descriptive_statistics_example_code.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to Carry out Descriptive Statistics in Python\n",
    "This Jupyter Notebook contains a lot of descriptive statistic examples and how to carry them out in Python. Note, this is the code for the blog post (https://www.marsja.se/pandas-python-descriptive-statistics/). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import trim_mean, kurtosis\n",
    "from scipy.stats.mstats import mode, gmean, hmean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate Data using Python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 20\n",
    "P = [\"noise\",\"quiet\"]\n",
    "Q = [1,2,3]\n",
    "\n",
    "values = [[998,511], [1119,620], [1300,790]]\n",
    "\n",
    "mus = np.concatenate([np.repeat(value, N) for value in values])\n",
    "\n",
    "data = pd.DataFrame(data = {'id': [subid for subid in range(N)]*(len(P)*len(Q))\n",
    "    ,'iv1': np.concatenate([np.array([p]*N) for p in P]*len(Q))\n",
    "    ,'iv2': np.concatenate([np.array([q]*(N*len(P))) for q in Q])\n",
    "    ,'rt': np.random.normal(mus, scale=112.0, size=N*len(P)*len(Q))})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary Statistics using Pandas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>iv2</th>\n",
       "      <th>rt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>120.000000</td>\n",
       "      <td>120.00000</td>\n",
       "      <td>120.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>9.500000</td>\n",
       "      <td>2.00000</td>\n",
       "      <td>895.187075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>5.790459</td>\n",
       "      <td>0.81992</td>\n",
       "      <td>303.933688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>256.061279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>4.750000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>621.471263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>9.500000</td>\n",
       "      <td>2.00000</td>\n",
       "      <td>901.873513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>14.250000</td>\n",
       "      <td>3.00000</td>\n",
       "      <td>1165.150726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>19.000000</td>\n",
       "      <td>3.00000</td>\n",
       "      <td>1527.972882</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               id        iv2           rt\n",
       "count  120.000000  120.00000   120.000000\n",
       "mean     9.500000    2.00000   895.187075\n",
       "std      5.790459    0.81992   303.933688\n",
       "min      0.000000    1.00000   256.061279\n",
       "25%      4.750000    1.00000   621.471263\n",
       "50%      9.500000    2.00000   901.873513\n",
       "75%     14.250000    3.00000  1165.150726\n",
       "max     19.000000    3.00000  1527.972882"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Grouped Descriptive Statistics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th colspan=\"3\" halign=\"left\">count</th>\n",
       "      <th colspan=\"3\" halign=\"left\">mean</th>\n",
       "      <th colspan=\"3\" halign=\"left\">std</th>\n",
       "      <th>min</th>\n",
       "      <th>...</th>\n",
       "      <th>25%</th>\n",
       "      <th colspan=\"3\" halign=\"left\">50%</th>\n",
       "      <th colspan=\"3\" halign=\"left\">75%</th>\n",
       "      <th colspan=\"3\" halign=\"left\">max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>iv2</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>1</th>\n",
       "      <th>...</th>\n",
       "      <th>3</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>iv1</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>noise</th>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1026.951799</td>\n",
       "      <td>1135.312393</td>\n",
       "      <td>1297.068445</td>\n",
       "      <td>116.655172</td>\n",
       "      <td>106.882390</td>\n",
       "      <td>103.210228</td>\n",
       "      <td>845.521745</td>\n",
       "      <td>...</td>\n",
       "      <td>1227.450836</td>\n",
       "      <td>1001.114388</td>\n",
       "      <td>1118.947202</td>\n",
       "      <td>1284.946095</td>\n",
       "      <td>1084.212908</td>\n",
       "      <td>1224.959876</td>\n",
       "      <td>1339.939327</td>\n",
       "      <td>1239.158920</td>\n",
       "      <td>1360.870424</td>\n",
       "      <td>1527.972882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>quiet</th>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>484.960325</td>\n",
       "      <td>647.627357</td>\n",
       "      <td>779.202128</td>\n",
       "      <td>97.308013</td>\n",
       "      <td>110.419398</td>\n",
       "      <td>128.151469</td>\n",
       "      <td>256.061279</td>\n",
       "      <td>...</td>\n",
       "      <td>696.056131</td>\n",
