EMG_Strain_Indicator_Example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Demonstratoin of EMG Indicator Relationship with Strain\n",
    "\n",
    "In this notebook, I demo that our chosen indicator of strain injury, the average high-frequency PSD of an EMG, is a good indicator of strain. \n",
    "\n",
    "We collect data while subjects clench their hand strongly with maximal grip exertion and observe the change in the EMG indicator statistic over time. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit  \n",
    "from scipy import stats \n",
    "import uncertainties as unc\n",
    "import uncertainties.unumpy as unp\n",
    "df = pd.read_excel(\"_data/Validation Data.xlsx\") \n",
    "data = df.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation Data:\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>AverageExtensor</th>\n",
       "      <th>AverageFlexor</th>\n",
       "      <th>StandardDev Extensor</th>\n",
       "      <th>StandardDev Flexor</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>2.180952</td>\n",
       "      <td>1.388414</td>\n",
       "      <td>0.689132</td>\n",
       "      <td>0.626056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1.871641</td>\n",
       "      <td>0.982701</td>\n",
       "      <td>0.613529</td>\n",
       "      <td>0.448125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1.576580</td>\n",
       "      <td>1.402149</td>\n",
       "      <td>0.333633</td>\n",
       "      <td>0.308973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1.307387</td>\n",
       "      <td>1.348856</td>\n",
       "      <td>0.903853</td>\n",
       "      <td>0.749291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>1.123944</td>\n",
       "      <td>1.153611</td>\n",
       "      <td>0.901007</td>\n",
       "      <td>0.268027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>1.139771</td>\n",
       "      <td>1.468687</td>\n",
       "      <td>0.675131</td>\n",
       "      <td>1.055553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1.361938</td>\n",
       "      <td>0.660053</td>\n",
       "      <td>1.348512</td>\n",
       "      <td>0.845283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>1.106798</td>\n",
       "      <td>1.011276</td>\n",
       "      <td>0.586705</td>\n",
       "      <td>0.884075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>1.232022</td>\n",
       "      <td>0.914680</td>\n",
       "      <td>0.157152</td>\n",
       "      <td>0.353176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>0.596450</td>\n",
       "      <td>0.986553</td>\n",
       "      <td>0.584054</td>\n",
       "      <td>0.886424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>1.286948</td>\n",
       "      <td>0.896629</td>\n",
       "      <td>0.622517</td>\n",
       "      <td>1.778483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>11</td>\n",
       "      <td>0.874309</td>\n",
       "      <td>0.611144</td>\n",
       "      <td>0.666194</td>\n",
       "      <td>1.037045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>12</td>\n",
       "      <td>0.810610</td>\n",
       "      <td>0.408791</td>\n",
       "      <td>0.271370</td>\n",
       "      <td>0.676419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>13</td>\n",
       "      <td>0.747792</td>\n",
       "      <td>1.382722</td>\n",
       "      <td>0.314924</td>\n",
       "      <td>0.565558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>14</td>\n",
       "      <td>0.330707</td>\n",
       "      <td>1.301354</td>\n",
       "      <td>0.334888</td>\n",
       "      <td>0.754674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>15</td>\n",
       "      <td>0.650493</td>\n",
       "      <td>0.782206</td>\n",
       "      <td>0.682818</td>\n",
       "      <td>1.212984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>16</td>\n",
       "      <td>0.349939</td>\n",
       "      <td>0.953095</td>\n",
       "      <td>0.511262</td>\n",
       "      <td>0.602680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>17</td>\n",
       "      <td>0.599156</td>\n",
