08-01-statistics-thinking.ipynb

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    "\n",
    "# 第五章 统计思维\n",
    "\n",
    "\n",
    "![image.png](./images/author.png)\n",
    "\n"
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    "![](./img/stats/preface2.png)\n",
    "\n",
    "\n",
    "1. Introduction\n",
    "2. A Crash Course in Python\n",
    "3. Visualizing Data\n",
    "4. Linear Algebra\n",
    "5. Statistics\n",
    "6. Probability\n",
    "7. Hypothesis and Inference\n",
    "8. Gradient Descent\n",
    "\n",
    "\n"
   ]
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    "<img src = './img/stats/school.png' width = '800px' > \n",
    "\n",
    "**The School of Athens** by Raphael (1509–1510), fresco at the Apostolic Palace, Vatican City. https://en.wikipedia.org/wiki/Platonic_Academy"
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    "<img src = './img/stats/socrats2.png' width = '800px' > \n",
    "\n",
    "The School of Athens by Raphael (1509–1510), fresco at the Apostolic Palace, Vatican City. https://en.wikipedia.org/wiki/Platonic_Academy"
   ]
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    "<img src = './img/stats/plato.jpg' width = '150px' align = 'right'> \n",
    "\n",
    "## Plato & Typological Thinking\n",
    "\n",
    "Pythagoras held that \n",
    "- all things are number\n",
    "- the cosmos comes from numerical principles. \n",
    "    \n",
    "`The theory of Forms` or `theory of Ideas` is a philosophical theory, concept, or world-view, attributed to Plato, that the `physical world` is not as real or true as timeless, absolute, unchangeable `ideas`."
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    "<img src = 'img/stats/plato2.png' width = '150px' align = 'right'> \n",
    "\n",
    "真实的知识存在于普遍而永恒的法则之中。\n",
    "\n",
    "The physical world of becoming is an imitation of the mathematical world of being.\n",
    "- the realm of being 本质世界(理念世界)\n",
    "    - perfect, eternal, and changeless forms, \n",
    "- sensible world of becoming  现实世界\n",
    "    - imperfect\n"
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    "### Social Physics: Taking Physics as a Role Model\n",
    "- French social thinker **Henri de Saint-Simon** 1803 described the idea of describing society using laws similar to those of the physical and biological sciences.\n",
    "- His student and collaborator was **Auguste Comte**, a French philosopher, the founder of sociology, who first defined the term \n",
    "\n",
    "> Social physics is that science which occupies itself with social phenomena, considered in the same light as astronomical, physical, chemical, and physiological phenomena, that is to say as being subject to **natural and invariable laws**, the discovery of which is the special object of its researches.\n",
    "\n",
    "- Computational Social Science\n",
    "\n",
    "https://en.wikipedia.org/wiki/Social_physics\n",
    "\n"
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    "<img src = './img/stats/Adolphe_Quételet.jpg' width = '200px' align = 'right'> \n",
    "\n",
    "**Lambert Adolphe Jacques Quetelet** (1796-1874)\n",
    "introducing statistical methods to the social sciences in his book titled **Essays on Social Physics**, \n",
    "- the concept of the \"average man\" \n",
    "- characterized by the mean values \n",
    "- follow a normal distribution. \n",
    "- He collected data about many such variables.\n",
    "    - developed the body mass index scale\n",
    "        \n",
    "> “His goal was to understand the statistical laws underlying such phenomena as crime rates, marriage rates or suicide rates. He wanted to explain the values of these variables by other social factors”."
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    "\n",
    "<img src = './img/stats/darwin.jpg' width = '200px' align = 'right'> \n",
    "\n",
    "## **Population Thinking**\n",
    "\n",
    "**Charles Robert Darwin** (12 February 1809 – 19 April 1882)\n",
    "\n",
    "> favourable variations would make organisms better at surviving and passing the variations on to their offspring, while unfavourable variations would be lost.\n",
    "\n",
    "- Variation is the basis of natural seletion. \n",
    "\n",
    "> 在类型逻辑中平均数是主要的内容。在总体逻辑中重要的是差异，平均数只是总体的一个特征值，是探讨真实原因的手段，而不是原因本身。"
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    "Statisticism  or Damn Lies\n",
    "\n",
    "\"统计至上主义\"天真地以为统计学是科学方法的完备基础。\n",
    "- 改进测量工具\n",
    "- 研究设计、概念化\n",
    "\n",
    "Duncan, O.D. 1984. Notes on Social Measurement, Historical and Critical. New York: Russell Sage Fundation, p.226."
