p1/stroop.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## P1: Test a Perceptual Phenomenon\n",
    "    \n",
    "    \n",
    "### Background Information\n",
    "\n",
    "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: for example RED, BLUE. In the incongruent words condition, the words displayed are color words whose names do not match the colors in which they are printed: for example PURPLE, ORANGE. 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.\n",
    "\n",
    "Stroop task applet: [applet](https://www.google.com/url?q=https%3A%2F%2Ffaculty.washington.edu%2Fchudler%2Fjava%2Fready.html&sa=D&sntz=1&usg=AFQjCNGc_1cOHZy4iwBhM93xXvCImuQ1sQ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. What is our independent variable? What is our dependent variable?\n",
    "\n",
    "Independent variable: task condition (a congruent/incongruent words condition)\n",
    "\n",
    "Dependent variable: reaction time of the task (measured with the time it takes to name the ink colors in equally-sized lists).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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.\n",
    "    \n",
    "Let us have:  \n",
    "population = any person that can perform the Stroop task (can read the list of words and recognize ink colors). The task definition does not put any extra constraints on the population.  \n",
    "$\\mu_c$ = mean reaction time of entire population on the congruent condition test  \n",
    "$\\mu_i$ = mean reaction time of the same entire population on the incogruent condition test  \n",
    "\n",
    "\n",
    "Test hypothesis:  \n",
    "**H0**: Task condition does not effect reaction time. Mean reaction time of the entire population is the same on both congruent and incogruent test.  \n",
    "$\\mu_c = \\mu_i$ \n",
    "\n",
    "**HA**: Task condition effects the reaction time. Congruent test has either significantly lower or significantly higher mean reaction time than the incogruent test.  \n",
    "$\\mu_c < \\mu_i$ or $\\mu_c > \\mu_i$\n",
    "\n",
    "We have results of two experiments performed on the same sample. This is a scenario for dependent t-test for paired samples.  \n",
    "We don't try to guess/decide if the congruent test or incogruent test will perform better, thus we'll use 2-tailed t-test.\n",
    "\n",
    "\n",
    "Alternatively, we could use *intererence* as dependent variable. Interference would be defined as reaction time on incongruent words condition minus reaction time on congruent words condition. In such case:  \n",
    "**H0**: Task is not interfered by the condition. Mean interference of the entire population = 0.  \n",
    "**HA**: Task is interfered by the condition. Mean population interference is either < 0 or intererence > 0.  \n",
    "We should also use 2-tailed t-test for this scenario (dependent samples).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Report some descriptive statistics regarding this dataset. Include at least one measure of central tendency and at least one measure of variability.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0      7.199\n",
      "1      1.950\n",
      "2     11.650\n",
      "3      7.057\n",
      "4      8.134\n",
      "5      8.640\n",
      "6      9.880\n",
      "7      8.407\n",
      "8     11.361\n",
      "9     11.802\n",
      "10     2.196\n",
      "11     3.346\n",
      "12     2.437\n",
      "13     3.401\n",
      "14    17.055\n",
      "15    10.028\n",
      "16     6.644\n",
      "17     9.790\n",
      "18     6.081\n",
      "19    21.919\n",
      "20    10.950\n",
      "21     3.727\n",
      "22     2.348\n",
      "23     5.153\n",
      "Name: Interference, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "path = r'./stroopdata.csv'\n",
    "df = pd.read_csv(path)\n",
    "df['Interference'] = df['Incongruent'] - df['Congruent']\n",
    "df\n",
    "print df['Interference']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Congruent test:\n",
      "\tmean = 14.051125\n",
      "\tstd  = 3.55935795765\n",
      "\n",
      "Incongruent test:\n",
      "\tmean = 22.0159166667\n",
      "\tstd  = 4.79705712247\n",
      "\n",
      "Interference (diff):\n",
      "\tmean = 7.96479166667\n",
      "\tstd  = 4.86482691036\n"
     ]
    }
   ],
   "source": [
    "print 'Congruent test:'\n",
    "c_mean, c_std = df['Congruent'].mean(), df['Congruent'].std()\n",
    "print '\\tmean = {0}'.format(c_mean)\n",
    "print '\\tstd  = {0}'.format(c_std)\n",
    "print\n",
    "\n",
    "print 'Incongruent test:'\n",
    "i_mean, i_std = df['Incongruent'].mean(), df['Incongruent'].std()\n",
    "print '\\tmean = {0}'.format(i_mean)\n",
    "print '\\tstd  = {0}'.format(i_std)\n",
    "print\n",
    "\n",
    "print 'Interference (diff):'\n",
    "d_mean, d_std = df['Interference'].mean(), df['Interference'].std()\n",
    "print '\\tmean = {0}'.format(d_mean)\n",
    "print '\\tstd  = {0}'.format(d_std)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmEAAAIACAYAAADKXbu0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlLkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa339e38b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmcAAAIACAYAAADHQ8vzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMAjhDAAAwCCEMwAAAIMQzgAAAAzyP+Q4hRlvAjN3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa339d4f490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmEAAAIACAYAAADKXbu0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nd/UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa33a5fd4d0>"