       "      <td>0.507360</td>\n",
       "      <td>0.476431</td>\n",
       "      <td>0.472124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>18</td>\n",
       "      <td>-0.063325</td>\n",
       "      <td>0.608596</td>\n",
       "      <td>0.346620</td>\n",
       "      <td>0.888334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>19</td>\n",
       "      <td>0.142416</td>\n",
       "      <td>0.337058</td>\n",
       "      <td>0.120496</td>\n",
       "      <td>0.753589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>20</td>\n",
       "      <td>0.666656</td>\n",
       "      <td>0.748811</td>\n",
       "      <td>0.498759</td>\n",
       "      <td>0.637098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>21</td>\n",
       "      <td>0.809773</td>\n",
       "      <td>0.930686</td>\n",
       "      <td>0.902776</td>\n",
       "      <td>1.170690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>22</td>\n",
       "      <td>0.301890</td>\n",
       "      <td>-0.108629</td>\n",
       "      <td>0.566594</td>\n",
       "      <td>0.392525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>23</td>\n",
       "      <td>0.389159</td>\n",
       "      <td>0.178854</td>\n",
       "      <td>0.973343</td>\n",
       "      <td>0.704515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>24</td>\n",
       "      <td>0.453184</td>\n",
       "      <td>-0.648233</td>\n",
       "      <td>1.399426</td>\n",
       "      <td>0.374123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>25</td>\n",
       "      <td>0.088161</td>\n",
       "      <td>-0.461997</td>\n",
       "      <td>0.625637</td>\n",
       "      <td>0.132912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>26</td>\n",
       "      <td>-0.065567</td>\n",
       "      <td>0.503265</td>\n",
       "      <td>0.278279</td>\n",
       "      <td>0.283616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>27</td>\n",
       "      <td>-0.277952</td>\n",
       "      <td>-0.266877</td>\n",
       "      <td>0.343535</td>\n",
       "      <td>0.369346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>28</td>\n",
       "      <td>-0.530001</td>\n",
       "      <td>-0.477848</td>\n",
       "      <td>0.161690</td>\n",
       "      <td>0.170183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>29</td>\n",
       "      <td>-0.388075</td>\n",
       "      <td>-0.564213</td>\n",
       "      <td>0.300910</td>\n",
       "      <td>0.435033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>30</td>\n",
       "      <td>-0.477851</td>\n",
       "      <td>-0.382566</td>\n",
       "      <td>0.303773</td>\n",
       "      <td>0.421307</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>31</td>\n",
       "      <td>-0.072840</td>\n",
       "      <td>-0.178337</td>\n",
       "      <td>0.883623</td>\n",
       "      <td>0.902834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>32</td>\n",
       "      <td>-0.905625</td>\n",
       "      <td>-0.884611</td>\n",
       "      <td>0.611167</td>\n",
       "      <td>0.104824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>33</td>\n",
       "      <td>-0.620437</td>\n",
       "      <td>-0.948726</td>\n",
       "      <td>0.289720</td>\n",
       "      <td>0.239579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>34</td>\n",
       "      <td>-0.522371</td>\n",
       "      <td>-0.817990</td>\n",
       "      <td>0.625451</td>\n",
       "      <td>0.368313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>35</td>\n",
       "      <td>-0.715942</td>\n",
       "      <td>-0.761668</td>\n",
       "      <td>0.298280</td>\n",
       "      <td>0.334617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>36</td>\n",
       "      <td>-0.753318</td>\n",
       "      <td>-0.554245</td>\n",
       "      <td>0.251605</td>\n",
       "      <td>0.136069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>37</td>\n",
       "      <td>-0.780043</td>\n",
       "      <td>-0.790978</td>\n",
       "      <td>0.348244</td>\n",
       "      <td>0.553732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>38</td>\n",