       "      <td>479.535898</td>\n",
       "      <td>645.823263</td>\n",
       "      <td>781.572539</td>\n",
       "      <td>556.722830</td>\n",
       "      <td>727.725189</td>\n",
       "      <td>859.728299</td>\n",
       "      <td>647.879485</td>\n",
       "      <td>852.280828</td>\n",
       "      <td>1032.398233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 24 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      count                     mean                                   std  \\\n",
       "iv2       1     2     3            1            2            3           1   \n",
       "iv1                                                                          \n",
       "noise  20.0  20.0  20.0  1026.951799  1135.312393  1297.068445  116.655172   \n",
       "quiet  20.0  20.0  20.0   484.960325   647.627357   779.202128   97.308013   \n",
       "\n",
       "                                      min  ...          25%          50%  \\\n",
       "iv2             2           3           1  ...            3            1   \n",
       "iv1                                        ...                             \n",
       "noise  106.882390  103.210228  845.521745  ...  1227.450836  1001.114388   \n",
       "quiet  110.419398  128.151469  256.061279  ...   696.056131   479.535898   \n",
       "\n",
       "                                         75%                            \\\n",
       "iv2              2            3            1            2            3   \n",
       "iv1                                                                      \n",
       "noise  1118.947202  1284.946095  1084.212908  1224.959876  1339.939327   \n",
       "quiet   645.823263   781.572539   556.722830   727.725189   859.728299   \n",
       "\n",
       "               max                            \n",
       "iv2              1            2            3  \n",
       "iv1                                           \n",
       "noise  1239.158920  1360.870424  1527.972882  \n",
       "quiet   647.879485   852.280828  1032.398233  \n",
       "\n",
       "[2 rows x 24 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_data = data.groupby(['iv1', 'iv2'])\n",
    "grouped_data['rt'].describe().unstack()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Getting the Mean Values in Pandas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>iv1</th>\n",
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       "      <th>1</th>\n",
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       "      <td>1135.312393</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>noise</td>\n",
       "      <td>3</td>\n",
       "      <td>1297.068445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>quiet</td>\n",
       "      <td>1</td>\n",
       "      <td>484.960325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>quiet</td>\n",
       "      <td>2</td>\n",
       "      <td>647.627357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>quiet</td>\n",
       "      <td>3</td>\n",
       "      <td>779.202128</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "     iv1  iv2           rt\n",
       "0  noise    1  1026.951799\n",
       "1  noise    2  1135.312393\n",
       "2  noise    3  1297.068445\n",
       "3  quiet    1   484.960325\n",
       "4  quiet    2   647.627357\n",
       "5  quiet    3   779.202128"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_data['rt'].mean().reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>iv1</th>\n",
       "      <th>iv2</th>\n",
       "      <th>rt</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "      <td>1026.951799</td>\n",
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       "      <th>1</th>\n",
       "      <td>noise</td>\n",
       "      <td>2</td>\n",
       "      <td>1135.312393</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>noise</td>\n",
       "      <td>3</td>\n",
       "      <td>1297.068445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>quiet</td>\n",
       "      <td>1</td>\n",
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       "      <td>quiet</td>\n",
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       "      <th>5</th>\n",
       "      <td>quiet</td>\n",
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       "      <td>779.202128</td>\n",
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      ],
      "text/plain": [
       "     iv1  iv2           rt\n",
       "0  noise    1  1026.951799\n",
       "1  noise    2  1135.312393\n",
       "2  noise    3  1297.068445\n",
       "3  quiet    1   484.960325\n",
       "4  quiet    2   647.627357\n",
       "5  quiet    3   779.202128"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_data['rt'].aggregate(np.mean).reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Geometric & Harmonic Mean in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### SciPy and Pandas Method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>iv1</th>\n",
