191438 ,0.1018851 , 0.07401536, 0.09868544 ,0.08360956,\n",
    " 0.0836364 , 0.02546924 ,0.04711281, 0.03847292, 0.03527682 ,0.06758647,\n",
    " 0.07268259, 0.06933188 ,0.10418098, 0.08129831, 0.02278439 ,0.09930495,\n",
    " 0.08766975, 0.02116457 ,0.04017943, 0.07872267, 0.03545013 ,0.0523051,\n",
    " 0.02183041 ,0.08935493, 0.09019051, 0.06819175])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "560dfab0-6ba9-4d89-912f-29e05213901f",
   "metadata": {},
   "outputs": [],
   "source": [
    "statistical_dependent_unfair_ratio=np.array(\n",
    "[1.13512979, 1.14248082 ,1.17182449, 1.06147486 ,1.10639029, 1.03366342,\n",
    " 1.10350219, 1.12574126 ,1.04156418, 1.04360555 ,1.03069349, 1.13877156,\n",
    " 1.17909021, 1.06987541 ,1.10147019, 1.15014108 ,1.14332855, 1.10438479,\n",
    " 1.13877833, 1.10990242 ,1.10565571, 1.13901673 ,1.16960037, 1.06240584,\n",
    " 1.09916614, 1.14994021 ,1.11025501, 1.03465347 ,1.17913832, 1.13220389,\n",
    " 1.10250438, 1.1069951 , 1.11441275, 1.03784472 ,1.11644963, 1.14955674,\n",
    " 1.07555639, 1.06637335, 1.09123401, 1.11524203 ,1.11362986, 1.13159556,\n",
    " 1.48664092, 1.05701395, 1.05258034, 1.11110501 ,1.11189351, 1.04490783,\n",
    " 1.06769056 ,1.09482578, 1.07257133, 1.1108436  ,1.1034    , 1.22967177,\n",
    " 1.10283706, 1.07943527, 1.21781678, 1.12760153 ,1.02720205, 1.31554134,\n",
    " 1.11876465, 1.07245269, 1.05593607, 1.13678201 ,1.08192411, 1.13476286,\n",
    " 1.05350743, 1.04199605, 1.13582174, 1.07510081 ,1.10643605, 1.09853226,\n",
    " 1.16875672, 1.11242466, 1.11648825, 1.10256625 ,1.14381962, 1.10679582,\n",
    " 1.11442078, 1.03138928, 1.06043175, 1.04956138 ,1.04255873, 1.09064272,\n",
    " 1.08736253, 1.08616001, 1.12826978, 1.1224271  ,1.02638335, 1.13020796,\n",
    " 1.11683361, 1.0242746 , 1.0431527 , 1.09748879 ,1.04123513, 1.06619255,\n",
    " 1.02665937, 1.11289316, 1.12683993, 1.09252573])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "61957ba7-ab05-4ea2-8acf-e4a87906f868",
   "metadata": {},
   "outputs": [],
   "source": [
    "statistical_dependent_unfair_variation=np.array(\n",
    "[0.10434468, 0.33642532 ,0.14365186, 0.20305485, 0.13729227, 0.20343153,\n",
    " 0.28150602 ,0.1080815  ,0.14160697, 0.22846555, 0.15208776, 0.11260321,\n",
    " 0.35889843 ,0.15998954 ,0.17199395, 0.19141943, 0.1290778 , 0.15797676,\n",
    " 0.29159358 ,0.11292328 ,0.11260661 ,0.21194431, 0.24151042, 0.07248861,\n",
    " 0.14431347 ,0.18236718 ,0.25926695 ,0.04234084, 0.13715278, 0.2402496,\n",
    " 0.21500354 ,0.11698053 ,0.18842497 ,0.13892237, 0.15359446, 0.14105818,\n",
    " 0.16927092 ,0.14185716 ,0.21210567 ,0.29884132, 0.26177614, 0.24082512,\n",
    " 0.38086422 ,0.18459475 ,0.22441119 ,0.17819878, 0.1676721  ,0.04371147,\n",
    " 0.10687459 ,0.41757288 ,0.16763252 ,0.16592902, 0.13085622, 0.36736861,\n",
    " 0.17746353 ,0.13796747 ,0.2625953  ,0.17571619, 0.18693375 ,0.29161663,\n",
    " 0.15674597 ,0.18856033 ,0.23766368 ,0.16252799 ,0.17243034 ,0.27736232,\n",
    " 0.20677062 ,0.26767621 ,0.17371046 ,0.1728675  ,0.20725065 ,0.13598433,\n",
    " 0.14329068 ,0.14114281 ,0.2300446  ,0.18561042 ,0.24570626 ,0.11140527,\n",
    " 0.22394348 ,0.03418195 ,0.23209035 ,0.18701691 ,0.04302609 ,0.15111925,\n",
    " 0.1155459  ,0.13789406 ,0.18099861 ,0.29219211, 0.21472733 ,0.15725957,\n",
    " 0.12239573 ,0.21894004, 0.24295996 ,0.07872267, 0.09543738 ,0.10054466,\n",
    " 0.08428278 ,0.1335804,  0.15815855 ,0.16954343])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "55673537-b442-4fff-8178-96b160380218",
   "metadata": {},
   "outputs": [],
   "source": [
    "statistical_dependent_unfair_accuracy = np.array(\n",
    "[0.83144, 0.80336, 0.82816, 0.8428 , 0.8332 , 0.82192, 0.82472, 0.82952, 0.83648,\n",
    " 0.85768, 0.86256, 0.8544 , 0.83072, 0.83416, 0.83056, 0.84736, 0.82872, 0.8504,\n",
    " 0.8028 , 0.846  , 0.84792, 0.84488, 0.82672, 0.82952, 0.85872, 0.83184 ,0.8432,\n",
    " 0.8448 , 0.8288 , 0.83896, 0.82336, 0.85304, 0.82344, 0.84784, 0.85144 ,0.86656,\n",
    " 0.8436 , 0.8288 , 0.8484 , 0.84024, 0.80872, 0.83744, 0.83224, 0.8448  ,0.826,\n",
    " 0.82168, 0.8484 , 0.85872, 0.84432, 0.80624, 0.8476 , 0.84616, 0.85368 ,0.81128,\n",
    " 0.86808, 0.84536, 0.82208, 0.84232, 0.82544, 0.83464, 0.84672, 0.83816 ,0.83592,\n",
    " 0.85624, 0.84096, 0.82824, 0.82576, 0.80104, 0.852  , 0.82864, 0.83088 ,0.82224,\n",
    " 0.84   , 0.858  , 0.84928, 0.82288, 0.8544 , 0.8456 , 0.83416, 0.83088 ,0.83048,\n",
    " 0.84912, 0.84456, 0.85056, 0.84048, 0.84032, 0.84376, 0.7964 , 0.84568 ,0.8356,\n",
    " 0.82296, 0.85056, 0.81576, 0.84512, 0.83216 ,0.8524 , 0.83832, 0.83904 ,0.8116,\n",
    " 0.84408])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "b9bea882-a5a6-4b26-835c-d112287d77f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1039.0, pvalue=3.2326779258988665e-07)"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(statistical_dependent_unfair_diff,statistical_dependent_fair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "ac109229-b5d8-438d-aa46-db8e966850fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=5831.0, pvalue=0.04243441413732605)"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(statistical_dependent_unfair_diff,statistical_dependent_fair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "b27dea1a-a3be-4014-b85e-7aea5fcd1dee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1217.0, pvalue=6.881249880501417e-06)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(statistical_dependent_unfair_ratio,statistical_dependent_fair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "97c72fe2-df49-416c-8f23-add9b95e6a91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=5787.0, pvalue=0.05464032451893515)"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(statistical_dependent_unfair_ratio,statistical_dependent_fair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "a9a38769-f935-4eaf-9931-0ee313e79c15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=2198.0, pvalue=0.2608721129080632)"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(statistical_dependent_unfair_variation,statistical_dependent_fair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "acf48eee-b5c9-4700-b923-f7b2287de62f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=5114.0, pvalue=0.781530842287596)"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(statistical_dependent_unfair_variation,statistical_dependent_fair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "87d8eb7b-5d18-4a9d-83cf-c0a7485ff8a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=2491.5, pvalue=0.9082965404239803)"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(statistical_dependent_unfair_accuracy,statistical_dependent_fair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "126adaff-ea60-45fa-8528-65da7dd92d8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=4955.0, pvalue=0.9134147460969848)"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(statistical_dependent_unfair_accuracy,statistical_dependent_fair_accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cd8de1f-7c85-48bf-9343-926ad20489f2",
   "metadata": {},
   "source": [
    "Loan Trials Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "5b63c8f7-4f77-40b0-a6c0-a3cb8b557563",
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_fair_diff=np.array( \n",
    "[0.43478976, 0.42935483 ,0.45700082, 0.44053609, 0.43154838, 0.45749954,\n",
    " 0.44828565, 0.4260765 , 0.43262872, 0.42614111, 0.42055023, 0.43825633,\n",
    " 0.45490721, 0.43809756, 0.42625228, 0.42667689, 0.43433891 ,0.43664885,\n",
    " 0.4621966 , 0.44306221, 0.44244923, 0.40529227, 0.45002743 ,0.440983,\n",
    " 0.43478976, 0.42042154, 0.42860871, 0.45128653, 0.43191079 ,0.42526024,\n",
    " 0.44795461, 0.43516098, 0.39209298, 0.41832766, 0.44221557 ,0.4263372,\n",
    " 0.43547245, 0.44640687, 0.42280553, 0.46592336, 0.41836407 ,0.43611189,\n",
    " 0.43458836, 0.42860871, 0.42688593, 0.43604022, 0.43218979 ,0.45609664,\n",
    " 0.42860871, 0.43609794, 0.4408744 , 0.42513647, 0.43335641 ,0.42780597,\n",
    " 0.42929764, 0.4212547 , 0.43802439, 0.45203736, 0.43848834 ,0.4606809,\n",
    " 0.39713225, 0.43632201, 0.44053663, 0.45172263, 0.44364638 ,0.439346,\n",
    " 0.4216119 , 0.43569868, 0.44096048, 0.43390674, 0.42280553 ,0.43170403,\n",
    " 0.43357278, 0.44551557, 0.45716517, 0.46120325, 0.43547245 ,0.4606809,\n",
    " 0.40250476, 0.45943078, 0.39581298 ,0.44151626, 0.44234752 ,0.46538858,\n",
    " 0.43473132, 0.42856029, 0.40234882 ,0.46253794, 0.41444353 ,0.42867679,\n",
    " 0.4018724 , 0.40779018, 0.43871098 ,0.42526024, 0.45496621 ,0.41836637,\n",
    " 0.4138096 , 0.44343918, 0.41540745 ,0.45259313])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "392bdc7d-6db8-4a65-8d03-cb55a8fdc848",
