StroopEffect & Boxplot.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "# Test a Perceptual Phenomenon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "editable": true
   },
   "source": [
    "Let's investigate a classic phenomenon from experimental psychology called the **Stroop Effect**. \n",
    " - Create a hypothesis regarding the outcome of the task, \n",
    " - then go through the task. You will then look at some data collected from others who have performed the same task and will compute some statistics describing the results. \n",
    " - Finally, you will interpret your results in terms of your hypotheses."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "Statistics is a major component of data analysis, it allows you to investigate data and make inferences based on your observations. A foundation in statistics also allows you to be a consumer of analyses that others perform, and allows you to relate to the conclusions others have drawn from their investigations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In a Stroop task, participants are presented with a list of words, with each word displayed in a color of ink. The participant’s task is to say out loud the color of the ink in which the word is printed. The task has two conditions: a congruent words condition, and an incongruent words condition. In the congruent words condition, the words being displayed are color words whose names match the colors in which they are printed. In the incongruent words condition, the words displayed are color words whose names do not match the colors in which they are printed. In each case, we measure the time it takes to name the ink colors in equally-sized lists. Each participant will go through and record a time from each condition."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### Analyzing the Stroop Effect\n",
    "Perform the analysis in the space below. Remember to follow [the instructions](https://docs.google.com/document/d/1-OkpZLjG_kX9J6LIQ5IltsqMzVWjh36QpnP2RYpVdPU/pub?embedded=True) and review the [project rubric](https://review.udacity.com/#!/rubrics/71/view) before submitting. \n",
    "\n",
    "(1) What is the independent variable? What is the dependent variable?"
   ]
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   "source": [
    "**> independent variable:** the binary conditions comprised of a congruent words condition, and an incongruent words condition \n",
    "\n",
    "**> dependent variable:** the time taken to name the ink colors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "(2) What is an appropriate set of hypotheses for this task? What kind of statistical test do you expect to perform? Justify your choices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "Is there any difference between the time under a congruent words condition $time_{congruent}$ and the time under a incongruent words condition $time_{incongruent}$? Assuming the data are normally distributed, we need to test the difference before and after some treatment on an the same individual with two dependent samples: **Paired t-test**. Plus, We seemingly have less sample sizes(n < 30), and the real variance is unknown.\n",
    "\n",
    "$\\mu_{incongruent}$ is the mean of the real population of the incongruent test.\n",
    "\n",
    "$\\mu_{congruent}$ is the mean of the real population of the congruent test.\n",
    "\n",
    "$H_0: \\mu_{incongruent} - \\mu_{congruent} = 0$ : Null: there is no difference of the mean in the time taken to name the color under the congruent condition and the incongruent condition. \n",
    "\n",
    "$H_1: \\mu_{incongruent} - \\mu_{congruent} \\neq 0$ : Alternative: there is a significant difference of the mean in the time taken to name the color under the congruent condition and the incongruent condition. \n",
    "\n",
    "Ultimately, we want to know if the stroop effect holds true in reality which means the reliability of the result when it comes to 'true population.' We have only tiny samples thus this is where a sort of inference should come in.  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now it’s your chance to try out the Stroop task for yourself. Go to this [link](https://faculty.washington.edu/chudler/java/ready.html), which has a Java-based applet for performing the Stroop task. Record the times that you received on the task (you do not need to submit your times to the site.) Now, download this [dataset](https://drive.google.com/file/d/0B9Yf01UaIbUgQXpYb2NhZ29yX1U/view) which contains results from a number of participants in the task. Each row of the dataset contains the performance for one participant, with the first number their results on the congruent task and the second number their performance on the incongruent task."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "(3) Report some descriptive statistics regarding this dataset. Include at least one measure of **central tendency** and at least one measure of **variability**. The name of the data file is 'stroopdata.csv'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Congruent</th>\n",
       "      <th>Incongruent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.079</td>\n",
       "      <td>19.278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>16.791</td>\n",
       "      <td>18.741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9.564</td>\n",
       "      <td>21.214</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Congruent  Incongruent\n",
       "0     12.079       19.278\n",
       "1     16.791       18.741\n",
       "2      9.564       21.214"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_csv('C:/Users/Minkun/Desktop/classes_1/NanoDeg/1.Data_AN/L6/stroopdata.csv')\n",
    "df.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 24 entries, 0 to 23\n",
      "Data columns (total 2 columns):\n",
      "Congruent      24 non-null float64\n",
      "Incongruent    24 non-null float64\n",
      "dtypes: float64(2)\n",
      "memory usage: 464.0 bytes\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Congruent      14.051125\n",
