analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chopsticks!\n",
    "\n",
    "A few researchers set out to determine the optimal length of chopsticks for children and adults. They came up with a measure of how effective a pair of chopsticks performed, called the \"Food Pinching Performance.\" The \"Food Pinching Performance\" was determined by counting the number of peanuts picked and placed in a cup (PPPC).\n",
    "\n",
    "### An investigation for determining the optimum length of chopsticks.\n",
    "[Link to Abstract and Paper](http://www.ncbi.nlm.nih.gov/pubmed/15676839)  \n",
    "*the abstract below was adapted from the link*\n",
    "\n",
    "Chopsticks are one of the most simple and popular hand tools ever invented by humans, but have not previously been investigated by [ergonomists](https://www.google.com/search?q=ergonomists). Two laboratory studies were conducted in this research, using a [randomised complete block design](http://dawg.utk.edu/glossary/whatis_rcbd.htm), to evaluate the effects of the length of the chopsticks on the food-serving performance of adults and children. Thirty-one male junior college students and 21 primary school pupils served as subjects for the experiment to test chopsticks lengths of 180, 210, 240, 270, 300, and 330 mm. The results showed that the food-pinching performance was significantly affected by the length of the chopsticks, and that chopsticks of about 240 and 180 mm long were optimal for adults and pupils, respectively. Based on these findings, the researchers suggested that families with children should provide both 240 and 180 mm long chopsticks. In addition, restaurants could provide 210 mm long chopsticks, considering the trade-offs between ergonomics and cost.\n",
    "\n",
    "### For the rest of this project, answer all questions based only on the part of the experiment analyzing the thirty-one adult male college students.\n",
    "Download the [data set for the adults](https://www.udacity.com/api/nodes/4576183932/supplemental_media/chopstick-effectivenesscsv/download), then answer the following questions based on the abstract and the data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. What is the independent variable in the experiment?\n",
    "The chopsticks lengths."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. What is the dependent variable in the experiment?\n",
    "The \"Food Pinching Performance\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. How is the dependent variable operationally defined?\n",
    "The \"Food Pinching Performance\" is defined by the number of peanuts picked and placed in a cup (PPPC)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Based on the description of the experiment and the data set, list at least two variables that you know were controlled.\n",
    "Think about the participants who generated the data and what they have in common. You don't need to guess any variables or read the full paper to determine these variables. (For example, it seems plausible that the material of the chopsticks was held constant, but this is not stated in the abstract or data description.)\n",
    "\n",
    "The controlled variables are: age (in 2 different groups), gender (only males were selected) and what the participants had to pick using chopsticks (peanuts)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# Pandas is a software library for data manipulation and analysis.\n",
    "# We commonly use shorter nicknames for certain packages. \n",
    "# Pandas is often abbreviated to pd."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Food.Pinching.Efficiency</th>\n",
       "      <th>Individual</th>\n",
       "      <th>Chopstick.Length</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>19.55</td>\n",
       "      <td>1</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>27.24</td>\n",
       "      <td>2</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28.76</td>\n",
       "      <td>3</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>31.19</td>\n",
       "      <td>4</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>21.91</td>\n",
       "      <td>5</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>27.62</td>\n",
       "      <td>6</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>29.46</td>\n",
       "      <td>7</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>26.35</td>\n",
       "      <td>8</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>26.69</td>\n",
       "      <td>9</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>30.22</td>\n",
       "      <td>10</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>27.81</td>\n",
       "      <td>11</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>23.46</td>\n",
       "      <td>12</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>23.64</td>\n",
       "      <td>13</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>27.85</td>\n",
       "      <td>14</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>20.62</td>\n",
       "      <td>15</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>25.35</td>\n",
       "      <td>16</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>28.00</td>\n",
       "      <td>17</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>23.49</td>\n",
       "      <td>18</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>27.77</td>\n",
       "      <td>19</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>18.48</td>\n",
       "      <td>20</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>23.01</td>\n",
       "      <td>21</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>22.66</td>\n",
       "      <td>22</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>23.24</td>\n",