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_fair_ratio=np.array( \n",
    "[1.90166927, 1.86228549 ,2.00068438, 1.88336532, 1.86412487, 1.95767628,\n",
    " 1.9289163  ,1.83814369 ,1.87561359, 1.83776891, 1.81345184, 1.89355301,\n",
    " 1.94755903 ,1.88127065 ,1.83951211, 1.8312589 , 1.86400193, 1.88809496,\n",
    " 1.97272559 ,1.9013197  ,1.89290075, 1.77214774, 1.9449769 , 1.91304378,\n",
    " 1.90166927 ,1.80903253 ,1.84964929, 1.95733283, 1.86514483, 1.86043389,\n",
    " 1.91617123 ,1.88448634 ,1.70656884, 1.81524006, 1.89987857, 1.86891082,\n",
    " 1.88202497 ,1.94071146 ,1.80195572, 2.01881908, 1.81282162, 1.87803508,\n",
    " 1.85500262 ,1.84964929 ,1.84437345, 1.86546221, 1.87340566, 1.97073441,\n",
    " 1.84964929 ,1.8669205  ,1.89915174, 1.85550616, 1.88645746, 1.82845362,\n",
    " 1.83790625 ,1.82617797 ,1.86057716, 1.95954814, 1.88255928, 1.97744977,\n",
    " 1.74241729 ,1.87316068 ,1.90817082, 1.94164239, 1.90692076, 1.88328714,\n",
    " 1.8201251  ,1.85654685 ,1.90644905, 1.87009188, 1.80195572, 1.86366023,\n",
    " 1.86424628 ,1.90881942 ,1.96148191, 1.98493757, 1.88202497, 1.97744977,\n",
    " 1.74580489 ,1.9845355  ,1.72248555, 1.90738282, 1.90709579, 2.00115999,\n",
    " 1.87421958 ,1.85942881 ,1.75245595, 1.99677807, 1.79293187, 1.85328788,\n",
    " 1.74198614 ,1.77642324 ,1.87612476, 1.86043389, 1.98800355, 1.80996694,\n",
    " 1.79469191 ,1.90496706, 1.80169755, 1.95495993])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "e319d54a-1e65-4e1f-8263-9abda594eda6",
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_fair_variation=np.array(\n",
    "[0.51310586, 0.49772593 ,0.53888333 ,0.49686412 ,0.49652516 ,0.51800371,\n",
    " 0.51323056 ,0.48801525 ,0.50142132 ,0.48790492 ,0.47882578 ,0.50545935,\n",
    " 0.5161625  ,0.4982956  ,0.48849762 ,0.48200298 ,0.4932946  ,0.50456609,\n",
    " 0.52148924 ,0.50415015 ,0.50062538 ,0.47097767 ,0.51986502 ,0.51355316,\n",
    " 0.51310586 ,0.47681471 ,0.49153571 ,0.5247242  ,0.49709603 ,0.50148131,\n",
    " 0.50777683 ,0.50397486 ,0.44136685 ,0.48309691 ,0.50440457 ,0.50545485,\n",
    " 0.50252216 ,0.52113667 ,0.46922591 ,0.53859991 ,0.48116587 ,0.49933203,\n",
    " 0.48709527 ,0.49153571 ,0.49103448 ,0.49252264 ,0.50207545 ,0.52665459,\n",
    " 0.49153571 ,0.49261737 ,0.50545456 ,0.49977986 ,0.50689983 ,0.47990735,\n",
    " 0.48430435 ,0.48593533 ,0.48745413 ,0.52483519 ,0.49889423 ,0.52406122,\n",
    " 0.4609824  ,0.4959917  ,0.51105461 ,0.5157875  ,0.50722044 ,0.49877576,\n",
    " 0.48191399 ,0.4869061  ,0.50988013 ,0.49752427 ,0.46922591 ,0.49667494,\n",
    " 0.49374803 ,0.5051094  ,0.52093069 ,0.52727091 ,0.50252216 ,0.52406122,\n",
    " 0.45618117 ,0.52918324 ,0.4485759  ,0.51021624 ,0.50872952 ,0.53061787,\n",
    " 0.4982965  ,0.49755135 ,0.46079879 ,0.53255448 ,0.47353005 ,0.49433086,\n",
    " 0.45470691 ,0.47030768 ,0.49599284 ,0.50148131 ,0.5357632  ,0.47919753,\n",
    " 0.47577928 ,0.505898  , 0.47784323 ,0.5223272 ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "39d5c022-407a-4914-bec9-8cd54025b0f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_fair_accuracy=np.array(\n",
    "[0.93747899 ,0.93704482, 0.93781513 ,0.93551821, 0.93703081 ,0.93560224,\n",
    " 0.93557423 ,0.93816527 ,0.93654062 ,0.93747899, 0.93777311 ,0.93553221,\n",
    " 0.93746499 ,0.93782913 ,0.93676471 ,0.93761905, 0.93621849 ,0.93677871,\n",
    " 0.93710084 ,0.93760504 ,0.93680672 ,0.93763305 ,0.93560224 ,0.93682073,\n",
    " 0.93747899 ,0.93753501 ,0.93782913 ,0.93696078 ,0.93808123 ,0.93542017,\n",
    " 0.93830532 ,0.93740896 ,0.93659664 ,0.93739496 ,0.93763305 ,0.93759104,\n",
    " 0.93812325 ,0.93810924 ,0.93795518 ,0.93516807 ,0.93715686 ,0.93666667,\n",
    " 0.93761905 ,0.93782913 ,0.93679272 ,0.93712885 ,0.93852941 ,0.93726891,\n",
    " 0.93782913 ,0.93598039 ,0.93578431 ,0.93658263 ,0.93554622 ,0.9357423,\n",
    " 0.93682073 ,0.93733894 ,0.93602241 ,0.93557423 ,0.93830532 ,0.93736695,\n",
    " 0.93784314 ,0.93686275 ,0.93683473 ,0.93662465 ,0.93616246 ,0.93378151,\n",
    " 0.93752101 ,0.93644258 ,0.93857143 ,0.93668067 ,0.93795518 ,0.93598039,\n",
    " 0.93794118 ,0.93739496 ,0.93897759 ,0.93816527 ,0.93812325 ,0.93736695,\n",
    " 0.9377451  ,0.93516807 ,0.93647059 ,0.93787115 ,0.93683473 ,0.93673669,\n",
    " 0.93705882 ,0.93854342 ,0.93642857 ,0.9377591  ,0.93833333 ,0.93838936,\n",
    " 0.93535014 ,0.93701681 ,0.93719888 ,0.93542017 ,0.93803922 ,0.93670868,\n",
    " 0.93782913 ,0.93747899 ,0.93738095 ,0.93876751])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "46123824-40e6-4290-a35f-a56472104303",
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_unfair_diff=np.array(\n",
    "[0.54221437 ,0.55022931 ,0.55233365, 0.57602233, 0.57891336 ,0.56719534,\n",
    " 0.56159235 ,0.54065947 ,0.56519807, 0.56301738, 0.56360943, 0.55606807,\n",
    " 0.58136341 ,0.55637519 ,0.558977  , 0.55399121, 0.55824265, 0.58109699,\n",
    " 0.58287976 ,0.55978673 ,0.55895263, 0.55124167, 0.56717182, 0.5688178,\n",
    " 0.54221437 ,0.54458105 ,0.56681509, 0.57467863, 0.55569509, 0.54878094,\n",
    " 0.5742142  ,0.56150803 ,0.57456525, 0.54306537, 0.55400282, 0.54511186,\n",
    " 0.56642113 ,0.56060695 ,0.55565945, 0.56287948, 0.56882437, 0.56311456,\n",
    " 0.57670641 ,0.56681509 ,0.56541351, 0.5776501 , 0.55826753, 0.5703923,\n",
    " 0.56681509 ,0.57680748 ,0.55996611, 0.55607192, 0.56119352, 0.58389761,\n",
    " 0.5607774  ,0.55877519 ,0.58434166, 0.56729638, 0.54521899, 0.56763518,\n",
    " 0.54235641 ,0.58035926 ,0.54810118, 0.56014753, 0.56285962 ,0.57399063,\n",
    " 0.55214557 ,0.5648071  ,0.54999199, 0.54412636, 0.55565945, 0.55800558,\n",
    " 0.56274939 ,0.57673872 ,0.56354694, 0.57095721, 0.56642113, 0.56763518,\n",
    " 0.55315424 ,0.57281858 ,0.54798732, 0.56714411, 0.55503976, 0.56721719,\n",
    " 0.58015754 ,0.54851645 ,0.56144245, 0.56606764, 0.54907267, 0.5518535,\n",
    " 0.55754114 ,0.53690963 ,0.57428031, 0.54878094, 0.55147042, 0.56614553,\n",
    " 0.54862276 ,0.57537835 ,0.54460233, 0.56814027])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "7aaf6c59-fe5a-467e-b4b1-45755654db86",
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_unfair_ratio=np.array(\n",
    "[2.80107643 ,2.82652325 ,2.94261183, 3.09556076 ,3.10867467 ,3.0245806,\n",
    " 2.98528322 ,2.81439879 ,3.04220073, 2.9513273  ,2.98983791 ,2.96025678,\n",
    " 3.1514923  ,2.82634999 ,2.97286001 ,2.90244851 ,2.97944036 ,3.11257472,\n",
    " 3.11333212 ,2.95117416 ,2.91617159 ,2.78745507 ,3.03313734 ,3.044864,\n",
    " 2.80107643 ,2.81954138 ,3.04393279 ,3.08913997 ,2.95540069 ,2.91113525,\n",
    " 3.05050234 ,2.95196401 ,3.05860276 ,2.81745155 ,2.90030709 ,2.86461975,\n",
    " 3.04737014, 3.00291694 ,2.84020683 ,3.05138298 ,3.0206     ,2.96823637,\n",
    " 3.09025134 ,3.04393279 ,3.04483234 ,3.08051942 ,2.91922692 ,3.01603132,\n",
    " 3.04393279 ,3.09753699 ,2.97464783 ,3.01796501 ,2.97963878 ,3.12181372,\n",
    " 2.93485264 ,2.9357368  ,3.1341994  ,3.05090106 ,2.82685128 ,3.01839246,\n",
    " 2.80679438 ,3.1275643  ,2.84425694 ,2.96253541 ,3.00055373 ,3.1082883,\n",
    " 2.9062303  ,3.00839974 ,2.84961918 ,2.86829399 ,2.84020683 ,2.94027322,\n",
    " 2.97564803 ,3.11387278 ,2.97031376 ,3.06864088 ,3.04737014 ,3.01839246,\n",
    " 2.85771235 ,3.07435253 ,2.81970133 ,2.944576   ,2.86735599 ,2.99873802,\n",
    " 3.14431413 ,2.8717705  ,2.98824867 ,3.01479689, 2.8515111  ,2.87373513,\n",
    " 2.89260182 ,2.77085056 ,2.9952105  ,2.91113525, 2.97346348 ,3.00811283,\n",
    " 2.93067555 ,3.05829354, 2.78155058 ,3.05127231])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "824c8759-ad5f-4f08-9372-93a5ab72eda7",
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_unfair_variation=np.array(\n",
    "[0.69440597, 0.69447632 ,0.71162842, 0.72068875, 0.72139131, 0.71570558,\n",
    " 0.71287427, 0.69838989 ,0.71906923, 0.70810366, 0.71295475, 0.71238901,\n",
    " 0.7260317 , 0.69077817 ,0.71290238, 0.70436042, 0.71398011, 0.72116943,\n",
    " 0.72083467, 0.7087554  ,0.70472759, 0.68747251, 0.7172008 , 0.71836537,\n",
    " 0.69440597, 0.69717856 ,0.71867348, 0.7211142 , 0.71214651, 0.7088123,\n",
    " 0.71675134, 0.70837298 ,0.71718775, 0.69749257, 0.70452926, 0.7038353,\n",
    " 0.71958321, 0.71626489 ,0.69448907, 0.72152673, 0.71465926, 0.70999026,\n",
    " 0.71952893, 0.71867348 ,0.72015931, 0.71869911, 0.70602682, 0.71357328,\n",
    " 0.71867348, 0.72098353 ,0.71258696, 0.72129719, 0.71234855, 0.72111036,\n",
    " 0.70688889, 0.70715626 ,0.72264423, 0.71938865, 0.69751526, 0.71459652,\n",
    " 0.69596139, 0.72291477, 0.69894235, 0.71022117, 0.71497936, 0.72378365,\n",
    " 0.70634328, 0.71435247, 0.69899619, 0.70504144, 0.69448907, 0.70907384,\n",
