PairedDifferenceT-test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performing the Paired Difference T-test to test the blood pressure results before and after the intervention are statistically significant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.preprocessing import scale\n",
    "\n",
    "from scipy import stats\n",
    "import researchpy as rp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>patient</th>\n",
       "      <th>sex</th>\n",
       "      <th>agegrp</th>\n",
       "      <th>bp_before</th>\n",
       "      <th>bp_after</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Male</td>\n",
       "      <td>30-45</td>\n",
       "      <td>143</td>\n",
       "      <td>153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>30-45</td>\n",
       "      <td>163</td>\n",
       "      <td>170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Male</td>\n",
       "      <td>30-45</td>\n",
       "      <td>153</td>\n",
       "      <td>168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>Male</td>\n",
       "      <td>30-45</td>\n",
       "      <td>153</td>\n",
       "      <td>142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>Male</td>\n",
       "      <td>30-45</td>\n",
       "      <td>146</td>\n",
       "      <td>141</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   patient   sex agegrp  bp_before  bp_after\n",
       "0        1  Male  30-45        143       153\n",
       "1        2  Male  30-45        163       170\n",
       "2        3  Male  30-45        153       168\n",
       "3        4  Male  30-45        153       142\n",
       "4        5  Male  30-45        146       141"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bp_reading = pd.read_csv('datasets/blood_pressure.csv')\n",
    "bp_reading.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(120, 5)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bp_reading.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>patient</th>\n",
       "      <td>120.0</td>\n",
       "      <td>60.500000</td>\n",
       "      <td>34.785054</td>\n",
       "      <td>1.0</td>\n",
       "      <td>30.75</td>\n",
       "      <td>60.5</td>\n",
       "      <td>90.25</td>\n",
       "      <td>120.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bp_before</th>\n",
       "      <td>120.0</td>\n",
       "      <td>156.450000</td>\n",
       "      <td>11.389845</td>\n",
       "      <td>138.0</td>\n",
       "      <td>147.00</td>\n",
       "      <td>154.5</td>\n",
       "      <td>164.00</td>\n",
       "      <td>185.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bp_after</th>\n",
       "      <td>120.0</td>\n",
       "      <td>151.358333</td>\n",
       "      <td>14.177622</td>\n",
       "      <td>125.0</td>\n",
       "      <td>140.75</td>\n",
       "      <td>149.5</td>\n",
       "      <td>161.00</td>\n",
       "      <td>185.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           count        mean        std    min     25%    50%     75%    max\n",
       "patient    120.0   60.500000  34.785054    1.0   30.75   60.5   90.25  120.0\n",
       "bp_before  120.0  156.450000  11.389845  138.0  147.00  154.5  164.00  185.0\n",
       "bp_after   120.0  151.358333  14.177622  125.0  140.75  149.5  161.00  185.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bp_reading.describe().T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Objective**\n",
    "\n",
    "Using p-test to see if whether the difference in the mean differ after or before the intervention is statistically significant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bp_reading[['bp_before', 'bp_after']].boxplot(figsize=(12, 8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LeveneResult(statistic=4.863729003161597, pvalue=0.028383666362347747)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.levene(bp_reading['bp_after'], bp_reading['bp_before'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The p-value is 2% which means the variance is different across these two samples. Levenes test tells us that we can't use Independet T-test to test the differences in the means between these two samples of data. And we need to use another test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>patient</th>\n",
       "      <th>sex</th>\n",
       "      <th>agegrp</th>\n",
       "      <th>bp_before</th>\n",
       "      <th>bp_after</th>\n",
       "      <th>bp_diff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Male</td>\n",
       "      <td>30-45</td>\n",
       "      <td>143</td>\n",
       "      <td>153</td>\n",
       "      <td>0.906743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>30-45</td>\n",
       "      <td>163</td>\n",
       "      <td>170</td>\n",
       "      <td>0.726496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Male</td>\n",
       "      <td>30-45</td>\n",
       "      <td>153</td>\n",
       "      <td>168</td>\n",
       "      <td>1.207155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>Male</td>\n",
       "      <td>30-45</td>\n",
       "      <td>153</td>\n",
       "      <td>142</td>\n",
       "      <td>-0.354987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>Male</td>\n",
       "      <td>30-45</td>\n",
       "      <td>146</td>\n",
       "      <td>141</td>\n",
       "      <td>0.005508</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   patient   sex agegrp  bp_before  bp_after   bp_diff\n",
       "0        1  Male  30-45        143       153  0.906743\n",
       "1        2  Male  30-45        163       170  0.726496\n",
       "2        3  Male  30-45        153       168  1.207155\n",
       "3        4  Male  30-45        153       142 -0.354987\n",
       "4        5  Male  30-45        146       141  0.005508"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Caclulating the residuals (difference)\n",
    "\n",
    "bp_reading['bp_diff'] = scale(bp_reading['bp_after'] - bp_reading['bp_before'])\n",
    "bp_reading.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seeing if these residuals are normally distributed using histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<AxesSubplot:title={'center':'bp_diff'}>]], dtype=object)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bp_reading[['bp_diff']].hist(figsize=(12, 8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Q-Q plot to see if the distribution is normal or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "stats.probplot(bp_reading['bp_diff'], plot=plt)\n",
    "plt.title('Blood pressure difference using Q-Q plot')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again performing Shapiro Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9926842451095581, 0.7841846942901611)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.shapiro(bp_reading['bp_diff'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, the residuals are normally distributed because the results are not significant as the p-value is 78%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the *rel* function of SciPy library to perform independent test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_relResult(statistic=-3.3371870510833657, pvalue=0.0011297914644840823)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_rel(bp_reading['bp_after'], bp_reading['bp_before'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The p-value is very much under the 5% threshold which means the test is significant.\n",
    "\n",
    "Since the above tests are not reliable, we further test with researchpy library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Wilcoxon signed-rank test</th>\n",
       "      <th>results</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mean for bp_after =</td>\n",
       "      <td>151.358333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mean for bp_before =</td>\n",
       "      <td>156.450000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>W value =</td>\n",
       "      <td>2234.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Z value =</td>\n",
       "      <td>-3.191600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Two sided p value =</td>\n",
       "      <td>0.001400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>r =</td>\n",
       "      <td>-0.206000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Wilcoxon signed-rank test      results\n",
       "0      Mean for bp_after =    151.358333\n",
       "1     Mean for bp_before =    156.450000\n",
       "2                W value =   2234.500000\n",
       "3                Z value =     -3.191600\n",
       "4      Two sided p value =      0.001400\n",
       "5                      r =     -0.206000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rp.ttest(bp_reading['bp_after'], bp_reading['bp_before'],\n",
    "        paired=True, equal_variances=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wilcoxon signed-rank test compares the medians between the two samples rather than the mean. \n",
    "\n",
    "The **W value** and **p value** tells that the differences in the medians between the paired samples are significant. The intervention performed had an impact on the individuals blood pressures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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    "name": "ipython",
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