       "      <td>23</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>22.82</td>\n",
       "      <td>24</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>17.94</td>\n",
       "      <td>25</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>26.67</td>\n",
       "      <td>26</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>28.98</td>\n",
       "      <td>27</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>21.48</td>\n",
       "      <td>28</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>14.47</td>\n",
       "      <td>29</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>28.29</td>\n",
       "      <td>30</td>\n",
       "      <td>180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>156</th>\n",
       "      <td>26.18</td>\n",
       "      <td>2</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>157</th>\n",
       "      <td>25.93</td>\n",
       "      <td>3</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>158</th>\n",
       "      <td>28.61</td>\n",
       "      <td>4</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>159</th>\n",
       "      <td>20.54</td>\n",
       "      <td>5</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>160</th>\n",
       "      <td>26.44</td>\n",
       "      <td>6</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>161</th>\n",
       "      <td>29.36</td>\n",
       "      <td>7</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>162</th>\n",
       "      <td>19.77</td>\n",
       "      <td>8</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>163</th>\n",
       "      <td>31.69</td>\n",
       "      <td>9</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>164</th>\n",
       "      <td>24.64</td>\n",
       "      <td>10</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>22.09</td>\n",
       "      <td>11</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>166</th>\n",
       "      <td>23.42</td>\n",
       "      <td>12</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>167</th>\n",
       "      <td>28.63</td>\n",
       "      <td>13</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>168</th>\n",
       "      <td>26.30</td>\n",
       "      <td>14</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>169</th>\n",
       "      <td>22.89</td>\n",
       "      <td>15</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>170</th>\n",
       "      <td>22.68</td>\n",
       "      <td>16</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>171</th>\n",
       "      <td>30.92</td>\n",
       "      <td>17</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>172</th>\n",
       "      <td>20.74</td>\n",
       "      <td>18</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>27.24</td>\n",
       "      <td>19</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>174</th>\n",
       "      <td>17.12</td>\n",
       "      <td>20</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>23.63</td>\n",
       "      <td>21</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>20.91</td>\n",
       "      <td>22</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>23.49</td>\n",
       "      <td>23</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>178</th>\n",
       "      <td>24.86</td>\n",
       "      <td>24</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>16.28</td>\n",
       "      <td>25</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>180</th>\n",
       "      <td>21.52</td>\n",
       "      <td>26</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>27.22</td>\n",
       "      <td>27</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>182</th>\n",
       "      <td>17.41</td>\n",
       "      <td>28</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>16.42</td>\n",
       "      <td>29</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>28.22</td>\n",
       "      <td>30</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>27.52</td>\n",
       "      <td>31</td>\n",
       "      <td>330</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>186 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Food.Pinching.Efficiency  Individual  Chopstick.Length\n",
       "0                       19.55           1               180\n",
       "1                       27.24           2               180\n",
       "2                       28.76           3               180\n",
       "3                       31.19           4               180\n",
       "4                       21.91           5               180\n",
       "5                       27.62           6               180\n",
       "6                       29.46           7               180\n",
       "7                       26.35           8               180\n",
       "8                       26.69           9               180\n",
       "9                       30.22          10               180\n",
       "10                      27.81          11               180\n",
       "11                      23.46          12               180\n",
       "12                      23.64          13               180\n",
       "13                      27.85          14               180\n",
       "14                      20.62          15               180\n",
       "15                      25.35          16               180\n",
       "16                      28.00          17               180\n",
       "17                      23.49          18               180\n",
       "18                      27.77          19               180\n",
       "19                      18.48          20               180\n",
       "20                      23.01          21               180\n",
       "21                      22.66          22               180\n",