    " 0.71103875, 0.72279644, 0.71045927, 0.71975243, 0.71958321, 0.71459652,\n",
    " 0.69875099, 0.71975552, 0.69535229, 0.70514399, 0.6992173 , 0.71200142,\n",
    " 0.72510201, 0.70323055, 0.71340864, 0.71563231, 0.69971637, 0.70219268,\n",
    " 0.70180233, 0.69233096, 0.7089037 , 0.7088123 , 0.71681073, 0.71397107,\n",
    " 0.71240396, 0.71636243, 0.69038187 ,0.7192969 ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "eccfb8f1-d596-4be0-8f07-ce4d2942d625",
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_unfair_accuracy=np.array(\n",
    "[0.93780112, 0.93760504 ,0.93742297 ,0.93603641 ,0.93715686, 0.93697479,\n",
    " 0.93582633, 0.9367507  ,0.93612045 ,0.93787115 ,0.93796919, 0.93640056,\n",
    " 0.93808123, 0.93957983 ,0.93677871 ,0.93743697 ,0.93703081, 0.93735294,\n",
    " 0.93833333, 0.93767507 ,0.93746499 ,0.93787115 ,0.93515406, 0.93642857,\n",
    " 0.93780112, 0.93808123 ,0.93732493 ,0.93635854 ,0.93810924, 0.93609244,\n",
    " 0.93757703, 0.93795518 ,0.93763305 ,0.93746499 ,0.93777311, 0.93805322,\n",
    " 0.9372549 , 0.93673669 ,0.93885154 ,0.93568627 ,0.93743697, 0.93759104,\n",
    " 0.93782913 ,0.93732493 ,0.93668067 ,0.93757703 ,0.93872549, 0.93746499,\n",
    " 0.93732493 ,0.93620448 ,0.93670868 ,0.9357423  ,0.9362605 , 0.93661064,\n",
    " 0.93780112 ,0.93679272, 0.93735294 ,0.93560224 ,0.93718487, 0.9369888,\n",
    " 0.93747899 ,0.93752101, 0.93778711 ,0.93655462 ,0.93666667, 0.93508403,\n",
    " 0.93757703 ,0.93714286, 0.93892157 ,0.93652661 ,0.93885154, 0.93641457,\n",
    " 0.93848739 ,0.93757703, 0.93864146 ,0.93771709 ,0.9372549 , 0.9369888,\n",
    " 0.93869748 ,0.93606443, 0.937507   ,0.93845938 ,0.93841737, 0.93656863,\n",
    " 0.93735294 ,0.93827731, 0.93613445 ,0.9377591 , 0.93817927, 0.93819328,\n",
    " 0.93764706 ,0.93746499, 0.93791317 ,0.93609244, 0.93690476, 0.93794118,\n",
    " 0.93719888 ,0.93810924, 0.93837535 ,0.93735294])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "c7da9398-0d5a-4e9b-9117-09f911fab062",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.8945820011567e-18)"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(loan_fair_diff,loan_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "id": "8ebb8e66-d5b1-412d-b9c3-70fe233b8239",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=0.0, pvalue=2.559547067908908e-34)"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(loan_fair_diff,loan_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "c715d8ab-3a02-44fc-b081-2c4b239e6c09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.8945820011567e-18)"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(loan_fair_ratio,loan_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "75dcf965-db8b-4b99-b5eb-28baa48d9363",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=0.0, pvalue=2.559547067908908e-34)"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(loan_fair_ratio,loan_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "521c5f78-16bd-473e-94f8-9e7cbd920329",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.8945820011567e-18)"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(loan_fair_variation,loan_unfair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "fc1fe57c-69f6-4c1c-b727-26de0b9ba051",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=0.0, pvalue=2.559547067908908e-34)"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(loan_fair_variation,loan_unfair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "1fe8a7a5-b824-490d-a522-cb040db0cfaa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1508.5, pvalue=0.0007423257227729147)"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(loan_fair_accuracy,loan_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "49023c80-6759-48aa-be6b-f8787aba0496",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=4439.5, pvalue=0.17119287636180147)"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(loan_fair_accuracy,loan_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65aa5be9-37ac-4b33-8ed2-8a345f234d84",
   "metadata": {},
   "source": [
    "Canabis Trials Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "6ded9045-e831-4b6f-b183-e3cad7a5092b",
   "metadata": {},
   "outputs": [],
   "source": [
    "canabis_fair_diff=np.array(\n",
    "[0.14077991, 0.49766355 ,0.22681159 ,0.2179803  ,0.18956044 ,0.44230769,\n",
    " 0.30927835, 0.32010582 ,0.35545723 ,0.09803922 ,0.19509476 ,0.25917603,\n",
    " 0.14349776, 0.71698113 ,0.2293578  ,0.12352941 ,0.13157895 ,0.1943149,\n",
    " 0.27430556, 0.40740741 ,0.22941889 ,0.32542373 ,0.34191176 ,0.,\n",
    " 0.11904762, 0.29565217 ,0.17699115 ,0.20484848 ,0.33409091 ,0.1875,\n",
    " 0.0851927 , 0.25108225 ,0.68807339 ,0.25917603 ,0.59090909 ,0.29276316,\n",
    " 0.10095238, 0.2037037  ,0.35224586 ,0.21849427 ,0.32670807 ,0.58714286,\n",
    " 0.13636364, 0.18389058 ,0.31731985 ,0.12232416 ,0.26666667 ,0.22145062,\n",
    " 0.1490566 , 0.33038348 ,0.4957265  ,0.26311189 ,0.40669241 ,0.09689441,\n",
    " 0.35185185, 0.3203125  ,0.3        ,0.27430556 ,0.1719457  ,0.36163522,\n",
    " 0.37719298, 0.20757576 ,0.20454545 ,0.54273504 ,0.15560641 ,0.2037037,\n",
    " 0.35660377 ,0.16964286 ,0.21149425 ,0.17594108 ,0.3245614  ,0.28228228,\n",
    " 0.55371901 ,0.23666667 ,0.         ,0.07859848 ,0.3203125  ,0.33333333,\n",
    " 0.375      ,0.16386555 ,0.19036697 ,0.31578947 ,0.13636364 ,0.14349776,\n",
    " 0.07552448 ,0.22969606 ,0.44       ,0.12663755 ,0.04347826 ,0.12669683,\n",
    " 0.05656566 ,0.         ,0.39047619 ,0.20509709 ,0.32542373 ,0.27033219,\n",
    " 0.53869048 ,0.48035714, 0.16666667 ,0.10095238])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "ca27291a-b5f3-4f0e-b765-3f76cf841c84",
   "metadata": {},
   "outputs": [],
   "source": [
    "canabis_fair_ratio=np.array(\n",
    "[1.31986532 ,2.99065421 ,1.32102564 ,1.50862069 ,2.45454545 ,2.76923077,\n",
    " 1.44776119 ,3.24074074 ,3.13274336 ,1.24390244 ,1.27173913 ,1.39285714,\n",
    " 1.16753927 ,       np.nan ,       np.nan ,1.33064516 ,1.39473684 ,1.27742549,\n",
    " 1.44632768 ,1.6875     ,1.32813853 ,2.62711864 ,1.7265625  ,       np.nan,\n",
    " 1.23050847 ,       np.nan  ,      np.nan ,1.33399209 ,1.71707317 ,       np.nan,\n",
    " 1.1372549  ,1.41428571  ,      np.nan ,1.39285714 ,4.54545455 ,1.8559322,\n",
    " 1.22701149 ,1.81481481 ,2.58510638 ,1.34810952 ,3.28695652 ,5.11,\n",
    " 1.375      ,1.47413793 ,3.22123894 ,1.57971014 ,1.78947368 ,1.32173913,\n",
    " 1.74528302 ,1.99115044 ,1.98305085 ,1.74689826 ,3.84684685 ,1.15694165,\n",
    " 2.05555556 ,2.28125    ,2.5        ,1.44632768 ,1.55367232 ,3.16981132,\n",
    " 2.13157895 ,1.31494253 ,1.33333333 ,4.25641026 ,1.21052632 ,1.81481481,\n",
    " 2.78301887 ,2.1875     ,1.4        ,1.26251526 ,2.94736842 ,2.27027027,\n",
    " 2.24074074 ,1.5503876  ,       np.nan ,1.15217391 ,2.28125    ,2.,\n",
    " 1.71818182 ,1.74603175 ,1.76146789 ,       np.nan ,1.27272727 ,1.16753927,\n",
    " 1.144      ,1.34845049 ,       np.nan ,1.22751323, 1.10869565 ,1.25217391,\n",
    " 1.12444444 ,       np.nan ,3.73333333 ,1.34920635, 2.62711864 ,3.43298969,\n",
    " 4.23214286 ,5.80357143, 1.5        ,1.22701149])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "492457d8-8d90-4062-a7d8-05c529ec2614",
   "metadata": {},
   "outputs": [],
   "source": [
    "canabis_fair_variation=np.array(\n",
    "[0.585      ,0.75       ,0.43333333 ,0.51260504 ,0.88888889, 0.625,\n",
    " 0.5        ,0.85714286 ,0.75       ,0.48363244 ,0.26355894, 0.43333333,\n",
    " 0.51666667 ,0.95652174 ,1.         ,0.66666667 ,0.61904762, 0.24019139,\n",
    " 0.38888889 ,0.66666667 ,0.30357143 ,0.7375     ,0.66666667, 1.,\n",
    " 0.51239669 ,1.         ,1.         ,0.31818182 ,0.53409091, 1.,\n",
    " 0.13631969 ,0.44736842 ,0.88235294 ,0.43333333 ,0.78571429 ,0.60416667,\n",
    " 0.51879699 ,0.69736842 ,0.71111111 ,0.43238095 ,0.72380952 ,0.7518797,\n",
    " 0.52574417 ,0.6        ,0.80714286 ,0.78899083 ,0.61111111, 0.4375,\n",
    " 0.8        ,0.54901961 ,0.4957265  ,0.56077075 ,0.74603175, 0.3875,\n",
    " 0.54666667 ,0.75       ,0.75454545 ,0.38888889 ,0.72727273, 0.78333333,\n",
    " 0.66666667 ,0.27424242 ,0.20454545 ,0.83333333 ,0.29473684, 0.69736842,\n",
    " 0.75454545 ,0.85714286 ,0.40616246 ,0.43358596 ,0.73333333, 0.77777778,\n",
    " 0.55371901 ,0.4837931  ,1.         ,0.45492662 ,0.75      , 0.61904762,\n",
    " 0.60416667 ,0.87272727 ,0.63888889 ,0.91304348 ,0.26      , 0.51666667,\n",
    " 0.42552448 ,0.36190476 ,0.91666667 ,0.45689655 ,0.54736842, 0.66666667,\n",
    " 0.75       ,1.         ,0.85714286 ,0.3987395  ,0.7375     ,0.88888889,\n",
    " 0.64285714 ,0.775      ,0.66666667 ,0.51879699])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "c355b6e5-e6e4-4850-9968-75f9c6db1dd3",