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    "The Paradigm of Demography\n",
    "\n",
    "\n",
    "Otis Dudley Duncan (1921-2004) 确立一种新的学术传统\n",
    "- 蔑视模仿自然科学试图寻找普遍规律的做法；\n",
    "- 记录和理解真实人口中的经验模式是第一要务；\n",
    "- 变异是人类社会的本质。\n",
    "    - 柏拉图：变异是对本质世界的拙劣复制。"
   ]
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    "<img src = './img/stats/aristotle2.png' width = '600px' > \n",
    "\n",
    "The School of Athens by Raphael (1509–1510), fresco at the Apostolic Palace, Vatican City. https://en.wikipedia.org/wiki/Platonic_Academy"
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   "source": [
    "<img src = './img/stats/galton.jpg' width = '200px' align = 'right'>\n",
    "\n",
    "### 本体论： 世界的本质\n",
    "\n",
    "> “我认为自然科学是以“挖掘”本质的世界中的真理为最终目的，这也是其精华所在。而社会科学是以“了解”形成的世界为最终目的。历史上很多人想在社会科学领域找到一种真理，能够适用于各个方面，并且做过许多这方面的尝试。我认为社会科学不应该是这样的。在社会科学中，我们的目的是要了解现实世界，而不是去挖掘永恒的真理。这可能和你们的想象不一样。......既然差异是世界的本质，那差异就应该是研究的对象。” --- 谢宇 \n",
    "\n",
    "- 高尔顿认为凯特莱的社会物理学用处不大，普通人不是万能的。\n",
    "    - 左手入冰，右手入火，平均温度？\n",
    "- 高尔顿说（社会）科学的探索必须关注变异和共变。\n",
    "    - variation & Co-variation\n"
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    "\n",
    "The measurements have both \n",
    "- a central tendency, or mean, and \n",
    "- a spread around this central value, or variance. \n",
    "<img src = './img/stats/galton.jpg' width = '200px' align = 'right'>\n",
    "   \n",
    "   - In the late 1860s, Galton conceived of a measure to quantify normal variation: \n",
    "        - the **standard deviation**.\n",
    "- \"Regression to mediocrity\"\n",
    "\n"
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    "### 认识论： 人类知识的起源、本质、方法及局限\n",
    "\n",
    "谢宇：“你到底能知道什么，你怎样认识世界。\"\n",
    "- 自然科学追求永恒真理，关注典型现象；\n",
    "    - 典型现象 & 平均人\n",
    "- 社会科学关注所有个案组成的总体的状况。"
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   "source": [
    "### 方法论： 使用什么方法\n",
    "\n",
    "谢宇：“社会科学之所以复杂，是因为我们运用的数据是通过观察所得，而观察所得的数据必然受到外来因素的影响，这些外来因素都可能解释你的数据。“\n",
    "- 自然科学使用实验来隔离外来因素的影响；\n",
    "- “社会科学可以使用统计排除一些外来影响，但你不能排除所有的外来因素”。"
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    "### Three Basic Principles of Social Science Research\n",
    "\n",
    "- Variability Principle\n",
    "    - Social Grouping Principle\n",
    "    - Social Context Principle"
   ]
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    "\n",
    "## Statistics for Describing Data\n",
    "\n",
    "\n",
    "The mathematics and techniques with which we understand data."
   ]
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    "from collections import Counter\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "\n",
    "matplotlib.style.use('ggplot')"
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   "source": [
    "def dot(v, w):\n",
    "    \"\"\"v_1 * w_1 + ... + v_n * w_n\"\"\"\n",
    "    return sum(v_i * w_i for v_i, w_i in zip(v, w))\n",
    "\n",
    "def sum_of_squares(v):\n",
    "    \"\"\"v_1 * v_1 + ... + v_n * v_n\"\"\"\n",
    "    return dot(v, v)\n"
   ]
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    "daily_minutes = [1,68.77,51.25,52.08,38.36,44.54,57.13,\n",
    "                 51.4,41.42,31.22,34.76,54.01,38.79,\n",
    "                 47.59,49.1,27.66,41.03,36.73,48.65,28.12,\n",
    "                 46.62,35.57,32.98,35,26.07,23.77,39.73,\n",
    "                 40.57,31.65,31.21,36.32,20.45,21.93,26.02,\n",
    "                 27.34,23.49,46.94,30.5,33.8,24.23,21.4,27.94,\n",
    "                 32.24,40.57,25.07,19.42,22.39,18.42,46.96,23.72,\n",
    "                 26.41,26.97,36.76,40.32,35.02,29.47,30.2,31,\n",
    "                 38.11,38.18,36.31,21.03,30.86,36.07,28.66,\n",
    "                 29.08,37.28,15.28,24.17,22.31,30.17,25.53,\n",
    "                 19.85,35.37,44.6,17.23,13.47,26.33,35.02,\n",
    "                 32.09,24.81,19.33,28.77,24.26,31.98,25.73,\n",
    "                 24.86,16.28,34.51,15.23,39.72,40.8,26.06,\n",
    "                 35.76,34.76,16.13,44.04,18.03,19.65,32.62,\n",
