P1_StroopEffectAnalysis/P1_StroopEffectAnalysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# 有关Stroop效应的数据分析报告"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## 一. 问题背景"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 1. Stroop效应"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "维基百科对“Stroop效应”的解释为：\n",
    "\n",
    "> \"斯特鲁普效应(Stroop effect)是指在心理学中干扰对反应时间影响的实验。这是1935年实验心理学家史楚普（John Ridley Stroop）所提出的著名的发现之一，指出环境刺激物理的各项特征，如果相融，则会使辨识加速，反应时间缩短；但若互不相融，则会造成干扰，使反应时间拉长。例如当测试者被要求说出某个颜色和其字面意义不符的词语时，被测者往往会反应速度下降，出错率上升。\"\n",
    "\n",
    "本数据分析报告对一份样本容量为24的测试样本进行相关的假设检验研究。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 2. 体验Stroop效应"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "通过实验指导文档中提供的连接进行了一次Stroop测试，在一致条件下使用的时间为**18.655s**，在不一致条件下使用的时间为**38.823s**。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## 二. 对Stroop效应的数据分析"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 1. 自变量和因变量"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "实验中的自变量为不同类型的测试条件，包括一致性测试条件（字面意思与颜色一致）和不一致性测试条件（字面意思与颜色不一致）；因变量为完成该测试需要花费的时间（单位：秒）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 2. 假设集"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "用$\\mu_I$表示在不一致条件下进行测试所花平均时间，用$\\mu_C$表示在一致条件下进行测试所花平均时间，故：\n",
    "\n",
    "$H_0$：不一致条件下进行测试所花平均时间与在一致条件下进行测试所花平均时间并无差异，即$\\mu_I = \\mu_C$；\n",
    "\n",
    "$H_a$：不一致条件下进行测试所花平均时间与在一致条件下进行测试所花平均时间有显著的不同，即$\\mu_I \\neq \\mu_C$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 3. 统计检验模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "该心理学实验是对同一受测者依次进行两种条件下的测试，然后分别记录其所花费的时间。由于两种测试之间有一种相互依赖的关系，且总体的参数未知，对这样的数据进行假设检验，第一判断是采用相依样本t-检验。但是在下结论之前，先来看看样本数据分布的直方图："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f345010f290>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7f344cd9f190>]], dtype=object)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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V2I5hk9s4DSd3syl0GNuxFVgeEWOS1gG3U9x+Y4KqYzuqqHsMRnNcwlyN7Rg2uY3TcLeM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\nMuTkbmaWISd3M7MMObmbmWXo/wOwU2dd1ROmyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f34503cfa10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = pd.read_csv('stroopdata.csv')\n",
    "data.hist(bins=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "从直方图中可以观察到，样本数据的分布**近似满足正态分布的形状**，加之我们对**两种条件下实验数据的测试是相互独立的**，因此满足使用t-分布的条件，所以决定对样本数据进行上述检验。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "参考资料：[OpenIntro Statistics](https://www.openintro.org/stat/)，3rd，Chapter 5 Inference for numerical data，对t-分布使用前提条件的说明。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 4. 描述性统计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean:\n",
      "Congruent      14.051125\n",
      "Incongruent    22.015917\n",
      "dtype: float64\n",
      "\n",
      "Median:\n",
      "Congruent      14.3565\n",
      "Incongruent    21.0175\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print('Mean:')\n",
    "print(data.mean())\n",
    "print('\\nMedian:')\n",
    "print(data.median())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "样本均值：$\\bar{x}_C=14.051125$，$\\bar{x}_I=22.015917$。\n",
    "\n",
    "一致性条件下样本数据中位数为14.3565，不一致条件下样本数据中位数为21.0175。\n",
    "\n",
    "样本标准差$s_C=3.559358$，$s_I=4.797057$。\n",
    "\n",
    "从这些数据上看，不一致条件下测试花费的时间要比一致条件下高。真的是这样吗？让我们通过柱状图来看一下两类测试数据的对比情况："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f344cbac4d0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD/CAYAAADhYy38AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ni4gEQgVdRCQQKugiIoFQQRcRCcT/Bxq9ReET2SvmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f344cb38bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "从上图可以明显看出，不一致条件下进行测试所消耗的时间，无一例外都比一致条件下要高，有的甚至高了很多。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 6. 对样本数据进行t检验"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对总体均值差的点估计，为$$\\mu_C-\\mu_I=\\bar{x}_C-\\bar{x}_I=14.051125-22.015917=−7.964792$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.864826910359056"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(data['Congruent']-data['Incongruent']).std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "然后对样本数据的差值求标准差，得到$s=23.33089025215998$，t统计量为$t=\\frac{\\mu_C-\\mu_I}{s/\\sqrt{n}}=−8.02070728$，P值$\\le0.0001$，对自由度为23，$\\alpha=0.05$而言，其t临界值为$t_{critical}=\\pm 2.069$，置信区间为[-10.02, -5.91]，由于t统计量位于t临界区中，所以在这个情况下我们**应当拒绝零假设**，即该均值的差在$\\alpha$为.05水平下具有统计显著性。不一致条件下受试者所花费的时间要大于一致条件下花费的时间。"
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    "## 三. 结论"
   ]
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    "假设检验得到的结论与我们观察到的事实相符合。即当单词字面意思与其颜色不一致时，受试者正确读出颜色的反应时间会增加。通过查阅维基百科相关资料，可以发现导致这一现象的原因有多种解释。第一种解释是人脑对文字的反应速度要比对颜色的反应速度快；第二种解释是人脑阅读文字所需的注意力比辨识颜色所需的注意力要少，花的时间就更少；第三种解释是人脑对文字的反应几乎是一种“自动的过程”，对颜色的辨识则不是；第四种解释是人脑对于不同信息的分析处理使用的脑回路是不同的，有一些处理回路（比如阅读）就要强一些，使用的时间也就短一些。虽然第三种解释比较普遍，我个人认为第四种解释要合理一些，因为大脑是后天训练出来的，对于大部分人而言，阅读文字是每天都可能碰到的事，而辨识颜色则不那么经常进行，所以对文字的反应速度当然要快些，当然，文字和颜色的互相干扰是会产生一定影响的，如果受试者不懂英语，看不懂文字，那么他/她的注意力会放在颜色上，这样反应速度应该会提高，用的时间会减少，当然，这只是一种“假设”，是不是真的是这样，还需要进行类似试验并使用统计学来推断。\n",
    "\n",
    "类似的试验任务还可以这样设计：\n",
    "\n",
    "1. 受试者分别按照试验指示的动作做相同的动作，然后再按照指示做完全相反的动作，记录两次测试的反应时间；\n",
    "2. 受试者首先对阿拉伯数字进行比大小，然后再对英文数字和阿拉伯数字比大小，比如three 5，记录两次测试的反应时间；"
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