   "metadata": {},
   "outputs": [],
   "source": [
    "canabis_fair_accuracy=np.array(\n",
    "[0.76694915, 0.72457627 ,0.7690678 , 0.71822034 ,0.71398305, 0.74576271,\n",
    " 0.68220339, 0.70550847 ,0.72881356, 0.72669492 ,0.71610169, 0.68855932,\n",
    " 0.74152542, 0.71186441 ,0.71822034, 0.75211864 ,0.75847458, 0.6970339,\n",
    " 0.74364407, 0.76059322 ,0.70338983, 0.74576271 ,0.69279661, 0.54237288,\n",
    " 0.75423729, 0.72033898 ,0.72033898, 0.66525424 ,0.74576271, 0.73305085,\n",
    " 0.70974576, 0.72033898 ,0.74364407, 0.68855932 ,0.69915254, 0.68644068,\n",
    " 0.74152542, 0.74576271 ,0.75847458, 0.75211864 ,0.61440678, 0.70762712,\n",
    " 0.75211864, 0.73728814 ,0.72245763, 0.70550847 ,0.69067797, 0.7309322,\n",
    " 0.75423729, 0.68644068 ,0.74152542, 0.69915254 ,0.72669492, 0.73940678,\n",
    " 0.70127119, 0.75211864 ,0.75847458, 0.74364407 ,0.71610169, 0.75847458,\n",
    " 0.74788136, 0.73516949 ,0.69279661, 0.70974576 ,0.73940678, 0.74576271,\n",
    " 0.75      , 0.73728814 ,0.72457627, 0.75       ,0.73305085, 0.74364407,\n",
    " 0.74576271, 0.75       ,0.59110169, 0.73940678 ,0.75211864, 0.70127119,\n",
    " 0.73305085, 0.68008475 ,0.72033898 ,0.72881356 ,0.66313559, 0.74152542,\n",
    " 0.72669492, 0.6970339  ,0.73728814 ,0.7309322  ,0.74152542, 0.74576271,\n",
    " 0.70974576, 0.53601695 ,0.75       ,0.75635593 ,0.74576271, 0.7690678,\n",
    " 0.70974576, 0.69491525 ,0.68644068 ,0.74152542])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "7de2793f-66f1-47e8-83a8-59d2bc7f7c2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "canabis_unfair_diff = np.array(\n",
    "[0.118308   ,0.56074766 ,0.21594203 ,0.11988304 ,0.1456044  ,0.24038462,\n",
    " 0.28865979 ,0.31084656 ,0.32890855 ,0.08823529 ,0.18596491 ,0.24794007,\n",
    " 0.10313901 ,0.53773585 ,0.1529052  ,0.09408602 ,0.14035088 ,0.25909091,\n",
    " 0.26388889 ,0.51041667 ,0.40086207 ,0.31694915 ,0.14285714 ,0.13605442,\n",
    " 0.1468254  ,0.50434783 ,0.39823009 ,0.25       ,0.19298246 ,0.1875,\n",
    " 0.51401869 ,0.29385965 ,0.49541284 ,0.24794007 ,0.38888889 ,0.3079096,\n",
    " 0.30666667 ,0.2037037  ,0.42080378 ,0.25286416 ,0.32670807 ,0.38714286,\n",
    " 0.12857143 ,0.13218391 ,0.34386852 ,0.37461774 ,0.24444444 ,0.22145062,\n",
    " 0.32830189 ,0.15339233 ,0.34444444 ,0.1981982  ,0.23680824 ,0.31801242,\n",
    " 0.196337   ,0.3046875  ,0.28148148 ,0.26388889 ,0.15100154 ,0.3427673,\n",
    " 0.29787234 ,0.20757576 ,0.28181818 ,0.52136752 ,0.32985075 ,0.2037037,\n",
    " 0.15660377 ,0.42857143 ,0.2        ,0.19967267 ,0.3245614  ,0.17117117,\n",
    " 0.14600551 ,0.18022528 ,0.41528239 ,0.05660377 ,0.3046875  ,0.13071895,\n",
    " 0.275      ,0.24141414 ,0.35206422 ,0.46491228 ,0.09135593 ,0.10313901,\n",
    " 0.11961722 ,0.19649123 ,0.45       ,0.16666667 ,0.06956522 ,0.11312217,\n",
    " 0.10747664 ,0.14444444 ,0.37380952 ,0.17254902, 0.31694915 ,0.30584192,\n",
    " 0.3422619  ,0.43571429 ,0.09589041 ,0.30666667])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "2cc1560e-405e-4f62-a3fc-655e438b7b4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "canabis_unfair_ratio=np.array( \n",
    "[1.21212121,        np.nan ,1.3010101  ,1.1659919  ,1.24090909 ,1.96153846,\n",
    " 1.4057971 , 3.17592593 ,2.97345133 ,1.17647059 ,1.24882629 ,1.36174863,\n",
    " 1.115     ,        np.nan  ,1.4587156  ,1.28225806 ,1.42105263 ,1.52777778,\n",
    " 1.42222222,        np.nan  ,4.20689655 ,2.58474576 ,1.16666667 ,1.40816327,\n",
    " 1.20555556,        np.nan  ,       np.nan  ,2.         ,1.57894737 ,1.26315789,\n",
    "        np.nan , 2.1754386  ,       np.nan  ,1.36174863 ,3.33333333 ,2.84745763,\n",
    " 1.44230769, 1.81481481 ,4.78723404 ,1.37728938 ,3.28695652 ,3.71,\n",
    " 1.35169492, 1.39655172 ,3.40707965 ,3.24770642 ,1.34920635 ,1.30926724,\n",
    " 2.64150943, 1.46017699 ,1.52542373 ,1.59459459 ,1.82882883 ,3.22608696,\n",
    " 1.5       , 2.21875    ,2.40740741 ,1.42222222 ,1.55367232 ,3.05660377,\n",
    " 1.42424242, 1.31494253 ,1.93939394 ,      np.nan  ,2.64925373 ,1.81481481,\n",
    " 1.39150943, 4.         ,1.42857143 ,1.2760181  ,2.94736842 ,1.51351351,\n",
    " 1.28042328, 1.25668449 ,3.90697674 ,1.11320755 ,2.21875    ,1.58823529,\n",
    " 2.04545455, 2.08636364 ,3.81651376 ,       np.nan ,1.125      ,1.115,\n",
    " 1.2084507 , 1.26666667 ,       np.nan  ,1.33333333 ,1.17391304 ,1.12755102,\n",
    " 1.27380952, 1.48148148 ,3.61666667 ,1.34920635 ,2.58474576 ,1.91752577,\n",
    " 3.05357143, 5.35714286 ,1.10606061 ,1.44230769])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "e1d011bd-999e-49a0-9084-e31128e2e882",
   "metadata": {},
   "outputs": [],
   "source": [
    "canabis_unfair_variation=np.array( \n",
    "[0.585      ,1.         ,0.43333333 ,0.57142857 ,0.41106719 ,0.67307692,\n",
    " 0.5        ,0.8015873  ,0.75       ,0.41666667 ,0.58152174 ,0.43333333,\n",
    " 0.5        ,0.95652174 ,0.58974359 ,0.66666667 ,0.61904762 ,0.50909091,\n",
    " 0.40888889 ,1.         ,0.80357143 ,0.7375     ,0.55555556 ,0.62666667,\n",
    " 0.6        ,0.95238095 ,1.         ,0.75       ,0.66666667 ,0.6,\n",
    " 0.89915966 ,0.69736842 ,0.94117647 ,0.43333333 ,0.78571429 ,0.78571429,\n",
    " 0.57142857 ,0.69736842 ,0.88888889 ,0.42438095 ,0.77594628 ,0.80451128,\n",
    " 0.52574417 ,0.6        ,0.75714286 ,0.75333333 ,0.66666667 ,0.45054348,\n",
    " 0.8        ,0.66666667 ,0.51282051 ,0.57971014 ,0.6092437  ,0.75714286,\n",
    " 0.66666667 ,0.67857143 ,0.75454545 ,0.40888889 ,0.72727273 ,0.78333333,\n",
    " 0.66666667 ,0.41446541 ,0.7        ,1.         ,0.75238095 ,0.69736842,\n",
    " 0.55454545 ,0.81714286 ,0.4745098  ,0.41523734 ,0.73333333 ,0.66666667,\n",
    " 0.47933884 ,0.50555556 ,0.8226601  ,0.38888889 ,0.67857143 ,0.73015873,\n",
    " 0.77777778 ,0.77777778 ,0.76388889 ,0.91304348 ,0.51555556 ,0.5,\n",
    " 0.5034965  ,0.53439153 ,0.91666667 ,0.5        ,0.54736842 ,0.5,\n",
    " 0.60747664 ,0.65833333 ,0.85714286 ,0.38343337 ,0.7375     ,0.66666667,\n",
    " 0.78571429 ,0.84117647, 0.50833333 ,0.57142857])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "e344ad5c-3c2c-438c-a183-a517c5542401",
   "metadata": {},
   "outputs": [],
   "source": [
    "canabis_unfair_accuracy=np.array(\n",
    "[0.76271186 ,0.75847458 ,0.77118644 ,0.75211864 ,0.76059322 ,0.77966102,\n",
    " 0.77118644 ,0.73516949 ,0.72457627 ,0.77330508 ,0.75       ,0.72881356,\n",
    " 0.76059322 ,0.76483051 ,0.73305085 ,0.75847458 ,0.76059322 ,0.75847458,\n",
    " 0.73940678 ,0.77754237 ,0.75847458 ,0.75635593 ,0.72669492 ,0.73516949,\n",
    " 0.77754237 ,0.74364407 ,0.74364407 ,0.74364407 ,0.7690678  ,0.76483051,\n",
    " 0.7690678  ,0.73728814 ,0.75847458 ,0.72881356 ,0.77754237 ,0.7309322,\n",
    " 0.75       ,0.76694915 ,0.76483051 ,0.75847458 ,0.75211864 ,0.76271186,\n",
    " 0.75       ,0.74576271 ,0.73516949 ,0.74364407 ,0.73728814 ,0.76694915,\n",
    " 0.76271186 ,0.74576271 ,0.75847458 ,0.74788136 ,0.76059322 ,0.73516949,\n",
    " 0.75211864 ,0.75211864 ,0.75211864 ,0.73940678 ,0.72245763 ,0.75635593,\n",
    " 0.75211864 ,0.77330508 ,0.78177966 ,0.74576271 ,0.74576271 ,0.76694915,\n",
    " 0.75211864 ,0.75847458 ,0.74576271 ,0.76694915 ,0.74152542 ,0.75423729,\n",
    " 0.75211864 ,0.77330508 ,0.78601695 ,0.74152542 ,0.75211864 ,0.7309322,\n",
    " 0.73305085 ,0.74576271 ,0.75211864 ,0.73940678 ,0.75       ,0.76059322,\n",
    " 0.72881356 ,0.75635593 ,0.74576271 ,0.75635593 ,0.75847458 ,0.75211864,\n",
    " 0.75       ,0.75847458 ,0.74364407 ,0.77542373 ,0.75635593 ,0.7690678,\n",