      ]
     },
     "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",
    "matplotlib.style.use('ggplot')\n",
    "\n",
    "fig = plt.figure(figsize=(10, 8))\n",
    "plt.hist([df['Congruent'], df['Incongruent']], bins = 15, label = ['congruent', 'incongruent'])\n",
    "plt.title('Plot #1: Reaction time for congruent and incogruent tests')\n",
    "plt.xlabel('reaction time (s)')\n",
    "plt.ylabel('# of samples')\n",
    "plt.legend(['Congruent', 'Incongruent'])\n",
    "plt.show()\n",
    "\n",
    "s = [x for x in xrange(len(df['Congruent']))]\n",
    "fig = plt.figure(figsize=(10, 8))\n",
    "plt.bar([x + 0.1 for x in s], df['Congruent'], width=0.4, color='r')\n",
    "plt.bar([x + 0.5 for x in s], df['Incongruent'], width=0.4)\n",
    "plt.title('Plot #2: Reaction time for congruent and incogruent for each participant')\n",
    "plt.xlabel('Participants')\n",
    "plt.ylabel('Reaction time (s)')\n",
    "plt.legend(['Congruent', 'Incongruent'])\n",
    "plt.show()\n",
    "\n",
    "fig = plt.figure(figsize=(10, 8))\n",
    "plt.hist(df['Interference'], bins = 12)\n",
    "plt.title('Plot #3: Increase in reaction time on incongruent test')\n",
    "plt.xlabel('reaction time increase == interference (s)')\n",
    "plt.ylabel('# of samples')\n",
    "#plt.legend(['Interference'])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot \\#1:  \n",
    "- histograms of both congruent and incogruent test starts to look like normal distribution\n",
    "- incongruent test reaction times are noticeably higher than cogruent test's.\n",
    "\n",
    "Plot \\#2:  \n",
    "- each participant reaction time was bigger on incogruent test\n",
    "\n",
    "Plot \\#3:\n",
    "- due to small number of samples there is no obvious answer what is the type of interference distribution.  \n",
    "  The most interesting candidates are: normal distribution, right-skewed and bimodal.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####5. Now, perform the statistical test and report your results. What is your 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?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "confidence level: 5%   \n",
    "n (# of samples): 24  \n",
    "df (degrees of freedom): 23  \n",
    "critical statistic value: +/-2.069  \n",
    "\n",
    "\n",
    "t = $\\frac{\\mu_i - \\mu_c}{s / \\sqrt{n}}$ = $\\frac{22.0159 - 14.0511}{4.8648 / \\sqrt{24}}$ = 8.0207\n",
    "\n",
    "The t-statistic rejects the null hypothesis.  \n",
    "With 95% confidence we can say that incongruent test has significantly different reaction time than congruent test.\n",
    "\n",
    "This is an expected result for me. I tried to do the test and there was noticeable difference in the way how the brain performs the task: congruent test seemed much more automatic (and as result, faster), than incongruent test.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(8.020706944109957, 4.1030005857111781e-08)\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "rvs = stats.ttest_rel(df['Incongruent'], df['Congruent'])\n",
    "print rvs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 6. Optional: What do you think is responsible for the effects observed? Can you think of an alternative or similar task that would result in a similar effect? Some research about the problem will be helpful for thinking about these two questions!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The congruent task was more about reading the colors than recognizing them.  \n",
    "The incogruent task was about recognizing the colors.  \n",
    "Both tasks have different levels of automations: people spend significantly more time reading than consciously naming colors which they see.\n",
    "    \n",
    "Probably similar results can be obrained if we replace any of the tasks with a task with similar automation level:\n",
    "- more-automated task: using bigger/smaller font\n",
    "- less-automated task: determine if number is odd/even\n",
    "\n",
    "Then:  \n",
    "**congruent task**: given an array of numbers (e.g. 30?), count how many of them are even. Even numbrers would be written with slighlty bigger font than odd ones.  \n",
    "**incogruent task**: count how many number are even. Some numbers are written with bigger font than others, but there is no correlation between parity and font size.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bibliography:\n",
    "    \n",
    "- [Stroop effect on Wikipedia](https://en.wikipedia.org/wiki/Stroop_effect)\n",
    "- [1 vs 2 tailed test](http://www.chem.utoronto.ca/coursenotes/analsci/StatsTutorial/12tailed.html)\n",
    "- [z-test vs t-test](http://www2.le.ac.uk/departments/biology/existing/introduction-to-statistics/comparisons/z-tests-and-t-tests)\n",
    "- [dependent t-test on Wikipedia](https://en.wikipedia.org/wiki/Student%27s_t-test#Dependent_t-test_for_paired_samples)\n",
    "- [dependent sample t-test example](http://stattrek.com/hypothesis-test/paired-means.aspx?Tutorial=AP)\n",
    "- [chemosensory cross-modal stroop effects](http://chemse.oxfordjournals.org/content/32/4/337.full)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}