Doing Things in Python That You'd Normally Do in Excel - Data Analysis for Strength & Conditioning Coaches (Turner et al., 2015).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Original Paper\n",
    "\n",
    "Turner et al. (2015). **Data Analysis for Strength and conditioning coaches: Using excel to analyze reliability, differences, and relationships.** *Strength Cond J*; 37(1): 76-83.\n",
    "\n",
    "https://www.researchgate.net/publication/272507171_Data_Analysis_for_Strength_and_Conditioning_Coaches_Using_Excel_to_Analyze_Reliability_Differences_and_Relationships\n",
    "\n",
    "#### Blog Post\n",
    "\n",
    "http://optimumsportsperformance.com/blog/doing-things-in-python-that-youd-normally-do-in-excel-data-analysis-for-strength-conditioning-coaches-turner-et-al-2015/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Data from Paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "dat = pd.DataFrame()\n",
    "dat['athlete'] = np.arange(start = 1, stop = 25, step = 1)\n",
    "dat['test_session'] = np.repeat(a = 1, repeats = 24)\n",
    "dat['cmj_1'] = [38.1,34.1,42.8,50.4,37,42.1,44.5,37.9,43.6,35.4,45.3,46.6,30.2,50.8,41,43.7,43.6,43.6,51.6,27.8,29,29,30.3,34.9]\n",
    "dat['cmj_2'] = [43.6,35.7,42.2,52.2,36.1,40.7,42.3,33.3,44.9,40.1,44.4,47.7,31,51.2,46.7,40.4,44.1,44.8,50.4,28.5,28.3,27.7,35.7,36.1]\n",
    "dat['cmj_3'] = [47.7,36,41.9,52.2,36.9,45.1,45.2,39.6,37.4,39.5,43.9,47.7,31.5,53.7,36.4,43,48.9,43.5,61.6,28.7,30.9,26.3,34.2,35.4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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>athlete</th>\n",
       "      <th>test_session</th>\n",
       "      <th>cmj_1</th>\n",
       "      <th>cmj_2</th>\n",
       "      <th>cmj_3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>38.1</td>\n",
       "      <td>43.6</td>\n",
       "      <td>47.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>34.1</td>\n",
       "      <td>35.7</td>\n",
       "      <td>36.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.2</td>\n",
       "      <td>41.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>50.4</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.1</td>\n",
       "      <td>36.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>42.1</td>\n",
       "      <td>40.7</td>\n",
       "      <td>45.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>44.5</td>\n",
       "      <td>42.3</td>\n",
       "      <td>45.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>37.9</td>\n",
       "      <td>33.3</td>\n",
       "      <td>39.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>43.6</td>\n",
       "      <td>44.9</td>\n",
       "      <td>37.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>35.4</td>\n",
       "      <td>40.1</td>\n",
       "      <td>39.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   athlete  test_session  cmj_1  cmj_2  cmj_3\n",
       "0        1             1   38.1   43.6   47.7\n",
       "1        2             1   34.1   35.7   36.0\n",
       "2        3             1   42.8   42.2   41.9\n",
       "3        4             1   50.4   52.2   52.2\n",
       "4        5             1   37.0   36.1   36.9\n",
       "5        6             1   42.1   40.7   45.1\n",
       "6        7             1   44.5   42.3   45.2\n",
       "7        8             1   37.9   33.3   39.6\n",
       "8        9             1   43.6   44.9   37.4\n",
       "9       10             1   35.4   40.1   39.5"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dat.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explore Basic Features of the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.frame.DataFrame"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Note that we created a pandas data frame\n",
    "\n",
    "type(dat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# How many rows?\n",
    "\n",
    "len(dat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24, 5)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rows x Columns\n",
    "\n",
    "dat.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['athlete', 'test_session', 'cmj_1', 'cmj_2', 'cmj_3'], dtype='object')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Column names\n",
    "\n",
    "dat.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get Mean & SD from Each CMJ Column"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1) Define a function for calculating our summary stats with one line of code**\n",
    "\n",
    "**2) Confirm that the stats are the same as that which is reported in the paper**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "## function for summary stats\n",
    "\n",
    "def summary_stats(val):\n",
    "    \n",
    "    avg = val.mean()\n",
    "    sd = val.std()\n",
    "    \n",
    "    results = [[\"CMJ Avg\", round(avg, 1)], [\"CMJ SD\", round(sd, 1)]]\n",