    " 0.75635593 ,0.77542373 ,0.76271186 ,0.75      ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "c0a12bac-8f14-4deb-81cb-9524312fd64d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=2038.0, pvalue=0.5719628067787756)"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(canabis_fair_diff,canabis_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "28968e92-80e2-4655-a59b-a6493b716573",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=4919.0, pvalue=0.8440660355779219)"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(canabis_fair_diff,canabis_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "3fbd9700-5fd1-446f-9414-a0c1bbc0ebef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1224.0, pvalue=0.00022951453012528037)"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(canabis_fair_ratio,canabis_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "id": "63ba5b6b-1171-4800-b163-7f00010225e1",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "`x` and `y` must not contain NaNs.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Input \u001b[0;32mIn [204]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mmannwhitneyu\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcanabis_fair_ratio\u001b[49m\u001b[43m,\u001b[49m\u001b[43mcanabis_unfair_ratio\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/.conda/envs/grisha/lib/python3.9/site-packages/scipy/stats/_mannwhitneyu.py:391\u001b[0m, in \u001b[0;36mmannwhitneyu\u001b[0;34m(x, y, use_continuity, alternative, axis, method)\u001b[0m\n\u001b[1;32m    181\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmannwhitneyu\u001b[39m(x, y, use_continuity\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, alternative\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mtwo-sided\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m    182\u001b[0m                  axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m, method\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mauto\u001b[39m\u001b[38;5;124m\"\u001b[39m):\n\u001b[1;32m    183\u001b[0m     \u001b[38;5;124mr\u001b[39m\u001b[38;5;124;03m'''Perform the Mann-Whitney U rank test on two independent samples.\u001b[39;00m\n\u001b[1;32m    184\u001b[0m \n\u001b[1;32m    185\u001b[0m \u001b[38;5;124;03m    The Mann-Whitney U test is a nonparametric test of the null hypothesis\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    387\u001b[0m \n\u001b[1;32m    388\u001b[0m \u001b[38;5;124;03m    '''\u001b[39;00m\n\u001b[1;32m    390\u001b[0m     x, y, use_continuity, alternative, axis_int, method \u001b[38;5;241m=\u001b[39m (\n\u001b[0;32m--> 391\u001b[0m         \u001b[43m_mwu_input_validation\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43muse_continuity\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43malternative\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmethod\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[1;32m    393\u001b[0m     x, y, xy \u001b[38;5;241m=\u001b[39m _broadcast_concatenate(x, y, axis)\n\u001b[1;32m    395\u001b[0m     n1, n2 \u001b[38;5;241m=\u001b[39m x\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m], y\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m]\n",
      "File \u001b[0;32m~/.conda/envs/grisha/lib/python3.9/site-packages/scipy/stats/_mannwhitneyu.py:133\u001b[0m, in \u001b[0;36m_mwu_input_validation\u001b[0;34m(x, y, use_continuity, alternative, axis, method)\u001b[0m\n\u001b[1;32m    131\u001b[0m x, y \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39matleast_1d(x), np\u001b[38;5;241m.\u001b[39matleast_1d(y)\n\u001b[1;32m    132\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m np\u001b[38;5;241m.\u001b[39misnan(x)\u001b[38;5;241m.\u001b[39many() \u001b[38;5;129;01mor\u001b[39;00m np\u001b[38;5;241m.\u001b[39misnan(y)\u001b[38;5;241m.\u001b[39many():\n\u001b[0;32m--> 133\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m`x` and `y` must not contain NaNs.\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m    134\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m np\u001b[38;5;241m.\u001b[39msize(x) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;129;01mor\u001b[39;00m np\u001b[38;5;241m.\u001b[39msize(y) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m:\n\u001b[1;32m    135\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m`x` and `y` must be of nonzero size.\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "\u001b[0;31mValueError\u001b[0m: `x` and `y` must not contain NaNs."
     ]
    }
   ],
   "source": [
    "mannwhitneyu(canabis_fair_ratio,canabis_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "a714f80a-31bb-4365-a8bf-cb31d61685ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1033.0, pvalue=0.08089608011224056)"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(canabis_fair_variation,canabis_unfair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "id": "42bd48c2-d8bc-4625-92a5-14ebd6995846",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=4588.5, pvalue=0.31510283215034995)"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(canabis_fair_variation,canabis_unfair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "bd48a729-2d0f-45fc-9b49-9e816122f61e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=103.0, pvalue=4.243672475518891e-16)"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(canabis_fair_accuracy,canabis_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "e5c88e2d-9e45-4d47-9814-d39946405894",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=1763.0, pvalue=2.4696854021287657e-15)"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(canabis_fair_accuracy,canabis_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "4e03a6bb-9363-451d-b217-5d044fd5ea09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.03245762689999987"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "canabis_fair_accuracy.mean()-canabis_unfair_accuracy.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b4a4cb7-49e6-49fe-b5f9-606c0fdd3342",
   "metadata": {},
   "source": [
    "COMPAS Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "b56745e4-4c35-4044-a0c7-fec162f357d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "compas_fair_diff=np.array( \n",
    "[0.15475715 ,0.13392678 ,0.14928239, 0.11059118 ,0.12965381 ,0.14925892,\n",
    " 0.18762921 ,0.12512284 ,0.1627438 , 0.13582473 ,0.11762066 ,0.13772663,\n",
    " 0.13544581 ,0.16352575 ,0.16745325, 0.14867067 ,0.15515064 ,0.15519386,\n",
    " 0.17702108 ,0.17770892 ,0.17343647, 0.15785495 ,0.14330594 ,0.1787167,\n",
    " 0.1236915  ,0.14484696 ,0.14200014, 0.15359661 ,0.17343647 ,0.15215817,\n",
    " 0.13487606 ,0.14125259 ,0.1302629 , 0.15461004 ,0.12776656 ,0.17434751,\n",
    " 0.15293869 ,0.1417171  ,0.18421181, 0.15220674 ,0.14650195 ,0.14342295,\n",
    " 0.14386901 ,0.14766474 ,0.16033946, 0.14411501 ,0.15625507 ,0.13311712,\n",
    " 0.13467206 ,0.11398834 ,0.14204967, 0.13811924 ,0.14386901 ,0.15185732,\n",
    " 0.1716277  ,0.15424465 ,0.16312623, 0.13681666 ,0.1787167  ,0.14887869,\n",
    " 0.13252238 ,0.18232263 ,0.14257249, 0.15597757 ,0.11799339 ,0.17622588,\n",
    " 0.15620957 ,0.15517798 ,0.15506629, 0.13403661 ,0.16527844 ,0.13045928,\n",
    " 0.2039876  ,0.17671958 ,0.14799921, 0.14406878 ,0.15258591 ,0.17366386,\n",
    " 0.19461413 ,0.15157526 ,0.13730581, 0.14106036 ,0.15545483 ,0.13377981,\n",
    " 0.16208912 ,0.16785804 ,0.13101899, 0.14056223, 0.14484899 ,0.15746467,\n",
    " 0.13097639 ,0.14224959 ,0.13392678, 0.17273107, 0.1451718  ,0.14715593,\n",
    " 0.17045911 ,0.11604854, 0.14786707, 0.1534941 ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "431b8ca2-cc29-4b27-8a77-d3db1f6d8f40",
   "metadata": {},
   "outputs": [],
   "source": [
    "compas_fair_ratio=np.array( \n",
    "[1.33946729 ,1.30375828 ,1.32658542 ,1.2174326  ,1.27754332 ,1.33147111,\n",
    " 1.44467794 ,1.26086033 ,1.36729821 ,1.29466295 ,1.24087694 ,1.30322624,\n",
    " 1.29520241 ,1.27416999 ,1.37031394 ,1.29837798 ,1.34329012 ,1.24937551,\n",
    " 1.40023406 ,1.41000419 ,1.39638435 ,1.35308285 ,1.32589008 ,1.41449531,\n",
    " 1.27579061 ,1.31697029 ,1.31914174 ,1.34407583 ,1.39638435 ,1.33856416,\n",
    " 1.29866921 ,1.30947359 ,1.27185301 ,1.36213336 ,1.28205072 ,1.38768647,\n",
    " 1.34113189 ,1.31359696 ,1.39794123 ,1.33823719 ,1.32050189 ,1.32940255,\n",
    " 1.31508693 ,1.34027093 ,1.38053537 ,1.3240233  ,1.34023282 ,1.29589246,\n",
    " 1.29623409 ,1.24046367 ,1.31107955 ,1.30751507 ,1.31508693 ,1.34823307,\n",
    " 1.39304691 ,1.34102722 ,1.38256984 ,1.2541511  ,1.41449531 ,1.32673847,\n",
    " 1.28473258 ,1.41964592 ,1.32261595 ,1.36106919 ,1.23906401 ,1.40595431,\n",
    " 1.3589163  ,1.3461474  ,1.34718165 ,1.29823147 ,1.36882332 ,1.28948935,\n",
    " 1.48534981 ,1.36474259 ,1.30153681 ,1.27999081 ,1.34790593 ,1.39814907,\n",
    " 1.46158904 ,1.33956963 ,1.30105896 ,1.30527349 ,1.35288246 ,1.29627229,\n",
    " 1.37913311 ,1.35708931 ,1.25025685 ,1.30887878 ,1.32441385 ,1.35748003,\n",
    " 1.29283516 ,1.3323203  ,1.30375828 ,1.39065502 ,1.31091914 ,1.32388387,\n",
    " 1.40607665 ,1.25516034 ,1.32185733 ,1.33833913])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "45f65f15-a018-4d35-ae7d-95c197d31015",
   "metadata": {},
   "outputs": [],
   "source": [
    "compas_fair_variation=np.array(\n",
    "[0.50277788 ,0.50850465 ,0.49448768 ,0.52839381 ,0.49044916 ,0.50537565,\n",
    " 0.53489823 ,0.47702603 ,0.50865864 ,0.49197558 ,0.46201814 ,0.50042514,\n",
    " 0.49691088 ,0.51284862 ,0.49989099 ,0.49843771 ,0.50334934 ,0.49400101,\n",
    " 0.51401454 ,0.52042826 ,0.5133931  ,0.51157212 ,0.51392676 ,0.52565536,\n",
    " 0.5023066  ,0.49473082 ,0.51028464 ,0.50940951 ,0.5133931  ,0.51038855,\n",
    " 0.50036692 ,0.49985222 ,0.46181846 ,0.53003357 ,0.49602095 ,0.50655378,\n",
    " 0.50779295 ,0.50066383 ,0.48923878 ,0.50207472 ,0.4974648  ,0.5178778,\n",