       "      <td>-0.640197</td>\n",
       "      <td>-0.420739</td>\n",
       "      <td>0.483193</td>\n",
       "      <td>0.423678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>39</td>\n",
       "      <td>-0.838726</td>\n",
       "      <td>-0.658068</td>\n",
       "      <td>0.469513</td>\n",
       "      <td>0.115690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>40</td>\n",
       "      <td>-0.715675</td>\n",
       "      <td>-0.749475</td>\n",
       "      <td>0.486163</td>\n",
       "      <td>0.232724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>41</td>\n",
       "      <td>-0.471784</td>\n",
       "      <td>-0.913015</td>\n",
       "      <td>0.895480</td>\n",
       "      <td>0.372751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>42</td>\n",
       "      <td>-0.213794</td>\n",
       "      <td>-0.511089</td>\n",
       "      <td>0.753993</td>\n",
       "      <td>0.447577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>43</td>\n",
       "      <td>-0.771447</td>\n",
       "      <td>-0.532880</td>\n",
       "      <td>0.261153</td>\n",
       "      <td>0.300300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>44</td>\n",
       "      <td>-0.813295</td>\n",
       "      <td>-0.299278</td>\n",
       "      <td>0.215314</td>\n",
       "      <td>0.566524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>45</td>\n",
       "      <td>-0.513353</td>\n",
       "      <td>-0.686057</td>\n",
       "      <td>0.921638</td>\n",
       "      <td>0.875635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>46</td>\n",
       "      <td>-0.493864</td>\n",
       "      <td>-0.490271</td>\n",
       "      <td>1.085175</td>\n",
       "      <td>0.698516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>47</td>\n",
       "      <td>-0.670637</td>\n",
       "      <td>-1.147785</td>\n",
       "      <td>0.459010</td>\n",
       "      <td>0.103487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>48</td>\n",
       "      <td>-0.838568</td>\n",
       "      <td>-0.449184</td>\n",
       "      <td>0.442476</td>\n",
       "      <td>1.397358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>49</td>\n",
       "      <td>-0.680453</td>\n",
       "      <td>-0.646240</td>\n",
       "      <td>0.479226</td>\n",
       "      <td>0.922875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>50</td>\n",
       "      <td>-0.772375</td>\n",
       "      <td>-0.522854</td>\n",
       "      <td>0.817685</td>\n",
       "      <td>1.051157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>51</td>\n",
       "      <td>-0.993595</td>\n",
       "      <td>-0.586789</td>\n",
       "      <td>0.168470</td>\n",
       "      <td>0.534713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>52</td>\n",
       "      <td>-0.654144</td>\n",
       "      <td>-0.731827</td>\n",
       "      <td>0.787757</td>\n",
       "      <td>0.599389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>53</td>\n",
       "      <td>-0.549108</td>\n",
       "      <td>-0.377748</td>\n",
       "      <td>1.011578</td>\n",
       "      <td>1.365544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>54</td>\n",
       "      <td>-0.824451</td>\n",
       "      <td>-0.811810</td>\n",
       "      <td>0.364287</td>\n",
       "      <td>0.429010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>55</td>\n",
       "      <td>-0.777662</td>\n",
       "      <td>-0.340383</td>\n",
       "      <td>0.430119</td>\n",
       "      <td>0.558847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>56</td>\n",
       "      <td>-0.905796</td>\n",
       "      <td>-0.419654</td>\n",
       "      <td>0.319531</td>\n",
       "      <td>0.504334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>57</td>\n",
       "      <td>-0.981100</td>\n",
       "      <td>-0.894427</td>\n",
       "      <td>0.096815</td>\n",
       "      <td>0.349474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>58</td>\n",
       "      <td>-1.160068</td>\n",
       "      <td>-1.083956</td>\n",
       "      <td>0.459996</td>\n",