    "    \n",
    "    return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['CMJ Avg', 39.7], ['CMJ SD', 7.2]]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# CMJ 1\n",
    "\n",
    "summary_stats(dat['cmj_1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['CMJ Avg', 40.3], ['CMJ SD', 7.2]]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# CMJ 2\n",
    "\n",
    "summary_stats(dat['cmj_2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['CMJ Avg', 41.1], ['CMJ SD', 8.4]]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# CMJ 3\n",
    "\n",
    "summary_stats(dat['cmj_3'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate Smallest Worthwhile Change (SWC) and Typical Error of Measurement (TEM)\n",
    "\n",
    "In the paper, Anthony Turner adds the values to each athlete within the same row, rather than creating a separate data frame for SWC and TEM. So we will structure the data in the same manner as he did."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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>athlete</th>\n",
       "      <th>test_session</th>\n",
       "      <th>cmj_1</th>\n",
       "      <th>cmj_2</th>\n",
       "      <th>cmj_3</th>\n",
       "      <th>best_cmj</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>38.1</td>\n",
       "      <td>43.6</td>\n",
       "      <td>47.7</td>\n",
       "      <td>47.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>34.1</td>\n",
       "      <td>35.7</td>\n",
       "      <td>36.0</td>\n",
       "      <td>36.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.2</td>\n",
       "      <td>41.9</td>\n",
       "      <td>42.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>50.4</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.1</td>\n",
       "      <td>36.9</td>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   athlete  test_session  cmj_1  cmj_2  cmj_3  best_cmj\n",
       "0        1             1   38.1   43.6   47.7      47.7\n",
       "1        2             1   34.1   35.7   36.0      36.0\n",
       "2        3             1   42.8   42.2   41.9      42.8\n",
       "3        4             1   50.4   52.2   52.2      52.2\n",
       "4        5             1   37.0   36.1   36.9      37.0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# First create a column to identify each athlete's max value across the 3 jumps\n",
    "# NOTE: specify that you are performing the max calculation across rows by indicating axis = 1\n",
    "\n",
    "dat['best_cmj'] = dat.iloc[:,2:5].max(axis = 1)\n",
    "dat.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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>athlete</th>\n",
       "      <th>test_session</th>\n",
       "      <th>cmj_1</th>\n",
       "      <th>cmj_2</th>\n",
       "      <th>cmj_3</th>\n",
       "      <th>best_cmj</th>\n",
       "      <th>avg</th>\n",
       "      <th>sd</th>\n",
       "      <th>cv_pct</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>38.1</td>\n",
       "      <td>43.6</td>\n",
       "      <td>47.7</td>\n",
       "      <td>47.7</td>\n",
       "      <td>43.1</td>\n",
       "      <td>4.8</td>\n",
       "      <td>0.1114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>34.1</td>\n",
       "      <td>35.7</td>\n",
       "      <td>36.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>35.3</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.2</td>\n",
       "      <td>41.9</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.3</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>50.4</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "      <td>51.6</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.1</td>\n",
       "      <td>36.9</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.7</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0136</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   athlete  test_session  cmj_1  cmj_2  cmj_3  best_cmj   avg   sd  cv_pct\n",
       "0        1             1   38.1   43.6   47.7      47.7  43.1  4.8  0.1114\n",
       "1        2             1   34.1   35.7   36.0      36.0  35.3  1.0  0.0283\n",
       "2        3             1   42.8   42.2   41.9      42.8  42.3  0.5  0.0118\n",
       "3        4             1   50.4   52.2   52.2      52.2  51.6  1.0  0.0194\n",
       "4        5             1   37.0   36.1   36.9      37.0  36.7  0.5  0.0136"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate a column for each athletes Average, SD, & CV% of CMJ\n",
    "\n",
    "dat['avg'] = round(dat.loc[:,['cmj_1', 'cmj_2', 'cmj_3']].mean(axis = 1), 1)\n",
    "dat['sd'] = round(dat.loc[:,['cmj_1', 'cmj_2', 'cmj_3']].std(axis = 1), 1)\n",
    "dat['cv_pct'] = round(dat['sd'] / dat['avg'], 4)\n",
    "\n",
    "dat.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.63"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Calculate SWC\n",