    " 0.49630201 ,0.52432601 ,0.53802221 ,0.50921513 ,0.49323807 ,0.50084788,\n",
    " 0.50125735 ,0.4711038  ,0.49963863 ,0.50391623 ,0.49630201 ,0.5185574,\n",
    " 0.52128723 ,0.50309438 ,0.52852842 ,0.49500524 ,0.52565536 ,0.50095809,\n",
    " 0.48950381 ,0.51509531 ,0.50836878 ,0.51905235 ,0.47939017 ,0.52219545,\n",
    " 0.51726587 ,0.50817448 ,0.51170303 ,0.50387688 ,0.49939825 ,0.50409665,\n",
    " 0.53271795 ,0.46709312 ,0.49093406 ,0.51309852 ,0.51681848 ,0.51023689,\n",
    " 0.53416299 ,0.51235016 ,0.49388549 ,0.48427856 ,0.50798378 ,0.50166042,\n",
    " 0.52508976 ,0.47663783 ,0.47100056 ,0.50092448 ,0.50526464 ,0.51297122,\n",
    " 0.5045943  ,0.52827954 ,0.50850465 ,0.51205017 ,0.4889883  ,0.49452019,\n",
    " 0.53554772 ,0.4970727 , 0.49715685 ,0.50089707])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "id": "9822693c-3f7f-4e7a-abba-e0493c538c7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "compas_fair_accuracy= np.array(\n",
    "[0.83439616, 0.82085333 ,0.83104332 ,0.82197094 ,0.82939978, 0.82953126,\n",
    " 0.8259812 , 0.82591546 ,0.82348301 ,0.83156926 ,0.82926829, 0.82874236,\n",
    " 0.82407468 ,0.82341726 ,0.82460062 ,0.82460062 ,0.8303859 , 0.82571823,\n",
    " 0.82709881 ,0.82946552 ,0.82381172 ,0.82874236 ,0.82729604, 0.82506081,\n",
    " 0.82216817 ,0.82979423 ,0.83117481 ,0.82788771 ,0.82381172, 0.82591546,\n",
    " 0.82460062 ,0.82933403 ,0.82854513 ,0.82295707 ,0.82039314, 0.82788771,\n",
    " 0.83058313 ,0.82414042 ,0.81697456 ,0.82578397 ,0.82861087, 0.8231543,\n",
    " 0.82637565 ,0.82617842 ,0.82729604 ,0.82709881 ,0.82256262, 0.82525804,\n",
    " 0.82828216, 0.82400894 ,0.83064887 ,0.82328578 ,0.82637565, 0.82460062,\n",
    " 0.82736178 ,0.83110907 ,0.82558675 ,0.82788771 ,0.82506081, 0.82913681,\n",
    " 0.82808494 ,0.82427191 ,0.82368023 ,0.82696733 ,0.82907107, 0.83176648,\n",
    " 0.82302281 ,0.82256262 ,0.82420617 ,0.82486359 ,0.82039314, 0.82861087,\n",
    " 0.82690158 ,0.82249688 ,0.82650713 ,0.82985997 ,0.82387746, 0.82032739,\n",
    " 0.82308855 ,0.82630991 ,0.82486359 ,0.82256262 ,0.82098481, 0.82282559,\n",
    " 0.82348301 ,0.82630991 ,0.82874236 ,0.83156926 ,0.82663862, 0.82703307,\n",
    " 0.82992571, 0.82657287 ,0.82085333 ,0.82821642 ,0.831635  , 0.82532378,\n",
    " 0.82210243 ,0.82624417 ,0.83248965 ,0.8280192 ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "48e928a2-b92f-45d9-b185-303f3eadc1c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "compas_unfair_diff=np.array(\n",
    "[0.13579014, 0.12102473 ,0.14242343 ,0.14766104 ,0.13622046 ,0.14998335,\n",
    " 0.17065516, 0.15103068 ,0.13963954 ,0.14868079 ,0.12235944 ,0.13688977,\n",
    " 0.15212455, 0.15198843 ,0.1519522  ,0.14082165 ,0.15283491 ,0.15701123,\n",
    " 0.16861535, 0.1677861  ,0.15182019 ,0.13852591 ,0.14490896 ,0.15889441,\n",
    " 0.14393004, 0.14681844 ,0.1602759  ,0.13049518 ,0.15182019 ,0.16826785,\n",
    " 0.13618896, 0.13534161 ,0.14198789 ,0.15024289 ,0.14684575 ,0.15829901,\n",
    " 0.14621686, 0.12964587 ,0.1383006  ,0.14565621 ,0.14748964 ,0.14206234,\n",
    " 0.15274517, 0.1647888  ,0.15954112 ,0.14271413 ,0.14527637 ,0.13876312,\n",
    " 0.13590451, 0.13533467 ,0.13468731 ,0.14032573 ,0.15274517 ,0.13364844,\n",
    " 0.18899993, 0.13922516 ,0.15897981 ,0.15289742 ,0.15889441 ,0.15441531,\n",
    " 0.12029537, 0.14366219 ,0.15002773 ,0.15624569 ,0.13422095 ,0.15952828,\n",
    " 0.14753154, 0.14008827 ,0.13982664 ,0.14001513 ,0.156566   ,0.14026239,\n",
    " 0.17487643, 0.12869021 ,0.17208658 ,0.1629899  ,0.15221138 ,0.16710956,\n",
    " 0.17614931, 0.14446455 ,0.14804494 ,0.13770028 ,0.11636713 ,0.14758079,\n",
    " 0.14784579, 0.15677461 ,0.14837429 ,0.14670095 ,0.14482576 ,0.14418136,\n",
    " 0.13843091, 0.14090499 ,0.12102473 ,0.16107971 ,0.13135359 ,0.12515235,\n",
    " 0.16975266, 0.12124826 ,0.13133726 ,0.14275247])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "id": "13f2004a-d004-4988-823a-f96bad508bf4",
   "metadata": {},
   "outputs": [],
   "source": [
    "compas_unfair_ratio=np.array( \n",
    "[1.32731504 ,1.29324309 ,1.34714221 ,1.37289762 ,1.32697632 ,1.36704334,\n",
    " 1.44227044 ,1.23929536 ,1.34003453 ,1.27253322 ,1.24217594 ,1.33334036,\n",
    " 1.30555021 ,1.3469836  ,1.3774384  ,1.31183499 ,1.38410585 ,1.31052621,\n",
    " 1.4347845  ,1.43044936 ,1.38323268 ,1.34151188 ,1.36942341 ,1.4038684,\n",
    " 1.35995385 ,1.3585349  ,1.39144058 ,1.31416327 ,1.38323268 ,1.38149833,\n",
    " 1.32412389 ,1.33956678 ,1.29686926 ,1.38891287 ,1.37081192 ,1.39138939,\n",
    " 1.35498498 ,1.3180451  ,1.32896615 ,1.36028039 ,1.36530023 ,1.36519146,\n",
    " 1.38006104 ,1.33042168 ,1.4245365  ,1.35900299 ,1.36118435 ,1.34812502,\n",
    " 1.33179618 ,1.33783544 ,1.32272324 ,1.35003474 ,1.38006104 ,1.33071529,\n",
    " 1.50388095 ,1.33832946 ,1.41286848 ,1.30028857 ,1.4038684  ,1.32873178,\n",
    " 1.29471269 ,1.34867748 ,1.38798381 ,1.40672516 ,1.27984074 ,1.41682194,\n",
    " 1.3810307  ,1.3416315  ,1.34054165 ,1.35877198 ,1.39696492 ,1.34888371,\n",
    " 1.44525734 ,1.29974849 ,1.33425883 ,1.30606642 ,1.38441706 ,1.45011239,\n",
    " 1.46168964 ,1.36641968 ,1.36306892 ,1.34582928 ,1.29404829 ,1.27408188,\n",
    " 1.35263796 ,1.38422399 ,1.28513668 ,1.35503717, 1.35422184 ,1.36162061,\n",
    " 1.33960024 ,1.366728   ,1.29324309 ,1.4082038,  1.30960291 ,1.31062992,\n",
    " 1.45397455 ,1.26686908 ,1.3130045  ,1.35205316])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "c66103c5-cb89-4601-85ab-674a98ce14ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "compas_unfair_variation=np.array(\n",
    "[0.55752918 ,0.5720389  ,0.56183107 ,0.57569614 ,0.55911942, 0.56360927,\n",
    " 0.58649292 ,0.53742369 ,0.55988913 ,0.54594811 ,0.53994962, 0.56334734,\n",
    " 0.56792213 ,0.58200164 ,0.56697647 ,0.56370314 ,0.57525237, 0.56296627,\n",
    " 0.58581814 ,0.58157911 ,0.57201596 ,0.57045848 ,0.58003352, 0.57891057,\n",
    " 0.57167771 ,0.56207712 ,0.57824029 ,0.55841871 ,0.57201596, 0.590393,\n",
    " 0.57019056 ,0.5781835  ,0.5502163  ,0.58656103 ,0.57688709, 0.56742049,\n",
    " 0.55792703 ,0.56641245 ,0.56959422 ,0.56677538 ,0.57083892, 0.58379067,\n",
    " 0.56907331 ,0.57416508 ,0.5996707  ,0.57388203 ,0.57318636, 0.57045172,\n",
    " 0.56231551 ,0.57272981 ,0.55422366 ,0.57202387 ,0.56907331, 0.5639872,\n",
    " 0.59940133 ,0.56273733 ,0.58699764 ,0.56274654 ,0.57891057, 0.56061028,\n",
    " 0.56465688 ,0.56053836 ,0.5850448  ,0.58799877 ,0.55301473, 0.59111417,\n",
    " 0.58402566 ,0.55938307 ,0.56065659 ,0.58419038 ,0.57444305, 0.56815087,\n",
    " 0.57801019 ,0.5420925  ,0.56116785 ,0.5630867  ,0.57814586, 0.60248297,\n",
    " 0.58929572 ,0.57878808 ,0.5639976  ,0.57369796 ,0.57635649, 0.56273173,\n",
    " 0.57695056 ,0.56592835 ,0.54689177 ,0.56289014 ,0.55888089, 0.57874169,\n",
    " 0.56257269 ,0.5921102  ,0.5720389  ,0.5791619 , 0.55059983, 0.56706911,\n",
    " 0.59886361 ,0.54783847 ,0.55180489 ,0.56740834])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "0b72cb05-ca39-4067-9415-523dce415c0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "compas_unfair_accuracy=np.array( \n",
    "[0.83755177, 0.82762475 ,0.8364999 , 0.83209519 ,0.83518506 ,0.83459339,\n",
    " 0.83301558, 0.83110907 ,0.83091184, 0.83768326 ,0.83715732 ,0.83531655,\n",
    " 0.83064887, 0.83117481 ,0.83143778, 0.83071461 ,0.8349221  ,0.83156926,\n",
    " 0.83281836, 0.83268687 ,0.83156926, 0.83525081 ,0.83472487 ,0.83170074,\n",
    " 0.8288081 , 0.83735455 ,0.83511932, 0.83321281 ,0.83156926 ,0.829597,\n",
    " 0.83130629, 0.83623693 ,0.83636842, 0.82749326 ,0.82847939 ,0.83577674,\n",
    " 0.83452764, 0.83426468 ,0.82808494, 0.83189797 ,0.83406745 ,0.82985997,\n",
    " 0.83170074, 0.82966274 ,0.82992571, 0.83354152 ,0.83387023 ,0.83202945,\n",
    " 0.83459339, 0.83327855 ,0.83577674, 0.82926829 ,0.83170074 ,0.82953126,\n",
    " 0.83078036, 0.835711   ,0.83301558, 0.83051739 ,0.83170074 ,0.83334429,\n",
    " 0.83104332, 0.83452764 ,0.82999145, 0.83341003 ,0.83511932 ,0.83531655,\n",
    " 0.82854513, 0.82821642 ,0.82854513, 0.83209519 ,0.82861087 ,0.83308132,\n",
    " 0.83656564, 0.83998422 ,0.83327855, 0.8349221  ,0.83097758 ,0.83156926,\n",
    " 0.82907107, 0.83091184 ,0.83255539, 0.82999145 ,0.82926829 ,0.83110907,\n",
    " 0.83137203, 0.83945829 ,0.83281836, 0.83715732 ,0.8328841  ,0.83281836,\n",
    " 0.835711  , 0.83124055 ,0.82762475, 0.83465913 ,0.83820919 ,0.83156926,\n",