       "      <td>0.395607</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Time  AverageExtensor  AverageFlexor  StandardDev Extensor  \\\n",
       "0      0         2.180952       1.388414              0.689132   \n",
       "1      1         1.871641       0.982701              0.613529   \n",
       "2      2         1.576580       1.402149              0.333633   \n",
       "3      3         1.307387       1.348856              0.903853   \n",
       "4      4         1.123944       1.153611              0.901007   \n",
       "5      5         1.139771       1.468687              0.675131   \n",
       "6      6         1.361938       0.660053              1.348512   \n",
       "7      7         1.106798       1.011276              0.586705   \n",
       "8      8         1.232022       0.914680              0.157152   \n",
       "9      9         0.596450       0.986553              0.584054   \n",
       "10    10         1.286948       0.896629              0.622517   \n",
       "11    11         0.874309       0.611144              0.666194   \n",
       "12    12         0.810610       0.408791              0.271370   \n",
       "13    13         0.747792       1.382722              0.314924   \n",
       "14    14         0.330707       1.301354              0.334888   \n",
       "15    15         0.650493       0.782206              0.682818   \n",
       "16    16         0.349939       0.953095              0.511262   \n",
       "17    17         0.599156       0.507360              0.476431   \n",
       "18    18        -0.063325       0.608596              0.346620   \n",
       "19    19         0.142416       0.337058              0.120496   \n",
       "20    20         0.666656       0.748811              0.498759   \n",
       "21    21         0.809773       0.930686              0.902776   \n",
       "22    22         0.301890      -0.108629              0.566594   \n",
       "23    23         0.389159       0.178854              0.973343   \n",
       "24    24         0.453184      -0.648233              1.399426   \n",
       "25    25         0.088161      -0.461997              0.625637   \n",
       "26    26        -0.065567       0.503265              0.278279   \n",
       "27    27        -0.277952      -0.266877              0.343535   \n",
       "28    28        -0.530001      -0.477848              0.161690   \n",
       "29    29        -0.388075      -0.564213              0.300910   \n",
       "30    30        -0.477851      -0.382566              0.303773   \n",
       "31    31        -0.072840      -0.178337              0.883623   \n",
       "32    32        -0.905625      -0.884611              0.611167   \n",
       "33    33        -0.620437      -0.948726              0.289720   \n",
       "34    34        -0.522371      -0.817990              0.625451   \n",
       "35    35        -0.715942      -0.761668              0.298280   \n",
       "36    36        -0.753318      -0.554245              0.251605   \n",
       "37    37        -0.780043      -0.790978              0.348244   \n",
       "38    38        -0.640197      -0.420739              0.483193   \n",
       "39    39        -0.838726      -0.658068              0.469513   \n",
       "40    40        -0.715675      -0.749475              0.486163   \n",
       "41    41        -0.471784      -0.913015              0.895480   \n",
       "42    42        -0.213794      -0.511089              0.753993   \n",
       "43    43        -0.771447      -0.532880              0.261153   \n",
       "44    44        -0.813295      -0.299278              0.215314   \n",
       "45    45        -0.513353      -0.686057              0.921638   \n",
       "46    46        -0.493864      -0.490271              1.085175   \n",
       "47    47        -0.670637      -1.147785              0.459010   \n",
       "48    48        -0.838568      -0.449184              0.442476   \n",
       "49    49        -0.680453      -0.646240              0.479226   \n",
       "50    50        -0.772375      -0.522854              0.817685   \n",
       "51    51        -0.993595      -0.586789              0.168470   \n",