    "                 35.59,39.43,14.18,35.24,40.13,41.82,35.45,\n",
    "                 36.07,43.67,24.61,20.9,21.9,18.79,27.61,27.21,\n",
    "                 26.61,29.77,20.59,27.53,13.82,33.2,25,33.1,36.65,\n",
    "                 18.63,14.87,22.2,36.81,25.53,24.62,26.25,18.21,\n",
    "                 28.08,19.42,29.79,32.8,35.99,28.32,27.79,35.88,29.06,\n",
    "                 36.28,14.1,36.63,37.49,26.9,18.58,38.48,24.48,\n",
    "                 18.95,33.55,14.24,29.04,32.51,25.63,22.22,19,\n",
    "                 32.73,15.16,13.9,27.2,32.01,29.27,33,13.74,20.42,\n",
    "                 27.32,18.23,35.35,28.48,9.08,24.62,20.12,35.26,\n",
    "                 19.92,31.02,16.49,12.16,30.7,31.22,34.65,13.13,\n",
    "                 27.51,33.2,31.57,14.1,33.42,17.44,10.12,24.42,\n",
    "                 9.82,23.39,30.93,15.03,21.67,31.09,33.29,22.61,\n",
    "                 26.89,23.48,8.38,27.81,32.35,23.84]\n"
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    "num_friends = [100,49,41,40,25,21,21,19,19,18,\n",
    "               18,16,15,15,15,15,14,14,13,13,\n",
    "               13,13,12,12,11,10,10,10,10,10,\n",
    "               10,10,10,10,10,10,10,10,10,10,\n",
    "               9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,\n",
    "               9,9,9,8,8,8,8,8,8,8,8,8,8,8,8,8\n",
    "               ,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,\n",
    "               6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,\n",
    "               6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,\n",
    "               5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,\n",
    "               4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,\n",
    "               3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,\n",
    "               2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,\n",
    "               1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,\n",
    "               1,1,1,1,1,1,1]"
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   "source": [
    "### Distribution and Histogram"
   ]
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_counts = Counter(map(int, daily_minutes))\n",
    "xs = range(69)\n",
    "ys = [time_counts[x] for x in xs]\n",
    "plt.bar(xs, ys)\n",
    "plt.axis([0,69,0,14])\n",
    "plt.title(\"Histogram of Time Counts\")\n",
    "plt.xlabel(\"# of Time\")\n",
    "plt.ylabel(\"# of people\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:44:55.414245Z",
     "start_time": "2023-11-24T06:44:55.159021Z"
    },
    "cell_style": "split",
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EhK2tLZ5++mloNBpcu3YNcXFxePDBB7F//370798fEydOxK5du7Br1y5MnTrVEiUREVErLHKIycPDAxqNBgDg5OQEf39/lJWVITs7GxEREQCAiIgIZGdnW6IcIiIygcW/Ua64uBgFBQUICgpCRUUFPDw8ADSGyJUrVxTn0Wq10Gq1AICEhASo1Wpcvmm8Wq02mv7yE2EAAJ+dmYbXN94bTdfM/HcDOzu7u7Juc2AvGrEPjdiHRneiDxYNiOrqaiQmJiImJgbOzs4mzxcVFYWoqCjDe51OZzT+1vc/drq7gVqtvivrNgf2ohH70Ih9aHRrH/z8/G57GRa7iqmurg6JiYkYMWIEQkNDAQBubm7Q6/UAAL1eD1dXV0uVQ0RErbBIQIgI1q9fD39/f4wbN84wPCQkBOnp6QCA9PR0DBkyxBLlEBGRCSxyiOnMmTPIyMhA9+7dsXDhQgBAdHQ0Jk6ciKSkJKSlpUGtVmP+/PmWKIeIiExgkYDo27cvtm/frjhu6dKlliiBiIhuE++kJiIiRQwIIiJSxIAgIiJFDAgiIlLEgCAiIkUMCCIiUsSAICIiRQwIIiJSxIAgIiJFDAgiIlLEgCAiIkUW/8Kgu039byYYXttu+MSKlRARWRb3IIiISBEDgoiIFDEgiIhIEQOCiIgUMSCIiEgRA4KIiBQxIIiISBEDgoiIFN0TN8qZejMbb3ojIjId9yCIiEgRA4KIiBQxIIiISBEDgoiIFDEgiIhI0W0FhE6nw9mzZ81VCxERtSMmXeaq0+nw5ptvorCwEACwdetWHD58GMePH8fMmTPNWR8REVmJSXsQf/nLXzBw4EBs2bIFdnaNmfLggw/ixIkTZi2OiIisx6SAyMvLw8SJE2Fj87/JnZ2dUVVVZbbCiIjIukwKCDc3N3z33XdGwy5evAi1Wm2WooiIyPpMOgcxfvx4rFq1ChMnTkRDQwMOHjyInTt3YuLEiWYuj4iIrMWkgHj44Yfh4uKC1NRUeHl5IT09HU8++SSGDh1q7vqIiMhKTH5Y39ChQxkIREQdSLMBkZaWZtICHn744VanWbduHXJycuDm5obExEQAwPbt25GamgpXV1cAQHR0NAYNGmTSOomIyPyaDYgDBw6YtABTAmLkyJF49NFHkZycbDT88ccfx4QJE5qZi4iIrKnZgIiPj79jK+nXrx+Ki4vv2PKIiMj8TD4H8f333yMnJwd6vR4eHh4YNGgQOnfu/KNW/vnnnyMjIwMajQbPPPMMXFxcFKfTarXQarUAgISEBKjValxuZpk3j7ut6Z4IAwD47Mw0mu7yrfM0M52l2dnZ8TLjH7AXjdiHRuxDozvRB5MC4uTJk3j99dfh5+cHtVqN0tJSbNy4ES+99BL69+/fphWPHj0akydPBgBs27YN7733HmbNmqU4bVRUFKKiogzvdTpds8u9eVxbprsTy7YEtVpt9RraC/aiEfvQiH1odGsf/Pz8bnsZJgXExo0b8fzzzyMsLMwwLCsrCxs3bsTq1atve6UA4O7ubngdGRmJVatWtWk5RERkHibdSa3X6zFs2DCjYUOHDkV5eXmbV6zX6w2vjxw5gm7durV5WUREdOeZtAcRHh6OPXv2YOzYsYZh//73vxEeHm7SSlavXo3Tp0/j6tWrmDlzJqZMmYJTp06hsLAQKpUK3t7eeP7559u2BUREZBYmBURBQQH27t2LTz75BJ6enigrK0NFRQV69+5tdLXTH//4R8X5586d22SYKZfHEhGR9ZgUEJGRkYiMjDR3LURE1I6YFBAjR440cxlERNTemHwfxL59+5CRkYGysjJ4enoiPDwco0aNMmdtRERkRSYFxI4dO5Ceno7x48cbrq395JNPoNfrMWnSJHPXSEREVmBSQKSmpmLZsmXw9vY2DAsODkZ8fDwDgojoHmXSfRDXr183PHX1hi5duqCmpsYsRRERkfWZFBADBgzAmjVrcOnSJdTU1OC///0v3nrrLQQHB5u7PiIishKTDjHNmDEDmzZtwsKFC1FXVwc7Ozs89NBDmD59urnrIyIiKzEpIJydnTFnzhzMmjULV69eRZcuXWBjY9LOBxER3aVM/pS/ePEiduzYgY8++gg2Nja4dOkSzp8/b87aiIjIikwKiKysLMTHx6OsrAwZGRkAgGvXruG9994za3FERGQ9Jh1i2r59O5YsWYKePXsiKysLANCjRw8UFhaaszYiIrIikwKioqICPXr0MBqmUqmgUqnMUpS11f+G35NNRGTSISaNRmM4tHTDoUOHEBQUZJaiiIjI+kzag5g+fTpWrFiBtLQ0XL9+HStXrsSlS5ewePFic9dHRERWYlJA+Pv7Y/Xq1Th69CgGDx4MLy8vDB48GI6Ojuauj4iIrMTkp7k6ODigb9++hqe5MhyIiO5tJgWETqfDmjVrkJubi86dO+P7779HUFAQYmNjjR7gR0RE9w6TTlInJydDo9EgJSUF7777LlJSUtCrVy8kJyebuz4iIrISkwLi3LlzmDp1quGwkqOjI6ZOnYpz586ZtTgiIrIekwKid+/eyMvLMxqWn5+P++67zyxFERGR9Zl0DsLHxwevvPIKBg0aBC8vL5SWluLYsWMYPnw4tm3bZpjuySefNFuhRERkWSYFRG1tLUJDQwEAV65cgb29PYYOHYqamhqUlpaatUAiIrIOkwJi1qxZ5q6DiIjaGX6pAxERKWJAEBGRIgYEEREpajYgtm7danh98uRJixRDRETtR7MBodVqDa9fe+01ixRDRETtR7NXMfXs2ROJiYkICAhAbW2t0f0ON+O9D0RE96ZmA2L+/PnQarUoKSmBiPB+ByKiDqbZgHBzc8MvfvELAEBDQwPvhSAi6mBMvlGusrISR48eNXwfxODBg+Hi4mLu+oiIyEpMusz17Nmz+O1vf4u9e/fi/Pnz0Gq1+O1vf4uzZ8+auz4iIrISk/YgNm/ejOeeew4/+9nPDMMyMzORkpKCV155xWzFERGR9ZgUEEVFRXjooYeMhg0bNgwbNmwwaSXr1q1DTk4O3NzckJiYCACorKxEUlISSkpK4O3tjXnz5vGQFRFRO2LSISZfX19kZmYaDcvKyoKPj49JKxk5ciQWLVpkNGzXrl3o378/1qxZg/79+2PXrl2mVUxERBZh0h5ETEwMEhIS8Nlnn0GtVqOkpARFRUWIi4szaSX9+vVDcXGx0bDs7GwsW7YMABAREYFly5Zh6tSpt1c9ERGZjUkB0adPH6xduxY5OTnQ6/UYPHgwBg0a9KMOCVVUVMDDwwMA4OHhgStXrjQ7rVarNdzZnZCQALVajcvNTHvzuLZMdzvzWJOdnZ3Va2gv2ItG7EMj9qHRneiDSQEBAC4uLggPD/9RK2urqKgoREVFGd7rdLpmp715XFumuxPLtgS1Wm31GtoL9qIR+9CIfWh0ax/8/PxuexlWe5qrm5sb9Ho9AECv18PV1dVapRARkQKrBURISAjS09MBAOnp6RgyZIi1SiEiIgUmH2L6MVavXo3Tp0/j6tWrmDlzJqZMmYKJEyciKSkJaWlpUKvVmD9/viVKISIiE5kcEDfuV2iLuXPnKg5funRpm5ZHRETmZ/Ihpt///vcAgE8//dRsxRARUfvR4h7Eyy+/DI1Gg8DAQDQ0NAAAPvzwQ4wdO9YixRERkfW0uAfx0ksvITg4GCUlJaipqcHLL7+Muro6nDx5ElVVVZaqkYiIrKDFgGhoaMCwYcPw1FNPwdHREQsXLoSIYM+ePVi4cCFiY2MtVScREVlYi4eY1qxZA51OZ/ja0e+//x729vZYsGABgMYH7hER0b2pxYD485//jPr6enz77bdYunQpNm3ahOrqamzYsAGBgYHQaDR8AisR0T2q1auYbG1tERgYCDs7O/zxj3+Eg4MD7r//fnz33Xd4//33LVEjERFZgcn3QUybNg0AoFKpEBYWhrCwMLMVRURE1mfyfRAjR44EAKxdu9ZctRARUTty289i4jkHIqKOwWoP6yMiovaNAUFERIoYEEREpIgBQUREihgQRESkiAFBRESKGBBERKSIAUFERIoYEEREpIgBQUREihgQRESkiAFBRESKGBBERKSIAUFERIoYEEREpIgBQUREihgQRESkiAFBRESKGBBERKSIAUFERIoYEEREpIgBQUREihgQRESkiAFBRESK7KxdwOzZs+Ho6AgbGxvY2toiISHB2iURERHaQUAAQHx8PFxdXa1dBhER3YSHmIiISFG72INYuXIlAOCRRx5BVFRUk/FarRZarRYAkJCQALVajcvNLOvmcW2Z7nbmsSY7Ozur19BesBeN2IdG7EOjO9EHqwfE8uXL4enpiYqKCqxYsQJ+fn7o16+f0TRRUVFGwaHT6Zpd3s3j2jLdnVi2JajVaqvX0F6wF43Yh0bsQ6Nb++Dn53fby7D6ISZPT08AgJubG4YMGYK8vDwrV0RERICVA6K6uhrXrl0zvD5x4gS6d+9uzZKIiOgHVj3EVFFRgddffx0AUF9fj+HDh2PAgAHWLImIiH5g1YDw8fHBa6+9Zs0SiIioGVY/B0FERO0TA4KIiBQxIIiISJHV74O4V9X/ZgIAwHbDJ4rDlcYREbUn3IMgIiJFDAgiIlLEgCAiIkUMCCIiUsSAICIiRQwIIiJSxIAgIiJFDAgiIlLEgCAiIkUMCCIiUsSAICIiRQwIIiJSxIAgIiJFDAgiIlLEgCAiIkUMCCIiUsQvDLpDWvoioJvHtXV5/AIiIrI07kEQEZEiBgQRESliQBARkSIGBBERKWJAEBGRIgYEEREpYkAQEZEiBgQRESnijXI/QltugGtuGZa8ye1eubnuxnZcRss3E5prvZZYF1Fb1P9mAi7/8PrH/I5yD4KIiBQxIIiISBEDgoiIFDEgiIhIEQOCiIgUWf0qpuPHjyMlJQUNDQ2IjIzExIkTrV0SERHBynsQDQ0N2LhxIxYtWoSkpCQcOnQIFy9etGZJRET0A6sGRF5eHnx9feHj4wM7OzuEhYUhOzvbmiUREdEPVCIi1lr54cOHcfz4ccycORMAkJGRgdzcXDz77LNG02m1Wmi1WgBAQkKCxeskIuqIrLoHoZRNKpWqybCoqCgkJCQgISEBcXFxliit3WMf/oe9aMQ+NGIfGt2JPlg1ILy8vFBaWmp4X1paCg8PDytWREREN1g1IHr16oWioiIUFxejrq4OmZmZCAkJsWZJRET0A6te5mpra4sZM2Zg5cqVaGhowKhRo9CtW7cW54mKirJQde0b+/A/7EUj9qER+9DoTvTBqiepiYio/eKd1EREpIgBQUREiqz+qA1TdeRHcuh0OiQnJ6O8vBwqlQpRUVEYO3YsKisrkZSUhJKSEnh7e2PevHlwcXGxdrlm19DQgLi4OHh6eiIuLq5D9uH777/H+vXrceHCBahUKrz44ovw8/PrcH345z//ibS0NKhUKnTr1g2zZs1CTU1Nh+jDunXrkJOTAzc3NyQmJgJAi/8Xdu7cibS0NNjY2GD69OkYMGBA6yuRu0B9fb3MmTNHvvvuO6mtrZUFCxbIhQsXrF2WxZSVlUl+fr6IiFRVVUlsbKxcuHBBtm7dKjt37hQRkZ07d8rWrVutWKXl7N69W1avXi2vvPKKiEiH7MPatWtFq9WKiEhtba1UVlZ2uD6UlpbKrFmz5Pr16yIikpiYKPv27eswfTh16pTk5+fL/PnzDcOa2/YLFy7IggULpKamRi5fvixz5syR+vr6VtdxVxxi6uiP5PDw8IBGowEAODk5wd/fH2VlZcjOzkZERAQAICIiokP0pLS0FDk5OYiMjDQM62h9qKqqwtdff42HH34YAGBnZ4fOnTt3uD4AjXuTNTU1qK+vR01NDTw8PDpMH/r169dkz6i5bc/OzkZYWBjs7e3RtWtX+Pr6Ii8vr9V13BWHmMrKyuDl5WV47+XlhdzcXCtWZD3FxcUoKChAUFAQKioqDDcWenh44MqVK1auzvw2b96MqVOn4tq1a4ZhHa0PxcXFcHV1xbp163D+/HloNBrExMR0uD54enpi/PjxePHFF9GpUycEBwcjODi4w/XhZs1te1lZGXr37m2YztPTE2VlZa0u767YgxATH8lxr6uurkZiYiJiYmLg7Oxs7XIs7ujRo3BzczPsTXVU9fX1KCgowOjRo/Hqq6/CwcEBu3btsnZZFldZWYns7GwkJyfjnXfeQXV1NTIyMqxdVruk9BlqirtiD4KP5ADq6uqQmJiIESNGIDQ0FADg5uYGvV4PDw8P6PV6uLq6WrlK8zpz5gy+/PJLHDt2DDU1Nbh27RrWrFnT4frg5eUFLy8vw1+Ew4YNw65duzpcH7766it07drVsJ2hoaE4e/Zsh+vDzZrb9ls/Q8vKyuDp6dnq8u6KPYiO/kgOEcH69evh7++PcePGGYaHhIQgPT0dAJCeno4hQ4ZYq0SL+PWvf43169cjOTkZc+fOxQMPPIDY2NgO1wd3d3d4eXnh0qVLABo/KAMCAjpcH9RqNXJzc3H9+nWICL766iv4+/t3uD7crLltDwkJQWZmJmpra1FcXIyioiIEBQW1ury75k7qnJwcbNmyxfBIjkmTJlm7JIv55ptvsHTpUnTv3t1waC06Ohq9e/dGUlISdDod1Go15s+ff09ezqfk1KlT2L17N+Li4nD16tUO14fCwkKsX78edXV16Nq1K2bNmgUR6XB92L59OzIzM2Fra4uePXti5syZqK6u7hB9WL16NU6fPo2rV6/Czc0NU6ZMwZAhQ5rd9h07dmDfvn2wsbFBTEwMBg4c2Oo67pqAICIiy7orDjEREZHlMSCIiEgRA4KIiBQxIIiISBEDgoiIFDEgiBSUl5cjPj4ezzzzDN57770m42tqapCQkIBp06bhjTfeUFzGgQMHsGLFCrPUt2zZMqSmpppl2UQ33BV3UhOZ6g9/+ANiY2NhY2ODN954A6tWrWrTcrRaLbp06YItW7YoPtbl8OHDqKiowKZNm2Bra6u4jBEjRmDEiBFtWj9Re8A9CLpn1NXVQafTwdfXF+fOnUNgYGCbl6XT6RAQENDsM79KSkrwk5/8pNlwqK+vb/O6idoL7kHQPePChQuGD/X8/PxWA+LMmTPYvHkzLl26BD8/P8TExKBPnz5ITk7GwYMHAQD/+te/sHDhQjz44IOG+bZv346dO3cCaHyM8vTp02FjY4PU1FT06tUL6enpGDNmDHx9fZGamorly5cDAP773/9i06ZNOHfuHFxdXfHkk08iLCwMAJCcnAwHBweUlJTg66+/RkBAAGJjY+Hr6wsAOHHiBDZt2gS9Xo/w8HCjh6999913ePvtt1FYWAg7Ozs88MADmDdv3p1rLHVYDAi66+3btw9btmxBXV0dRAQxMTGorq5Gp06d8Pe//x2vvvoqunbtajRPZWUlEhISMH36dPzsZz9DVlYWEhISsGbNGsyePRtA4wPOfvWrXzVZ35QpUwA0fjDHxsYCAPbv34/c3FyEhYXh3XffRX19PTIzMw3zVFdXY8WKFZgyZQoWLVqE8+fPY+XKlejWrRu6desGADh06BD+7//+D4GBgUhOTsYHH3yAuXPn4sqVK0hMTMSLL76IkJAQ7NmzB3v37kV4eDgA4IMPPkBwcDDi4+NRV1eHc+fO3fkmU4fEQ0x01xs1ahQ2b94MjUaDlStX4vXXX0e3bt2wZcsWbN68uUk4AI3P9vL19UV4eDhsbW0xfPhw+Pn54ejRo22uw8PDA4899hhsbW3RqVOnJuvz9vbGqFGjYGtrC41Gg9DQUBw+fNgwTWhoKIKCggz1FBYWAgCOHTuGgIAADBs2DHZ2dnj88cfh7u5umM/Ozg4lJSXQ6/Xo1KkT+vbt2+ZtILoZ9yDorlZZWYk5c+ZARFBdXY1ly5ahtrYWADB9+nT88pe/xOOPP95kvrKyMnh7exsN8/b2NulLVJqjVqubHVdSUoLc3FzExMQYhtXX1xv2AgAYfeg7ODiguroaAKDX642+MEulUhm9nzp1Kj744AMsWrQInTt3xrhx4wzfNkf0YzAg6K7m4uKCzZs349ChQzh16hSef/55vPbaaxgzZozReYNbeXp64osvvjAaptPpTPsi9zbw8vJCv379sGTJktue193d3ehZ/iJi9N7d3R0zZ84E0Pjk3+XLl6Nfv36G8xdEbcVDTHRPuPmqpcLCwla/dW7gwIEoKirCwYMHDecLLl68iEGDBpmlvsGDB6OoqAgZGRmoq6tDXV0d8vLycPHixVbnHTRoEC5cuIAvvvgC9fX1+Oyzz1BeXm4Yn5WVZQiMzp07AwBsbPhfm3487kHQPeHcuXN46KGHcPXqVdjY2LT6/P8uXbogLi4OKSkp2LBhA3x9fREXF2e2bx9zcnLC4sWLsWXLFmzZsgUigh49emDatGmtzuvq6or58+cjJSUF69atQ3h4OPr06WMYn5+fj82bN6Oqqgru7u6YPn264nkXotvF74MgIiJF3A8lIiJFDAgiIlLEgCAiIkUMCCIiUsSAICIiRQwIIiJSxIAgIiJFDAgiIlL0/4T/DEBKStnVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "friend_counts = Counter(num_friends)\n",
    "xs = range(101)\n",
    "ys = [friend_counts[x] for x in xs]\n",
    "plt.bar(xs, ys)\n",
    "plt.axis([0,101,0,25])\n",
    "plt.title(\"Histogram of Friend Counts\")\n",
    "plt.xlabel(\"# of friends\")\n",
    "plt.ylabel(\"# of people\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can also draw them with ``plt.hist``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:45:34.839354Z",
     "start_time": "2023-11-24T06:45:34.613178Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(daily_minutes, bins = 50)\n",
    "plt.xlabel('Daily minutes')\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:45:38.427211Z",
     "start_time": "2023-11-24T06:45:38.230593Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(num_friends, bins= 50)\n",