    " 0.82999145, 0.83176648 ,0.83584248, 0.83630268])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "b1b5834c-3a80-4445-9144-3ecbaf04898a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=1886.0, pvalue=0.02801358583718831)"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(compas_fair_diff,compas_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "fe38a9ae-549a-44d0-9841-3cf5b8b0d28c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=5545.0, pvalue=0.18337688577278544)"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(compas_fair_diff,compas_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "9817e957-73da-4990-a746-877a4975c032",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=983.0, pvalue=1.1459571812467224e-07)"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(compas_fair_ratio,compas_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "12bb20a3-dc30-4a71-97b9-d346894a318c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=3706.0, pvalue=0.0015748076092037301)"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(compas_fair_ratio,compas_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "48917046-715d-461c-a069-365cd8141b1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.895680685825538e-18)"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(compas_fair_variation,compas_unfair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "dc98853f-1534-44a3-9de6-60c91af4776e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=1.0, pvalue=2.6390949369347782e-34)"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(compas_fair_variation,compas_unfair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "63652572-f0fb-45a2-b02c-0720bdbe9bcf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.888873574131199e-18)"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(compas_fair_accuracy,compas_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "a7103dbe-5bbe-4781-8506-7602ed21841f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=649.0, pvalue=2.1485228692037647e-26)"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(compas_fair_accuracy,compas_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "5d648cad-4542-4f03-abc1-45b1b7559ebe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.006485437699999985"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compas_fair_accuracy.mean()- compas_unfair_accuracy.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "8b1e8911-d92d-48b1-8202-0f7e5fb0279d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0036767847999999714"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compas_fair_diff.mean() - compas_unfair_diff.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "e7cac0fa-f861-41ea-aa44-142b7a9d24db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.02137861139999986"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compas_fair_ratio.mean() - compas_unfair_ratio.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "67c0c20a-e43e-45b0-89ee-6d7998ddac37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.06527353430000016"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compas_fair_variation.mean() - compas_unfair_variation.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0731fa28-5b6d-494e-beb7-3700d11a31b3",
   "metadata": {},
   "source": [
    "GPA race+sex Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "id": "610ff603-2950-4483-96d3-db8439512154",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_sex_fair_diff = np.array([0.16398017, 0.19865848, 0.20448048, 0.17474169, 0.17003019, 0.09428269,\n",
    " 0.1833384  ,0.1383376 , 0.20140903, 0.10891611, 0.16073009, 0.16498639,\n",
    " 0.20292424 ,0.18317197, 0.15869042, 0.17723    ,0.17423007, 0.17162698,\n",
    " 0.1950874  ,0.16818728, 0.19653619, 0.13289919 ,0.22980769, 0.19616241,\n",
    " 0.21014329 ,0.16761234, 0.15865787, 0.18338661 ,0.17575107 ,0.21448623,\n",
    " 0.13633963 ,0.14087214, 0.16305085, 0.1404569  ,0.17853774 ,0.14804502,\n",
    " 0.22100522, 0.15183212, 0.14140551, 0.18857704 ,0.15712859 ,0.15329154,\n",
    " 0.11676695, 0.10381819, 0.09471481, 0.15761179 ,0.18317197 ,0.17088175,\n",
    " 0.16931217, 0.21577665, 0.14598669, 0.14020448 ,0.15434434 ,0.16691729,\n",
    " 0.13289919, 0.15210395, 0.14969693, 0.21891534 ,0.22418301, 0.11536097,\n",
    " 0.11063308, 0.13104839, 0.17397733, 0.15339201 ,0.20979612, 0.18175433,\n",
    " 0.13882382, 0.14961069, 0.11524823, 0.12395418, 0.18317197, 0.16498639,\n",
    " 0.18442682, 0.19225008, 0.17001224, 0.18503401 ,0.20199147, 0.1701741,\n",
    " 0.1692454 , 0.16678287, 0.13415857, 0.20140903, 0.17419825, 0.14287722,\n",
    " 0.21908988, 0.11919911, 0.18633178, 0.17938001, 0.13969197, 0.16398017,\n",
    " 0.16900249, 0.17096569, 0.18573527, 0.16449121, 0.16530006, 0.11987768,\n",
    " 0.16730769, 0.13633963, 0.14642174, 0.17862359])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "id": "35174c83-9e0b-4c3b-8e2c-512f0c724560",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_sex_fair_ratio=np.array(\n",
    "[1.22494715, 1.29573023, 1.31012873 ,1.25444842 ,1.24596601, 1.12064988,\n",
    " 1.25448464, 1.1902142 , 1.28453021 ,1.13778544 ,1.22655288, 1.23459002,\n",
    " 1.30654513, 1.26589479, 1.22169984 ,1.25292198 ,1.2439221 , 1.25478645,\n",
    " 1.28498062, 1.2364142 , 1.28878788 ,1.18273639 ,1.3535503 , 1.28879467,\n",
    " 1.31159177, 1.23970368, 1.22060999 ,1.26226257 ,1.24927957, 1.32012871,\n",
    " 1.18576274, 1.19453772, 1.22114943 ,1.19491977 ,1.25505391, 1.21572274,\n",
    " 1.34624151, 1.21576143, 1.18786733 ,1.26813298 ,1.22155131, 1.21579876,\n",
    " 1.15370344, 1.13401984, 1.12312925 ,1.21532878 ,1.26589479 ,1.23923445,\n",
    " 1.23703704, 1.32680735, 1.19715729 ,1.19017836 ,1.22206685 ,1.24342105,\n",
    " 1.18273639, 1.20882068, 1.21018054 ,1.32837302 ,1.33076181 ,1.15647973,\n",
    " 1.14349438, 1.17473118, 1.24828015 ,1.21304446 ,1.30197927 ,1.25659434,\n",
    " 1.18766924, 1.21626891, 1.1536643  ,1.16256286 ,1.26589479 ,1.23459002,\n",
    " 1.26752022, 1.28320711, 1.24100636 ,1.26280193 ,1.29983108 ,1.24207865,\n",
    " 1.24406968, 1.23127225, 1.1813625  ,1.28453021 ,1.25142016 ,1.19206446,\n",
    " 1.34033379, 1.15098555, 1.27367481 ,1.25012142, 1.19079018 ,1.22494715,\n",
    " 1.23955693, 1.25185268, 1.26648974 ,1.2273849,  1.22620008 ,1.16346956,\n",
    " 1.23641304, 1.18576274, 1.19871522 ,1.26074938])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "id": "c1c22d8f-3764-489c-ba92-b161d3d4ccfb",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_sex_fair_variation=np.array(\n",
    "[0.16398017, 0.22863746, 0.21776777 ,0.17474169, 0.18701431, 0.15450538,\n",
    " 0.18844004, 0.15143695, 0.20140903 ,0.13941846, 0.18875601, 0.18032657,\n",
    " 0.21984038, 0.18317197, 0.16196255 ,0.18555987, 0.17423007, 0.21881108,\n",
    " 0.20190489 ,0.17019596, 0.19653619 ,0.17582283, 0.22980769, 0.19616241,\n",
    " 0.21014329, 0.18910804, 0.16063903 ,0.20746329, 0.18311262, 0.21448623,\n",
    " 0.13633963, 0.15086207, 0.16305085 ,0.15827944, 0.19314516, 0.20793034,\n",
    " 0.22100522, 0.1980999 , 0.17146595 ,0.20393048, 0.17390555, 0.16267105,\n",
    " 0.14879494, 0.10484612, 0.1294843  ,0.15761179, 0.18317197, 0.17088175,\n",
    " 0.16931217, 0.22863248, 0.14598669 ,0.14020448, 0.21886284, 0.19301335,\n",
    " 0.17582283, 0.15210395, 0.17323529 ,0.21891534, 0.22418301, 0.14249664,\n",
    " 0.15474539, 0.13104839, 0.17733884 ,0.15339201 ,0.20979612, 0.18175433,\n",
    " 0.13882382, 0.19553362, 0.12353085 ,0.14845693 ,0.18317197, 0.18032657,\n",
    " 0.20284167, 0.20479707, 0.17471063 ,0.18503401 ,0.20199147, 0.18698186,\n",
    " 0.17674245, 0.16678287, 0.13415857 ,0.20140903 ,0.20184484, 0.18825025,\n",
    " 0.24996355, 0.19448691, 0.18905695 ,0.17938001, 0.15873874, 0.16398017,\n",
    " 0.18879664, 0.19349409, 0.19053848 ,0.16449121, 0.18104338, 0.15795678,\n",
    " 0.16910979, 0.13633963, 0.14856997 ,0.18650213])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "id": "a32ac509-5d64-4413-8bc6-6a3970e7c809",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_sex_fair_accuracy=np.array(\n",
    "[0.83591149, 0.84139416, 0.83179949, 0.82220482 ,0.83101625, 0.83591149,\n",
    " 0.83473664, 0.82729587, 0.82240063, 0.83649892 ,0.84687684, 0.83591149,\n",
    " 0.8400235 , 0.82690425, 0.82984139, 0.83414921 ,0.83082044, 0.82670844,\n",
    " 0.83904445, 0.84315645, 0.83865283, 0.82964558 ,0.82729587, 0.83473664,\n",
    " 0.8319953 , 0.83238692, 0.83101625, 0.84374388 ,0.82729587, 0.83317016,\n",
    " 0.83845702, 0.82827492, 0.84158997, 0.82807911 ,0.83297435, 0.82435872,\n",
    " 0.83454083, 0.83591149, 0.83023301, 0.81319757 ,0.83277854, 0.8239671,\n",
    " 0.83591149, 0.84315645, 0.82768749, 0.83473664 ,0.82690425, 0.84061093,\n",
    " 0.83336597, 0.8339534 , 0.83649892, 0.84021931 ,0.82298806, 0.82200901,\n",
    " 0.82964558, 0.83571568, 0.83336597, 0.83904445 ,0.82161739, 0.83062463,\n",
    " 0.83317016, 0.83277854, 0.8400235 , 0.82925397 ,0.82161739, 0.83434502,\n",
    " 0.82905816, 0.82220482, 0.81515567, 0.82631682 ,0.82690425, 0.83591149,\n",