       "22                      23.24          23               180\n",
       "23                      22.82          24               180\n",
       "24                      17.94          25               180\n",
       "25                      26.67          26               180\n",
       "26                      28.98          27               180\n",
       "27                      21.48          28               180\n",
       "28                      14.47          29               180\n",
       "29                      28.29          30               180\n",
       "..                        ...         ...               ...\n",
       "156                     26.18           2               330\n",
       "157                     25.93           3               330\n",
       "158                     28.61           4               330\n",
       "159                     20.54           5               330\n",
       "160                     26.44           6               330\n",
       "161                     29.36           7               330\n",
       "162                     19.77           8               330\n",
       "163                     31.69           9               330\n",
       "164                     24.64          10               330\n",
       "165                     22.09          11               330\n",
       "166                     23.42          12               330\n",
       "167                     28.63          13               330\n",
       "168                     26.30          14               330\n",
       "169                     22.89          15               330\n",
       "170                     22.68          16               330\n",
       "171                     30.92          17               330\n",
       "172                     20.74          18               330\n",
       "173                     27.24          19               330\n",
       "174                     17.12          20               330\n",
       "175                     23.63          21               330\n",
       "176                     20.91          22               330\n",
       "177                     23.49          23               330\n",
       "178                     24.86          24               330\n",
       "179                     16.28          25               330\n",
       "180                     21.52          26               330\n",
       "181                     27.22          27               330\n",
       "182                     17.41          28               330\n",
       "183                     16.42          29               330\n",
       "184                     28.22          30               330\n",
       "185                     27.52          31               330\n",
       "\n",
       "[186 rows x 3 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = '~/projects/nglgzz/data/chopsticks/chopstick-effectiveness.csv'\n",
    "# Change the path to the location where the chopstick-effectiveness.csv \n",
    "# file is located on your computer.\n",
    "# If you get an error when running this block of code, be sure\n",
    "# chopstick-effectiveness.csv is located at the path on your computer.\n",
    "\n",
    "dataFrame = pd.read_csv(path)\n",
    "dataFrame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's do a basic statistical calculation on the data using code! Run the block of code below to calculate the average \"Food Pinching Efficiency\" for all 31 participants and all chopstick lengths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25.00559139784947"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataFrame['Food.Pinching.Efficiency'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This number is helpful, but the number doesn't let us know which of the chopstick lengths performed best for the thirty-one male junior college students. Let's break down the data by chopstick length. The next block of code will generate the average \"Food Pinching Effeciency\" for each chopstick length. Run the block of code below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Chopstick.Length</th>\n",
       "      <th>Food.Pinching.Efficiency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>180</td>\n",
       "      <td>24.935161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>210</td>\n",
       "      <td>25.483871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>240</td>\n",
       "      <td>26.322903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>270</td>\n",
       "      <td>24.323871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>300</td>\n",
       "      <td>24.968065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>330</td>\n",
       "      <td>23.999677</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Chopstick.Length  Food.Pinching.Efficiency\n",
       "0               180                 24.935161\n",
       "1               210                 25.483871\n",
       "2               240                 26.322903\n",
       "3               270                 24.323871\n",
       "4               300                 24.968065\n",
       "5               330                 23.999677"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meansByChopstickLength =\n",
    "    dataFrame.groupby('Chopstick.Length')['Food.Pinching.Efficiency'].mean().reset_index()\n",
    "meansByChopstickLength\n",
    "\n",
    "# reset_index() changes Chopstick.Length from an index to column.\n",
    "# Instead of the index being the length of the chopsticks,\n",
    "# the index is the row numbers 0, 1, 2, 3, 4, 5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5. Which chopstick length performed the best for the group of thirty-one male junior college students?\n",