    "plt.xlabel(\"# of friends\")\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Unfortunately, this chart is still too difficult to interpret. \n",
    "- So you start generating some statistics. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-30T04:21:07.745547Z",
     "start_time": "2019-01-30T04:21:07.742911Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### From Max to Min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:46:06.575390Z",
     "start_time": "2023-11-24T06:46:06.572143Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "204 100 1\n"
     ]
    }
   ],
   "source": [
    "num_points = len(num_friends)               # 204\n",
    "\n",
    "largest_value = max(num_friends)            # 100\n",
    "smallest_value = min(num_friends)           # 1\n",
    "\n",
    "print(num_points, largest_value, smallest_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:46:38.191405Z",
     "start_time": "2023-11-24T06:46:38.188665Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "sorted_values = sorted(num_friends)\n",
    "smallest_value = sorted_values[0]           # 1\n",
    "\n",
    "second_smallest_value = sorted_values[1]    # 1\n",
    "second_largest_value = sorted_values[-2]    # 49"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Mean, Median, Mode, and Quantile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:46:59.734270Z",
     "start_time": "2023-11-24T06:46:59.731552Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def mean(x):\n",
    "    return sum(x) / len(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:47:07.170381Z",
     "start_time": "2023-11-24T06:47:07.167217Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean(num_friends) 7.333333333333333\n"
     ]
    }
   ],
   "source": [
    "print(\"mean(num_friends)\", mean(num_friends))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:47:18.935438Z",
     "start_time": "2023-11-24T06:47:18.931182Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.333333333333333"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:47:58.559297Z",
     "start_time": "2023-11-24T06:47:58.555279Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def median(v):\n",
    "    \"\"\"finds the 'middle-most' value of v\"\"\"\n",
    "    n = len(v)\n",
    "    sorted_v = sorted(v)\n",
    "    midpoint = n // 2\n",
    "\n",
    "    if n % 2 == 1: \n",
    "        # if odd, return the middle value\n",
    "        return sorted_v[midpoint]\n",
    "    else:\n",
    "        # if even, return the average of the middle values\n",
    "        lo = midpoint - 1\n",
    "        hi = midpoint\n",
    "        return (sorted_v[lo] + sorted_v[hi]) / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:48:04.406959Z",
     "start_time": "2023-11-24T06:48:04.403794Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "median(num_friends) 6.0\n"
     ]
    }
   ],
   "source": [
    "print(\"median(num_friends)\", median(num_friends))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:48:11.653139Z",
     "start_time": "2023-11-24T06:48:11.648774Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:49:37.994491Z",
     "start_time": "2023-11-24T06:49:37.991560Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def quantile(x, p):\n",
    "    \"\"\"returns the pth-percentile value in x\"\"\"\n",
    "    p_index = int(p * len(x))\n",
    "    return sorted(x)[p_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:50:02.266228Z",
     "start_time": "2023-11-24T06:50:02.262220Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quantile(num_friends, 0.10) 1\n",
      "quantile(num_friends, 0.25) 3\n",
      "quantile(num_friends, 0.50) 6\n",
      "quantile(num_friends, 0.75) 9\n",
      "quantile(num_friends, 0.90) 13\n"
     ]
    }
   ],
   "source": [
    "print(\"quantile(num_friends, 0.10)\", quantile(num_friends, 0.10))\n",
    "print(\"quantile(num_friends, 0.25)\", quantile(num_friends, 0.25))\n",