       "      <th>iv2</th>\n",
       "      <th>rt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>noise</td>\n",
       "      <td>1</td>\n",
       "      <td>1020.844654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>noise</td>\n",
       "      <td>2</td>\n",
       "      <td>1130.412242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>noise</td>\n",
       "      <td>3</td>\n",
       "      <td>1293.177643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>quiet</td>\n",
       "      <td>1</td>\n",
       "      <td>474.585599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>quiet</td>\n",
       "      <td>2</td>\n",
       "      <td>638.322355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>quiet</td>\n",
       "      <td>3</td>\n",
       "      <td>768.855048</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "     iv1  iv2           rt\n",
       "0  noise    1  1020.844654\n",
       "1  noise    2  1130.412242\n",
       "2  noise    3  1293.177643\n",
       "3  quiet    1   474.585599\n",
       "4  quiet    2   638.322355\n",
       "5  quiet    3   768.855048"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_data['rt'].apply(gmean, axis=None).reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Harmonic using Scipy & Pandas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\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>iv1</th>\n",
       "      <th>iv2</th>\n",
       "      <th>rt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>noise</td>\n",
       "      <td>1</td>\n",
       "      <td>1014.932257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>noise</td>\n",
       "      <td>2</td>\n",
       "      <td>1125.368076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>noise</td>\n",
       "      <td>3</td>\n",
       "      <td>1289.285734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>quiet</td>\n",
       "      <td>1</td>\n",
       "      <td>462.783258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>quiet</td>\n",
       "      <td>2</td>\n",
       "      <td>628.544592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>quiet</td>\n",
       "      <td>3</td>\n",
       "      <td>758.169721</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     iv1  iv2           rt\n",
       "0  noise    1  1014.932257\n",
       "1  noise    2  1125.368076\n",
       "2  noise    3  1289.285734\n",
       "3  quiet    1   462.783258\n",
       "4  quiet    2   628.544592\n",
       "5  quiet    3   758.169721"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_data['rt'].apply(hmean, axis=None).reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Trimmed Mean in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>iv1</th>\n",
       "      <th>iv2</th>\n",
       "      <th>rt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>noise</td>\n",
       "      <td>1</td>\n",
       "      <td>1020.327150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>noise</td>\n",
       "      <td>2</td>\n",
       "      <td>1137.905279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>noise</td>\n",
       "      <td>3</td>\n",
       "      <td>1294.063819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>quiet</td>\n",
       "      <td>1</td>\n",
       "      <td>490.396308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>quiet</td>\n",
       "      <td>2</td>\n",
       "      <td>646.668327</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>quiet</td>\n",
       "      <td>3</td>\n",
       "      <td>780.845745</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     iv1  iv2           rt\n",
       "0  noise    1  1020.327150\n",
       "1  noise    2  1137.905279\n",
       "2  noise    3  1294.063819\n",
       "3  quiet    1   490.396308\n",
       "4  quiet    2   646.668327\n",
       "5  quiet    3   780.845745"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trimmed_mean = grouped_data['rt'].apply(trim_mean, .1)\n",
    "trimmed_mean.reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pandas Median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>iv1</th>\n",
       "      <th>iv2</th>\n",
       "      <th>rt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>noise</td>\n",
       "      <td>1</td>\n",
       "      <td>1001.114388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>noise</td>\n",
       "      <td>2</td>\n",
       "      <td>1118.947202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>noise</td>\n",
       "      <td>3</td>\n",
       "      <td>1284.946095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>quiet</td>\n",
       "      <td>1</td>\n",