    "# Turner uses 0.2 * Btw Subject Standard Deviation of their best CMJ (per Hopkins)\n",
    "\n",
    "effect_of_interest = 0.2\n",
    "swc = round(effect_of_interest * dat['best_cmj'].std(), 2)\n",
    "swc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.049"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## calculate typical error measurement as a CV%\n",
    "# Turner takes the average of all of the athletes CV% across their 3 jumps\n",
    "\n",
    "tem_cv = round(dat['cv_pct'].mean(), 3)\n",
    "tem_cv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Add the SWC and TEM to each row for each athlete to specify training targets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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>athlete</th>\n",
       "      <th>test_session</th>\n",
       "      <th>cmj_1</th>\n",
       "      <th>cmj_2</th>\n",
       "      <th>cmj_3</th>\n",
       "      <th>best_cmj</th>\n",
       "      <th>avg</th>\n",
       "      <th>sd</th>\n",
       "      <th>cv_pct</th>\n",
       "      <th>goal_swc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>38.1</td>\n",
       "      <td>43.6</td>\n",
       "      <td>47.7</td>\n",
       "      <td>47.7</td>\n",
       "      <td>43.1</td>\n",
       "      <td>4.8</td>\n",
       "      <td>0.1114</td>\n",
       "      <td>49.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>34.1</td>\n",
       "      <td>35.7</td>\n",
       "      <td>36.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>35.3</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0283</td>\n",
       "      <td>37.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.2</td>\n",
       "      <td>41.9</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.3</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0118</td>\n",
       "      <td>44.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>50.4</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "      <td>51.6</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0194</td>\n",
       "      <td>53.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.1</td>\n",
       "      <td>36.9</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.7</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0136</td>\n",
       "      <td>38.63</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   athlete  test_session  cmj_1  cmj_2  cmj_3  best_cmj   avg   sd  cv_pct  \\\n",
       "0        1             1   38.1   43.6   47.7      47.7  43.1  4.8  0.1114   \n",
       "1        2             1   34.1   35.7   36.0      36.0  35.3  1.0  0.0283   \n",
       "2        3             1   42.8   42.2   41.9      42.8  42.3  0.5  0.0118   \n",
       "3        4             1   50.4   52.2   52.2      52.2  51.6  1.0  0.0194   \n",
       "4        5             1   37.0   36.1   36.9      37.0  36.7  0.5  0.0136   \n",
       "\n",
       "   goal_swc  \n",
       "0     49.33  \n",
       "1     37.63  \n",
       "2     44.43  \n",
       "3     53.83  \n",
       "4     38.63  "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Add the SWC to each athletes Best CMJ to identify a goal for the next round of testing\n",
    "\n",
    "dat['goal_swc'] = swc + dat['best_cmj']\n",
    "dat.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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>athlete</th>\n",
       "      <th>test_session</th>\n",
       "      <th>cmj_1</th>\n",
       "      <th>cmj_2</th>\n",
       "      <th>cmj_3</th>\n",
       "      <th>best_cmj</th>\n",
       "      <th>avg</th>\n",
       "      <th>sd</th>\n",
       "      <th>cv_pct</th>\n",
       "      <th>goal_swc</th>\n",
       "      <th>error_measurement</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>38.1</td>\n",
       "      <td>43.6</td>\n",
       "      <td>47.7</td>\n",
       "      <td>47.7</td>\n",
       "      <td>43.1</td>\n",
       "      <td>4.8</td>\n",
       "      <td>0.1114</td>\n",
       "      <td>49.33</td>\n",
       "      <td>2.3373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>34.1</td>\n",
       "      <td>35.7</td>\n",
       "      <td>36.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>35.3</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0283</td>\n",
       "      <td>37.63</td>\n",
       "      <td>1.7640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.2</td>\n",
       "      <td>41.9</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.3</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0118</td>\n",
       "      <td>44.43</td>\n",
       "      <td>2.0972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>50.4</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "      <td>51.6</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0194</td>\n",