       "52    52        -0.654144      -0.731827              0.787757   \n",
       "53    53        -0.549108      -0.377748              1.011578   \n",
       "54    54        -0.824451      -0.811810              0.364287   \n",
       "55    55        -0.777662      -0.340383              0.430119   \n",
       "56    56        -0.905796      -0.419654              0.319531   \n",
       "57    57        -0.981100      -0.894427              0.096815   \n",
       "58    58        -1.160068      -1.083956              0.459996   \n",
       "\n",
       "    StandardDev Flexor  \n",
       "0             0.626056  \n",
       "1             0.448125  \n",
       "2             0.308973  \n",
       "3             0.749291  \n",
       "4             0.268027  \n",
       "5             1.055553  \n",
       "6             0.845283  \n",
       "7             0.884075  \n",
       "8             0.353176  \n",
       "9             0.886424  \n",
       "10            1.778483  \n",
       "11            1.037045  \n",
       "12            0.676419  \n",
       "13            0.565558  \n",
       "14            0.754674  \n",
       "15            1.212984  \n",
       "16            0.602680  \n",
       "17            0.472124  \n",
       "18            0.888334  \n",
       "19            0.753589  \n",
       "20            0.637098  \n",
       "21            1.170690  \n",
       "22            0.392525  \n",
       "23            0.704515  \n",
       "24            0.374123  \n",
       "25            0.132912  \n",
       "26            0.283616  \n",
       "27            0.369346  \n",
       "28            0.170183  \n",
       "29            0.435033  \n",
       "30            0.421307  \n",
       "31            0.902834  \n",
       "32            0.104824  \n",
       "33            0.239579  \n",
       "34            0.368313  \n",
       "35            0.334617  \n",
       "36            0.136069  \n",
       "37            0.553732  \n",
       "38            0.423678  \n",
       "39            0.115690  \n",
       "40            0.232724  \n",
       "41            0.372751  \n",
       "42            0.447577  \n",
       "43            0.300300  \n",
       "44            0.566524  \n",
       "45            0.875635  \n",
       "46            0.698516  \n",
       "47            0.103487  \n",
       "48            1.397358  \n",
       "49            0.922875  \n",
       "50            1.051157  \n",
       "51            0.534713  \n",
       "52            0.599389  \n",
       "53            1.365544  \n",
       "54            0.429010  \n",
       "55            0.558847  \n",
       "56            0.504334  \n",
       "57            0.349474  \n",
       "58            0.395607  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Validation Data:\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regressionStats(x, y, xName, xUnit, yName, yUnit, popType):\n",
    "    # get R^2 value\n",
    "    corrcoef = np.corrcoef(x, y)\n",
    "    corrxy = corrcoef[0,1]\n",
    "    r2 = corrxy**2\n",
    "\n",
    "    # get regression parameter values from scipy library function\n",
    "    def f(x, a, b):\n",
    "        return a * x + b\n",
    "    poptimal, pcovariance = curve_fit(f, x, y)\n",
    "    a = poptimal[0]\n",
    "    b = poptimal[1]\n",
    "\n",
    "    # calculate parameters 95% confidence interval\n",
    "    aCI ,bCI = unc.correlated_values(poptimal, pcovariance)\n",
    "\n",
    "    # calculate regression 95% confidence interval\n",
    "    xReg = np.linspace(min(x), max(x), 100)\n",
    "    yReg = aCI*xReg + bCI\n",
    "    nomReg = unp.nominal_values(yReg)\n",
    "    stdReg = unp.std_devs(yReg)\n",
    "\n",
    "    # plot\n",
    "    plt.plot(x, y, 'o', c='blue', label='Data')\n",
    "    plt.plot(x, a*x + b, c='black', label='Regression Line')\n",
    "    plt.plot(xReg, nomReg - 1.96 * stdReg, c='red', label='95% Confidence Region')\n",
    "    plt.plot(xReg, nomReg + 1.96 * stdReg, c='red')\n",
    "    plt.title(\"Normalized Power v. Time for Extensor Radialis Brevis\")\n",
    "    plt.ylabel(yName + \" (\" + yUnit + \")\")\n",