    "print(\"quantile(num_friends, 0.50)\", quantile(num_friends, 0.50))\n",
    "print(\"quantile(num_friends, 0.75)\", quantile(num_friends, 0.75))\n",
    "print(\"quantile(num_friends, 0.90)\", quantile(num_friends, 0.90))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:50:10.066567Z",
     "start_time": "2023-11-24T06:50:10.062324Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(num_friends, 90)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:50:19.352249Z",
     "start_time": "2023-11-24T06:50:19.349091Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def mode(x):\n",
    "    \"\"\"returns a list, might be more than one mode\"\"\"\n",
    "    counts = Counter(x)\n",
    "    max_count = max(counts.values())\n",
    "    return [x_i for x_i, count in counts.items()\n",
    "            if count == max_count]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:50:25.650978Z",
     "start_time": "2023-11-24T06:50:25.648206Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mode(num_friends) [6, 1]\n"
     ]
    }
   ],
   "source": [
    "print(\"mode(num_friends)\", mode(num_friends))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:50:40.250466Z",
     "start_time": "2023-11-24T06:50:40.246531Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(np.bincount(num_friends))\n",
    "# Only the first occurrence is returned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-07T00:46:24.313036Z",
     "start_time": "2020-06-07T00:46:24.308848Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 22, 17, 20, 20, 17, 22, 15, 13, 18, 15,  1,  2,  4,  2,  4,  1,\n",
       "        0,  2,  2,  0,  2,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "        0,  0,  0,  0,  0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,\n",
       "        0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "        0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "        0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.bincount(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:50:51.326267Z",
     "start_time": "2023-11-24T06:50:50.757122Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ModeResult(mode=array([1]), count=array([22]))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "stats.mode(num_friends, axis=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:51:01.057730Z",
     "start_time": "2023-11-24T06:51:01.055308Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def data_range(x):\n",
    "    return max(x) - min(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:51:03.952286Z",
     "start_time": "2023-11-24T06:51:03.948202Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data_range(num_friends) 99\n"
     ]
    }
   ],
   "source": [
    "print(\"data_range(num_friends)\", data_range(num_friends))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:51:25.304672Z",
     "start_time": "2023-11-24T06:51:25.300022Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "interquartile_range(num_friends) 6\n"
     ]
    }
   ],
   "source": [
    "def interquartile_range(x):\n",
    "    return quantile(x, 0.75) - quantile(x, 0.25)\n",
    "print(\"interquartile_range(num_friends)\", interquartile_range(num_friends))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T01:02:16.315716Z",
     "start_time": "2019-10-31T01:02:16.198370Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "<img src = './img/stats/boxplot.png' width = '600px' > "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:52:20.733886Z",
     "start_time": "2023-11-24T06:52:19.872664Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.set(style=\"ticks\", palette=\"pastel\")\n",
    "sns.boxplot(y = daily_minutes);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T06:52:25.349748Z",
     "start_time": "2023-11-24T06:52:25.266510Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.set(style=\"ticks\", palette=\"pastel\")\n",