    "\n",
    "The one 240mm long"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
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kKcbCdpiZdYokYhRcRDczszHICcTMzEpxAjEzs1KcQMzMrBQnELOsUqnQ1zeTvr6ZVCqV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\nBGblMQs47LBLWbT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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f37d4e25fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Causes plots to display within the notebook rather than in a new window\n",
    "%pylab inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(x = meansByChopstickLength['Chopstick.Length'], \n",
    "            y = meansByChopstickLength['Food.Pinching.Efficiency'])\n",
    "\n",
    "plt.xlabel(\"Length in mm\")\n",
    "plt.ylabel(\"Efficiency in PPPC\")\n",
    "plt.title(\"Average Food Pinching Efficiency by Chopstick Length\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 6. Based on the scatterplot created from the code above, interpret the relationship you see. What do you notice?\n",
    "Chopstick lengths affect pinching efficiency, making it reach the higest point with 240mm and the lowest with 330mm. Also in the first 3 lengths the efficiency increases with increasing length, after that there's a big gap and the next values are all lower than the previous ones, a part in 300mm where the efficiency is pretty similar to 180mm.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### In the abstract the researchers stated that their results showed food-pinching performance was significantly affected by the length of the chopsticks, and that chopsticks of about 240 mm long were optimal for adults.\n",
    "\n",
    "#### 7a. Based on the data you have analyzed, do you agree with the claim?\n",
    "Yes, I do.\n",
    "\n",
    "#### 7b. Why?\n",
    "Observing the scatter plot and the data given from this controlled experiment it looks like the food-pinching performance is affected by the lenght of the chopsticks and that chopsticks of about 240mm are optimal for adults. However if we are to use just this data and not do any further test I would agree with the statement just if it was referred to the sample of the experiment, because we can't be sure that the difference of means between different chopsticks lengths is not caused by some lurking variable or due to chance.\n",
    "\n",
    "After running a repeated measures ANOVA test with the data provided, I can say that the difference in food-pinching performance was most likely not due to chance. So, I can now say the experiment showed that food-pinching performance was affected by chopsticks lengths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SS Condition: 106.85812043\n",
      "SS Error: 634.634046237\n",
      "MS Condition: 21.371624086\n",
      "MS Error: 4.23089364158\n",
      "F-Statistic: 5.0513262437\n"
     ]
    }
   ],
   "source": [
    "# I run a repeated measures ANOVA to check if there's any\n",
    "# significative difference between the efficiency mean\n",
    "# of different chopstick lengths.\n",
    "\n",
    "# I start by dividing the dataframe by lengths,\n",
    "groupsLabels = meansByChopstickLength[\"Chopstick.Length\"].to_dict().values()\n",
    "groupsByLength = dataFrame.groupby(\"Chopstick.Length\")\n",
    "groupsByLength = [groupsByLength.get_group(length)[\"Food.Pinching.Efficiency\"].to_dict().values() \n",
    "                  for length in groupsLabels]\n",
    "\n",
    "# I then find the mean for each group,\n",
    "groupMeans = meansByChopstickLength[\"Food.Pinching.Efficiency\"].to_dict().values()\n",
    "nSubjects = 31\n",
    "\n",
    "# each subject,\n",
    "subjectMeans = dataFrame.groupby(\"Individual\")[\"Food.Pinching.Efficiency\"].mean().reset_index()\n",
    "subjectMeans = subjectMeans[\"Food.Pinching.Efficiency\"].to_dict().values()\n",
    "\n",
    "# and the grand mean...\n",
    "grandMean = dataFrame[\"Food.Pinching.Efficiency\"].mean()\n",
    "\n",
    "# then I calculate the in-between groups variation,\n",
    "ssCondition = nSubjects * sum([(groupMean - grandMean)**2 for groupMean in groupMeans])\n",
    "print \"SS Condition: \" + str(ssCondition)\n",
    "\n",
    "# the within groups variation,\n",
    "ssWithin = []\n",
    "for i, x in enumerate(groupMeans):\n",
    "    ssWithin.append(sum([(xi - x)**2 for xi in groupsByLength[i]]))\n",
    "ssWithin = sum(ssWithin)\n",
    "\n",
    "# the within subject variation,\n",
    "ssSubject = len(groupMeans) * sum([(xi - grandMean)**2 for xi in subjectMeans])\n",
    "\n",
    "# and the error variation.  \n",
    "ssError = ssWithin - ssSubject\n",
    "print \"SS Error: \" + str(ssError)\n",
    "\n",
    "# I finally calculate the mean sum of squares for the condition and the error,\n",
    "msCondition = ssCondition / (len(groupMeans) - 1)\n",
    "msError = ssError / ((nSubjects -1)*(len(groupMeans) - 1))\n",
    "print \"MS Condition: \" + str(msCondition)\n",
    "print \"MS Error: \" + str(msError)\n",
    "\n",
    "# and I use them to determine the F-statistic\n",
    "fStat = msCondition / msError\n",
    "print \"F-Statistic: \" + str(fStat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
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   },
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   "source": [
    "# With the f-statistic and the df values found I then calculate the p-value\n",
    "# F(5, 150)=5.0513, p=.0003 \n",
    "\n",
    "# Given the result of the test, I can now reject the null hypothesis and agree with the\n",
    "# claim that the difference on the pinching efficiency means for the different chopstick lengths \n",
    "# are most likely not due to chance. "
   ]
  }
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