       "Incongruent    22.015917\n",
       "dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Congruent      3.559358\n",
       "Incongruent    4.797057\n",
       "dtype: float64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Congruent</th>\n",
       "      <th>Incongruent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>24.000000</td>\n",
       "      <td>24.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>14.051125</td>\n",
       "      <td>22.015917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.559358</td>\n",
       "      <td>4.797057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>8.630000</td>\n",
       "      <td>15.687000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>11.895250</td>\n",
       "      <td>18.716750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>14.356500</td>\n",
       "      <td>21.017500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>16.200750</td>\n",
       "      <td>24.051500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>22.328000</td>\n",
       "      <td>35.255000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Congruent  Incongruent\n",
       "count  24.000000    24.000000\n",
       "mean   14.051125    22.015917\n",
       "std     3.559358     4.797057\n",
       "min     8.630000    15.687000\n",
       "25%    11.895250    18.716750\n",
       "50%    14.356500    21.017500\n",
       "75%    16.200750    24.051500\n",
       "max    22.328000    35.255000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "(4) Provide one or two visualizations that show the distribution of the sample data. Write one or two sentences noting what you observe about the plot or plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1da573a0550>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1da593a0be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.hist(df.Congruent, alpha=0.3, label='Congruent')\n",
    "plt.hist(df.Incongruent, alpha=0.3, label='Incongruent')\n",
    "\n",
    "plt.xlabel('time in sec')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1da5cc58208>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1da57554588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# boxplot, which shows the distribution and highlight probable outliers.\n",
    "\n",
    "# Create a figure instance\n",
    "fig = plt.figure(1, figsize=(9, 6))\n",
    "\n",
    "# Create an axes instance\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "data_to_plot = [df.Congruent, df.Incongruent]\n",
    "\n",
    "# Create the boxplot and get fill color in boxes\n",
    "bp = ax.boxplot(data_to_plot, patch_artist=True); bp\n",
    "\n",
    "# Custom x-axis labels\n",
    "ax.set_xticklabels(['Congruent', 'Incongruent'])\n",
    "\n",
    "plt.title('Box plot of the two distributions')\n",
    "## change outline color, fill color and linewidth of the boxes\n",
    "#for box in bp['boxes']:\n",
    "    # change outline color\n",
    "#    box.set( color='#7570b3', linewidth=2)\n",
    "    # change fill color\n",
    "#    box.set( facecolor = '#1b9e77' )\n",
    "\n",
    "## change color and linewidth of the whiskers\n",
    "#for whisker in bp['whiskers']:\n",
    "#    whisker.set(color='#7570b3', linewidth=2)\n",
    "\n",
    "## change color and linewidth of the caps\n",
    "#for cap in bp['caps']:\n",
    "#    cap.set(color='#7570b3', linewidth=2)\n",
    "\n",
    "## change color and linewidth of the medians\n",
    "#for median in bp['medians']:\n",
    "#    median.set(color='#b2df8a', linewidth=2)\n",
    "\n",
    "## change the style of fliers and their fill\n",
    "#for flier in bp['fliers']:\n",
    "#    flier.set(marker='o', color='#e7298a', alpha=0.5)\n",
    "\n",
    "\n",
    "# save ?\n",
    "#import matplotlib as mpl \n",
    "\n",
    "## agg backend is used to create plot as a .png file\n",
    "#mpl.use('agg')\n",
    "\n",
    "## Save the figure\n",
    "#fig.savefig('fig1.png', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Seemingly, given the shape of these two distributions, 'Incongruent group' shows more records of delayed time to name the color. We might need to test the significance of their difference in means. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "(5) Now, perform the statistical test and report the results. What is the confidence level and your critical statistic value? Do you reject the null hypothesis or fail to reject it? Come to a conclusion in terms of the experiment task. Did the results match up with your expectations?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_relResult(statistic=-8.020706944109957, pvalue=4.1030005857111781e-08)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# First, we can do 'paired t-test'\n",
    "\n",
    "import scipy.stats as stats\n",
    "\n",
    "stats.ttest_rel(df['Congruent'], df['Incongruent'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "Its P-value is 0.000000041 (the probability of the acceptance of Null) which is far smaller than 0.025 (the level of significance in the two tailed test); therefore, we reject the Null, saying there is a significant difference in their means. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10.41912098716289, -5.5104623461704474)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can say the Confidence level alpha = 0.05 for 95% CI (two tailed), so (P-value < 0.025). we can find the C.I\n",
    "\n",
    "import statsmodels.stats.api as sm\n",
    "cm = sm.CompareMeans(sm.DescrStatsW(df['Congruent']), sm.DescrStatsW(df['Incongruent']))\n",
    "cm.tconfint_diff(usevar='pooled')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "If we have t-distribution graph..\n",
    "\n",
    "Compare the t-value to the critical t-value. If the absolute value of the t-value is greater than the critical t-value, we reject the null hypothesis. If the absolute value of the t-value is less than the critical t-value, you fail to reject the null hypothesis."
   ]
  }
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