       "      <td>479.535898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>quiet</td>\n",
       "      <td>2</td>\n",
       "      <td>645.823263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>quiet</td>\n",
       "      <td>3</td>\n",
       "      <td>781.572539</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     iv1  iv2           rt\n",
       "0  noise    1  1001.114388\n",
       "1  noise    2  1118.947202\n",
       "2  noise    3  1284.946095\n",
       "3  quiet    1   479.535898\n",
       "4  quiet    2   645.823263\n",
       "5  quiet    3   781.572539"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pandas Only:\n",
    "# grouped_data['rt'].median().reset_index()\n",
    "# Pandas + NumPy\n",
    "grouped_data['rt'].aggregate(np.median).reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scipy Mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>iv1</th>\n",
       "      <th>iv2</th>\n",
       "      <th>rt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>noise</td>\n",
       "      <td>1</td>\n",
       "      <td>([845.5217454205024], [1.0])</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>noise</td>\n",
       "      <td>2</td>\n",
       "      <td>([882.9328302299256], [1.0])</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>noise</td>\n",
       "      <td>3</td>\n",
       "      <td>([1067.3199212997692], [1.0])</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>quiet</td>\n",
       "      <td>1</td>\n",
       "      <td>([256.0612793705232], [1.0])</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>quiet</td>\n",
       "      <td>2</td>\n",
       "      <td>([403.0922504450879], [1.0])</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>quiet</td>\n",
       "      <td>3</td>\n",
       "      <td>([539.8025053743281], [1.0])</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     iv1  iv2                             rt\n",
       "0  noise    1   ([845.5217454205024], [1.0])\n",
       "1  noise    2   ([882.9328302299256], [1.0])\n",
       "2  noise    3  ([1067.3199212997692], [1.0])\n",
       "3  quiet    1   ([256.0612793705232], [1.0])\n",
       "4  quiet    2   ([403.0922504450879], [1.0])\n",
       "5  quiet    3   ([539.8025053743281], [1.0])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_data['rt'].apply(mode, axis=None).reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Median, Standard Deviation, Mean, and Trimmed Mean in a Pandas Dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>iv1</th>\n",
       "      <th>iv2</th>\n",
       "      <th>median</th>\n",
       "      <th>std</th>\n",
       "      <th>mean</th>\n",
       "      <th>trimmed_mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>noise</td>\n",
       "      <td>1</td>\n",
       "      <td>1001.114388</td>\n",
       "      <td>116.655172</td>\n",
       "      <td>1026.951799</td>\n",
       "      <td>1020.327150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>noise</td>\n",
       "      <td>2</td>\n",
       "      <td>1118.947202</td>\n",
       "      <td>106.882390</td>\n",
       "      <td>1135.312393</td>\n",
       "      <td>1137.905279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>noise</td>\n",
       "      <td>3</td>\n",
       "      <td>1284.946095</td>\n",
       "      <td>103.210228</td>\n",
       "      <td>1297.068445</td>\n",
       "      <td>1294.063819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>quiet</td>\n",
       "      <td>1</td>\n",
       "      <td>479.535898</td>\n",
       "      <td>97.308013</td>\n",
       "      <td>484.960325</td>\n",
       "      <td>490.396308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>quiet</td>\n",
       "      <td>2</td>\n",
       "      <td>645.823263</td>\n",
       "      <td>110.419398</td>\n",
       "      <td>647.627357</td>\n",
       "      <td>646.668327</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>quiet</td>\n",
       "      <td>3</td>\n",
       "      <td>781.572539</td>\n",
       "      <td>128.151469</td>\n",
       "      <td>779.202128</td>\n",
       "      <td>780.845745</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     iv1  iv2       median         std         mean  trimmed_mean\n",
       "0  noise    1  1001.114388  116.655172  1026.951799   1020.327150\n",
       "1  noise    2  1118.947202  106.882390  1135.312393   1137.905279\n",
       "2  noise    3  1284.946095  103.210228  1297.068445   1294.063819\n",
       "3  quiet    1   479.535898   97.308013   484.960325    490.396308\n",
       "4  quiet    2   645.823263  110.419398   647.627357    646.668327\n",
       "5  quiet    3   781.572539  128.151469   779.202128    780.845745"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "descr = grouped_data['rt'].aggregate([np.median, np.std, np.mean]).reset_index()\n",