    "    plt.xlabel(xName + \" (\" + xUnit + \")\")\n",
    "    plt.ylim((-2,3))\n",
    "    plt.legend(loc='best')\n",
    "    plt.savefig('extensorCI.png', dpi=300)\n",
    "    plt.show()\n",
    "    \n",
    "    # print r2 and parameter confidence intervals\n",
    "    print(\"R Squared:\", r2)\n",
    "    print('Regresion Parameter means with 95% Confidence Interval:')\n",
    "    print('slope (m): ' + str(aCI))\n",
    "    print('intercept (b): ' + str(bCI))\n",
    "    \n",
    "    # print data interpretation message\n",
    "    r2Percent = round(r2*100,2)\n",
    "    if (r2 < 0.5):\n",
    "        print(\"\\nINTERPRETATION: The R^2 value shows that only \" + str(r2Percent) + \"% of the variability in \"\n",
    "              + yName + \" can be explained by \" + xName + \".\")\n",
    "    elif (r2 < 0.8): \n",
    "        print('\\nINTERPRETATION: The R^2 value shows that ' + str(r2Percent) + '% of the variability in '\n",
    "              + str(yName) + ' can be explained by ' + str(xName) + '.')\n",
    "    else: \n",
    "        print('\\nINTERPRETATION: The R^2 value shows that a large percent (' + str(r2Percent) + '%) of the variability in '\n",
    "              + str(yName) + ' can be explained by ' + str(xName) + '.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ttestStat(metric, d1, d2, sigLevel):\n",
    "    statistic, pvalue = stats.ttest_ind(d1, d2, equal_var = False)\n",
    "\n",
    "    print(\"HYPOTHESES:\")\n",
    "    print(\"Null Hypothesis: \\u03BC Normal \" + metric + \" = \\u03BC SA \" + metric)\n",
    "    print(\"Alternative Hypothesis: \\u03BC Normal \" + metric + \" != \\u03BC SA \" + metric)\n",
    "    print(\"Significance level: \\u03B1 = \" + str(sigLevel) + \"\\n\")\n",
    "\n",
    "    print(\"TEST: 2-sided t-test with unknown, unequal variance\\n\")\n",
    "\n",
    "\n",
    "    print(\"RESULT: t-stat = \" + str(statistic) + \", p-value = \" + str(pvalue) + \"\\n\")\n",
    "\n",
    "    if (pvalue < sigLevel):\n",
    "        print(\"CONCLUSION: Since p < \\u03B1 = \" + str(sigLevel) + \", we reject the null hypothesis.\" + \n",
    "              \" Thus, there is sufficient evidence to believe that the populations have different mean \" + metric + \".\")\n",
    "    else:\n",
    "        print(\"CONCLUSION: Since p > \\u03B1 = \" + str(sigLevel) + \", we fail to reject the null hypothesis.\" + \n",
    "              \" Thus, there is insufficient evidence that the populations have different mean \" + metric + \".\")\n",
    "\n",
    "    plt1 = sns.violinplot(x='popType',y=metric, data=alldf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R Squared: 0.8455057951261857\n",
      "Regresion Parameter means with 95% Confidence Interval:\n",
      "slope (m): -0.0456+/-0.0026\n",
      "intercept (b): 1.33+/-0.09\n",
      "\n",
      "INTERPRETATION: The R^2 value shows that a large percent (84.55%) of the variability in Average Extensor Power can be explained by Time.\n"
     ]
    }
   ],
   "source": [
    "# Normal HR vs. RMSSD\n",
    "regressionStats(df.Time, df.AverageExtensor, \"Time\", \"s\", \"Average Extensor Power\", \"Standard Deviations\", \"Normalized\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R Squared: 0.7476548966099626\n",
      "Regresion Parameter means with 95% Confidence Interval:\n",
      "slope (m): -0.0403+/-0.0031\n",
      "intercept (b): 1.17+/-0.10\n",
      "\n",
      "INTERPRETATION: The R^2 value shows that 74.77% of the variability in Average Flexor Power can be explained by Time.\n"
     ]
    }
   ],
   "source": [
    "# SA HR vs. RMSSD\n",
    "regressionStats(df.Time, df.AverageFlexor, \"Time\", \"s\", \"Average Flexor Power\", \"Standard Deviations\", \"Normalized\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "There is a significant trend in the average flexor and extensor muscle EMG powers as exertion time increases. This means change in the power of this frequency band could be a good predictor of muscle over-exertion."
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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