       "      <td>53.83</td>\n",
       "      <td>2.5578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.1</td>\n",
       "      <td>36.9</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.7</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0136</td>\n",
       "      <td>38.63</td>\n",
       "      <td>1.8130</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   athlete  test_session  cmj_1  cmj_2  cmj_3  best_cmj   avg   sd  cv_pct  \\\n",
       "0        1             1   38.1   43.6   47.7      47.7  43.1  4.8  0.1114   \n",
       "1        2             1   34.1   35.7   36.0      36.0  35.3  1.0  0.0283   \n",
       "2        3             1   42.8   42.2   41.9      42.8  42.3  0.5  0.0118   \n",
       "3        4             1   50.4   52.2   52.2      52.2  51.6  1.0  0.0194   \n",
       "4        5             1   37.0   36.1   36.9      37.0  36.7  0.5  0.0136   \n",
       "\n",
       "   goal_swc  error_measurement  \n",
       "0     49.33             2.3373  \n",
       "1     37.63             1.7640  \n",
       "2     44.43             2.0972  \n",
       "3     53.83             2.5578  \n",
       "4     38.63             1.8130  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Add the error measurement to each athletes Best CMJ\n",
    "\n",
    "dat['error_measurement'] = tem_cv * dat['best_cmj']\n",
    "dat.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "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>athlete</th>\n",
       "      <th>test_session</th>\n",
       "      <th>cmj_1</th>\n",
       "      <th>cmj_2</th>\n",
       "      <th>cmj_3</th>\n",
       "      <th>best_cmj</th>\n",
       "      <th>avg</th>\n",
       "      <th>sd</th>\n",
       "      <th>cv_pct</th>\n",
       "      <th>goal_swc</th>\n",
       "      <th>error_measurement</th>\n",
       "      <th>adj_swc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>38.1</td>\n",
       "      <td>43.6</td>\n",
       "      <td>47.7</td>\n",
       "      <td>47.7</td>\n",
       "      <td>43.1</td>\n",
       "      <td>4.8</td>\n",
       "      <td>0.1114</td>\n",
       "      <td>49.33</td>\n",
       "      <td>2.3373</td>\n",
       "      <td>52.59769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>34.1</td>\n",
       "      <td>35.7</td>\n",
       "      <td>36.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>35.3</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0283</td>\n",
       "      <td>37.63</td>\n",
       "      <td>1.7640</td>\n",
       "      <td>40.89769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.2</td>\n",
       "      <td>41.9</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.3</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0118</td>\n",
       "      <td>44.43</td>\n",
       "      <td>2.0972</td>\n",
       "      <td>47.69769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>50.4</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "      <td>52.2</td>\n",
       "      <td>51.6</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0194</td>\n",
       "      <td>53.83</td>\n",
       "      <td>2.5578</td>\n",
       "      <td>57.09769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.1</td>\n",
       "      <td>36.9</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.7</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0136</td>\n",
       "      <td>38.63</td>\n",
       "      <td>1.8130</td>\n",
       "      <td>41.89769</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   athlete  test_session  cmj_1  cmj_2  cmj_3  best_cmj   avg   sd  cv_pct  \\\n",
       "0        1             1   38.1   43.6   47.7      47.7  43.1  4.8  0.1114   \n",
       "1        2             1   34.1   35.7   36.0      36.0  35.3  1.0  0.0283   \n",
       "2        3             1   42.8   42.2   41.9      42.8  42.3  0.5  0.0118   \n",
       "3        4             1   50.4   52.2   52.2      52.2  51.6  1.0  0.0194   \n",
       "4        5             1   37.0   36.1   36.9      37.0  36.7  0.5  0.0136   \n",
       "\n",
       "   goal_swc  error_measurement   adj_swc  \n",
       "0     49.33             2.3373  52.59769  \n",
       "1     37.63             1.7640  40.89769  \n",
       "2     44.43             2.0972  47.69769  \n",
       "3     53.83             2.5578  57.09769  \n",
       "4     38.63             1.8130  41.89769  "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# One issue is that the SWC is a small fraction (0.2) of the between subject SD\n",
    "# We could use a larger magnitude than 0.2.\n",
    "# For example, we can adjust the swc to be 0.6 instead of 0.2\n",
    "\n",
    "dat['adj_swc'] = 0.6 * dat['best_cmj'].std() + dat['best_cmj']\n",