    "descr['trimmed_mean'] = pd.Series(trimmed_mean.values, index=descr.index)\n",
    "descr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measures of Variability in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pandas Standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>iv1</th>\n",
       "      <th>iv2</th>\n",
       "      <th>rt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>noise</td>\n",
       "      <td>1</td>\n",
       "      <td>116.655172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>noise</td>\n",
       "      <td>2</td>\n",
       "      <td>106.882390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>noise</td>\n",
       "      <td>3</td>\n",
       "      <td>103.210228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>quiet</td>\n",
       "      <td>1</td>\n",
       "      <td>97.308013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>quiet</td>\n",
       "      <td>2</td>\n",
       "      <td>110.419398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>quiet</td>\n",
       "      <td>3</td>\n",
       "      <td>128.151469</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     iv1  iv2          rt\n",
       "0  noise    1  116.655172\n",
       "1  noise    2  106.882390\n",
       "2  noise    3  103.210228\n",
       "3  quiet    1   97.308013\n",
       "4  quiet    2  110.419398\n",
       "5  quiet    3  128.151469"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_data['rt'].std().reset_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inter quartile range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>iv1</th>\n",
       "      <th>iv2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">noise</th>\n",
       "      <th>1</th>\n",
       "      <td>940.329336</td>\n",
       "      <td>1001.114388</td>\n",
       "      <td>1084.212908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1090.169199</td>\n",
       "      <td>1118.947202</td>\n",
       "      <td>1224.959876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1227.450836</td>\n",
       "      <td>1284.946095</td>\n",
       "      <td>1339.939327</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">quiet</th>\n",
       "      <th>1</th>\n",
       "      <td>438.928725</td>\n",
       "      <td>479.535898</td>\n",
       "      <td>556.722830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>575.828113</td>\n",
       "      <td>645.823263</td>\n",
       "      <td>727.725189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>696.056131</td>\n",
       "      <td>781.572539</td>\n",
       "      <td>859.728299</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   25%          50%          75%\n",
       "iv1   iv2                                       \n",
       "noise 1     940.329336  1001.114388  1084.212908\n",
       "      2    1090.169199  1118.947202  1224.959876\n",
       "      3    1227.450836  1284.946095  1339.939327\n",
       "quiet 1     438.928725   479.535898   556.722830\n",
       "      2     575.828113   645.823263   727.725189\n",
       "      3     696.056131   781.572539   859.728299"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_data.describe()['rt'][['25%', '50%', '75%']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pandas Variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>iv1</th>\n",
       "      <th>iv2</th>\n",
       "      <th>rt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>noise</td>\n",
       "      <td>1</td>\n",
       "      <td>13608.429057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>noise</td>\n",
       "      <td>2</td>\n",
       "      <td>11423.845263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>noise</td>\n",
       "      <td>3</td>\n",
       "      <td>10652.351196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>quiet</td>\n",
       "      <td>1</td>\n",
       "      <td>9468.849482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>quiet</td>\n",
       "      <td>2</td>\n",
       "      <td>12192.443446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>quiet</td>\n",
       "      <td>3</td>\n",
       "      <td>16422.798900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     iv1  iv2            rt\n",
       "0  noise    1  13608.429057\n",
       "1  noise    2  11423.845263\n",
       "2  noise    3  10652.351196\n",
       "3  quiet    1   9468.849482\n",
       "4  quiet    2  12192.443446\n",
       "5  quiet    3  16422.798900"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_data['rt'].var().reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Saving Pandas Summary Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "descr.to_csv('Descriptive_Statistics_in_Python.csv', index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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