    " 0.84158997, 0.83297435, 0.82651263, 0.83375759 ,0.8278833 , 0.8278833,\n",
    " 0.82475034, 0.83082044, 0.82651263, 0.82240063 ,0.83336597, 0.83101625,\n",
    " 0.82651263, 0.83179949, 0.83179949, 0.84178578 ,0.84256902, 0.83591149,\n",
    " 0.83865283, 0.83023301, 0.8361073 , 0.8278833  ,0.82455453, 0.83904445,\n",
    " 0.83943607, 0.83845702, 0.83082044, 0.82905816])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "id": "796b72e0-1c20-4a67-a347-363d24d237f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_sex_unfair_diff=np.array(\n",
    "[0.18880493, 0.2425087 , 0.23192771, 0.18330409 ,0.2039275,  0.20069752,\n",
    " 0.22244341, 0.17536278, 0.24734645, 0.1702381  ,0.20231461, 0.21677705,\n",
    " 0.24678789, 0.20956836, 0.23609023, 0.23324868 ,0.24134812 ,0.21130952,\n",
    " 0.27894881, 0.22225274, 0.22845339, 0.18689963 ,0.25707229, 0.25502056,\n",
    " 0.20697351, 0.2270633 , 0.2438141 , 0.25957408 ,0.22620237, 0.19834711,\n",
    " 0.18079648, 0.24434779, 0.22872797, 0.21726981 ,0.28424865, 0.19858452,\n",
    " 0.22112412, 0.21170976, 0.20700831, 0.26031103 ,0.21830092, 0.21954023,\n",
    " 0.21439801, 0.19639786, 0.17183293, 0.19300138 ,0.20956836, 0.19647911,\n",
    " 0.24944037, 0.24859232, 0.15839922, 0.18890356 ,0.22468403, 0.21612364,\n",
    " 0.18689963, 0.22727814, 0.22221424, 0.26583082 ,0.2309057 , 0.15758869,\n",
    " 0.14988896, 0.22698186, 0.23928187, 0.22908994 ,0.23679234, 0.1882761,\n",
    " 0.20329429, 0.22177888, 0.154447  , 0.1998174  ,0.20956836, 0.21677705,\n",
    " 0.23238279, 0.26052912, 0.24813001, 0.19047619 ,0.25728489, 0.22827903,\n",
    " 0.26373325, 0.17057959, 0.21549877, 0.24734645, 0.28892128, 0.19189134,\n",
    " 0.28885952, 0.1705627 , 0.20679314, 0.18397503, 0.23950829, 0.18880493,\n",
    " 0.20078753, 0.23161583, 0.27981339, 0.18802651, 0.20209749, 0.18578406,\n",
    " 0.25054945, 0.18079648, 0.23268079, 0.21991495])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "id": "a8fbb4fb-5b66-4205-875d-16a843f75517",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_sex_unfair_ratio=np.array(\n",
    "[1.28058511, 1.40213467 ,1.38654618 ,1.27662254 ,1.32672256 ,1.30923801,\n",
    " 1.36716563, 1.26916148 ,1.41224409 ,1.25422222 ,1.31853789 ,1.3426476,\n",
    " 1.41718905, 1.33479823 ,1.38014528 ,1.3804175  ,1.39420193 ,1.33809524,\n",
    " 1.48898085, 1.34495477, 1.36963245 ,1.28738331 ,1.448309   ,1.42889822,\n",
    " 1.31785218, 1.36828559, 1.3999647  ,1.43154192 ,1.36560616 ,1.30545455,\n",
    " 1.26630833, 1.41664431, 1.3670286  ,1.35177016 ,1.51018989 ,1.31649408,\n",
    " 1.35229945, 1.34434719, 1.3259786  ,1.45879819 ,1.35379804 ,1.3576779,\n",
    " 1.333221  , 1.2998763 , 1.25676185 ,1.29360848 ,1.33479823 ,1.30966816,\n",
    " 1.41271044, 1.41699356, 1.23055886 ,1.29078413 ,1.36837731 ,1.35182919,\n",
    " 1.28738331, 1.3787969 , 1.36338564 ,1.46151184 ,1.36176291 ,1.23467012,\n",
    " 1.21342884, 1.37452007, 1.3997758  ,1.37551856 ,1.40362331 ,1.29152428,\n",
    " 1.31575497, 1.36381704, 1.22631838 ,1.31343905 ,1.33479823 ,1.3426476,\n",
    " 1.3834316 , 1.44615612, 1.41569834 ,1.28717949 ,1.44686323 ,1.36409061,\n",
    " 1.45736019, 1.24639273, 1.34574527 ,1.41224409 ,1.51857666 ,1.29996807,\n",
    " 1.51352803, 1.25040057, 1.32761609 ,1.2718437  ,1.39723326 ,1.28058511,\n",
    " 1.31521483, 1.38696792, 1.49247157 ,1.29272309 ,1.30744617 ,1.29163777,\n",
    " 1.42300557, 1.26630833, 1.37624979 ,1.36271686])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "id": "1b724c1d-169e-4230-9bbe-29ac9a45c1d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "gpa_race_sex_unfair_variation=np.array(\n",
    "[0.27464729, 0.29246895 ,0.32592593, 0.29004736 ,0.28954451, 0.26851915,\n",
    " 0.32485365, 0.24742102 ,0.28239247, 0.26035714 ,0.29079079, 0.29197005,\n",
    " 0.32749832, 0.27727161, 0.30166836, 0.33045106 ,0.32108844, 0.26388889,\n",
    " 0.37340775, 0.27027756, 0.29386154, 0.25320365 ,0.37363225, 0.31214116,\n",
    " 0.31914614, 0.28017226, 0.30078832, 0.33349624 ,0.28514112, 0.23437028,\n",
    " 0.21250363, 0.34759977, 0.31398437, 0.26533166 ,0.34285714, 0.28254902,\n",
    " 0.31527094, 0.27407407, 0.30676245, 0.32680401 ,0.33006867, 0.29441946,\n",
    " 0.26299309 ,0.28593064, 0.25055533, 0.26765734 ,0.27727161, 0.29986068,\n",
    " 0.32525264, 0.34262166, 0.21082656, 0.31190343 ,0.29402572, 0.30150376,\n",
    " 0.25320365, 0.32777778, 0.29848921, 0.36574757 ,0.28682488, 0.22846715,\n",
    " 0.19576818, 0.34632035, 0.28926473, 0.32776094 ,0.35210884, 0.27416667,\n",
    " 0.29653136, 0.33271865, 0.24985923 ,0.2614899  ,0.27727161, 0.29197005,\n",
    " 0.33540281, 0.3629183 , 0.30310078, 0.28410311 ,0.34529506, 0.27686203,\n",
    " 0.3611815 , 0.23356009, 0.30907948, 0.28239247 ,0.37333843, 0.23419242,\n",
    " 0.34659091, 0.23230212, 0.28249991, 0.24785544 ,0.31205882, 0.27464729,\n",
    " 0.2620036 , 0.31724933, 0.34681818, 0.28359016, 0.21312366, 0.29844683,\n",
    " 0.3413416 , 0.21250363, 0.31328626, 0.30716233])\n",
    "gpa_race_sex_unfair_accuracy=np.array( \n",
    "[0.85079303, 0.84687684 ,0.84531036, 0.83277854 ,0.83845702, 0.84452712,\n",
    " 0.84433131, 0.84080674 ,0.84354807, 0.84198159, 0.85098884, 0.84393969,\n",
    " 0.84335226, 0.83982769 ,0.8400235 , 0.84198159, 0.84021931, 0.83649892,\n",
    " 0.84628941, 0.85314275 ,0.84707265, 0.84335226, 0.84119836, 0.84393969,\n",
    " 0.8380654 , 0.84354807 ,0.84785588, 0.85607989, 0.84080674, 0.84296064,\n",
    " 0.84433131, 0.83904445 ,0.85040141, 0.84100255, 0.84256902, 0.83277854,\n",
    " 0.84296064, 0.84139416 ,0.84198159, 0.82984139, 0.83708635, 0.83865283,\n",
    " 0.84863912, 0.84844331 ,0.84178578, 0.84393969, 0.83982769, 0.84374388,\n",
    " 0.83728216, 0.8421774  ,0.85157627, 0.84491874, 0.84256902, 0.83473664,\n",
    " 0.84335226, 0.84883493 ,0.83943607, 0.8441355 , 0.84178578, 0.84296064,\n",
    " 0.85529665, 0.8441355  ,0.84883493, 0.83728216, 0.8319953 , 0.83963188,\n",
    " 0.84785588, 0.83649892 ,0.83708635, 0.83904445, 0.83982769, 0.84393969,\n",
    " 0.84863912, 0.84883493 ,0.84296064, 0.84550617, 0.83865283, 0.84139416,\n",
    " 0.83493245, 0.84491874 ,0.83786959 ,0.84354807, 0.84511455, 0.84021931,\n",
    " 0.84393969, 0.84687684 ,0.85000979 ,0.84668103, 0.85275113, 0.85079303,\n",
    " 0.84158997, 0.83649892 ,0.84433131 ,0.84374388, 0.84315645, 0.84237321,\n",
    " 0.84276483, 0.84433131, 0.85040141 ,0.83532407])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "edf66889-9a85-4c4d-bc20-b099cacdd9d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=12.0, pvalue=5.593433910723826e-18)"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_race_sex_fair_diff,gpa_race_sex_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "id": "227ac750-4317-490d-98ab-254b41bd76a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=1063.0, pvalue=6.682066773028819e-22)"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_race_sex_fair_diff,gpa_race_sex_unfair_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "id": "357a0027-3ece-4844-bbde-59fb953a7ba6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=3.0, pvalue=4.264162277244541e-18)"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_race_sex_fair_ratio,gpa_race_sex_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "id": "7deca0d2-be31-4df8-8293-7aa83b6d5440",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=773.0, pvalue=5.3169108387954825e-25)"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_race_sex_fair_ratio,gpa_race_sex_unfair_ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "id": "0da79e52-f2d7-4ddf-92bc-d76b2bb5a100",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.8945820011567e-18)"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_race_sex_fair_variation,gpa_race_sex_unfair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "id": "8668fce4-84a3-44a6-b4a8-d2660afbaeb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=86.0, pvalue=3.3175676240036885e-33)"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_race_sex_fair_variation,gpa_race_sex_unfair_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "id": "40d26a46-0cbb-4740-8755-c92d9129b1e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=3.889312402158803e-18)"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wilcoxon(gpa_race_sex_fair_accuracy,gpa_race_sex_unfair_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "id": "fb149c51-bafa-4c60-bd56-038b6c3748f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=848.0, pvalue=3.49541388071285e-24)"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mannwhitneyu(gpa_race_sex_fair_accuracy,gpa_race_sex_unfair_accuracy)"
   ]
  }
 ],
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