    "dat.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**NOTE:** Now the improvement for some athletes that already have a high CMJ at baseline might be untainable, as an improvement for them (given their starting athleticism) might be smaller. Care should be taken when determining such training targets. The heterogeneity of the group also needs to be considered given that the between subject SD was used in the calculation of SWC."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show group performance improvements using Cohen's d\n",
    "\n",
    "Since our data is structured as 3 CMJ's performed in a single session, we will just select jumps 1 and 2 and *pretend* that they are representing an initial CMJ and then a CMJ followed up after a period of training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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>athlete</th>\n",
       "      <th>test_session</th>\n",
       "      <th>cmj_1</th>\n",
       "      <th>cmj_2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>38.1</td>\n",
       "      <td>43.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>34.1</td>\n",
       "      <td>35.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>42.8</td>\n",
       "      <td>42.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>50.4</td>\n",
       "      <td>52.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>37.0</td>\n",
       "      <td>36.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   athlete  test_session  cmj_1  cmj_2\n",
       "0        1             1   38.1   43.6\n",
       "1        2             1   34.1   35.7\n",
       "2        3             1   42.8   42.2\n",
       "3        4             1   50.4   52.2\n",
       "4        5             1   37.0   36.1"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dat_pre_post = dat.iloc[:, 0:4]\n",
    "dat_pre_post.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "## get summary stats of the two jumping periods\n",
    "\n",
    "avg_pre = dat_pre_post['cmj_1'].mean()\n",
    "sd_pre = dat_pre_post['cmj_1'].std()\n",
    "\n",
    "avg_post = dat_pre_post['cmj_2'].mean()\n",
    "sd_post = dat_pre_post['cmj_2'].std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "39.72083333333333 7.2086288370358576 40.337500000000006 7.236910973252512\n"
     ]
    }
   ],
   "source": [
    "print(avg_pre,\n",
    "      sd_pre,\n",
    "      avg_post,\n",
    "      sd_post)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6166666666666742"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate mean difference\n",
    "\n",
    "mean_diff = avg_post - avg_pre\n",
    "mean_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.22278374814474"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate pooed SD\n",
    "# NOTE: To square the standard deviations in Python use the ** operator instead of the ^ symbol, which is commonly used\n",
    "\n",
    "sd_pooled = math.sqrt((sd_post**2 + sd_pre**2) / 2)\n",
    "sd_pooled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08537797726881587"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate Cohen's d Effect Size\n",
    "\n",
    "ES = mean_diff / sd_pooled\n",
    "ES"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The difference between jump 1 and jump 2, for the group, was found to be trival.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "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>Effect Size Statistic</th>\n",
       "      <th>Qualitative Descriptor</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>&lt; 0.2</td>\n",
       "      <td>Trivial</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.2 - 0.6</td>\n",
       "      <td>Small</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.6 - 1.2</td>\n",
       "      <td>Moderate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.2 - 2.0</td>\n",
       "      <td>Large</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.0 - 4.0</td>\n",
       "      <td>Very Large</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>&gt; 4.0</td>\n",
       "      <td>Extremely Large</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Effect Size Statistic Qualitative Descriptor\n",
       "0                 < 0.2                Trivial\n",
       "1             0.2 - 0.6                  Small\n",
       "2             0.6 - 1.2               Moderate\n",
       "3             1.2 - 2.0                  Large\n",
       "4             2.0 - 4.0             Very Large\n",
       "5                 > 4.0        Extremely Large"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "es_interpretation = pd.DataFrame()\n",
    "es_interpretation['Effect Size Statistic'] = ['< 0.2', '0.2 - 0.6', '0.6 - 1.2', '1.2 - 2.0', '2.0 - 4.0', '> 4.0']\n",
    "es_interpretation['Qualitative Descriptor'] = ['Trivial', 'Small', 'Moderate', 'Large', 'Very Large', 'Extremely Large']\n",
    "\n",
    "es_interpretation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}