    "sns.boxplot(y = num_friends);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Variance and Standard Deviation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$\\sigma = \\sqrt{\\frac{\\sum_{i=1}^N (x_i - \\overline{x})^2}{N-1} }$$\n",
    "\n",
    "$$\\sigma ^ 2 = \\frac{\\sum_{i=1}^N (x_i - \\overline{x})^2}{N-1} $$\n",
    "\n",
    "[样本方差为何除以n-1?](https://blog.csdn.net/hearthougan/article/details/77859173)\n",
    "\n",
    "![](./images/variance.png)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:08:57.924296Z",
     "start_time": "2023-11-24T07:08:57.920545Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def de_mean(x):\n",
    "    \"\"\"translate x by subtracting its mean \n",
    "    so the result has mean 0\"\"\"\n",
    "    x_bar = mean(x)\n",
    "    return [x_i - x_bar for x_i in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:09:00.564857Z",
     "start_time": "2023-11-24T07:09:00.561084Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variance(num_friends) 81.54351395730716\n"
     ]
    }
   ],
   "source": [
    "def variance(x):\n",
    "    \"\"\"assumes x has at least two elements\"\"\"\n",
    "    n = len(x)\n",
    "    deviations = de_mean(x)\n",
    "    return sum_of_squares(deviations) / (n - 1)\n",
    "\n",
    "print(\"variance(num_friends)\", variance(num_friends))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-07T00:46:46.040828Z",
     "start_time": "2020-06-07T00:46:46.037238Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "81.14379084967321\n"
     ]
    }
   ],
   "source": [
    "print(np.var(num_friends))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:09:15.748400Z",
     "start_time": "2023-11-24T07:09:15.744926Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard_deviation(num_friends) 9.03014473623248\n"
     ]
    }
   ],
   "source": [
    "def standard_deviation(x):\n",
    "    return math.sqrt(variance(x))\n",
    "\n",
    "print(\"standard_deviation(num_friends)\", standard_deviation(num_friends))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:09:30.885212Z",
     "start_time": "2023-11-24T07:09:30.880815Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.007984838446012"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(num_friends)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Covariance, Correlation, and Scatter Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:14:24.418111Z",
     "start_time": "2023-11-24T07:14:24.272182Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "matplotlib.style.use('ggplot')\n",
    "plt.scatter(num_friends, daily_minutes, \n",
    "            alpha = .1)\n",
    "plt.xlabel('number of friends')\n",
    "plt.ylabel('daily minutes')\n",
    "plt.title('outliers')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-07T00:47:12.419944Z",
     "start_time": "2020-06-07T00:47:11.189052Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.set(style=\"white\")\n",
    "g = sns.jointplot(num_friends, daily_minutes, \n",
    "                  kind=\"kde\", height=7, space=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:16:43.170995Z",
     "start_time": "2023-11-24T07:16:43.166805Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "covariance(num_friends, daily_minutes) 22.425435139573064\n"
     ]
    }
   ],
   "source": [
    "def covariance(x, y):\n",
    "    n = len(x)\n",
    "    return dot(de_mean(x), de_mean(y)) / (n - 1)\n",
    "\n",
    "print(\"covariance(num_friends, daily_minutes)\", covariance(num_friends, daily_minutes))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:16:54.541237Z",
     "start_time": "2023-11-24T07:16:54.535031Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 81.54351396,  22.42543514],\n",
       "       [ 22.42543514, 100.78589895]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cov(num_friends, daily_minutes) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:19:08.529661Z",
     "start_time": "2023-11-24T07:19:08.525039Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "correlation(num_friends, daily_minutes) 0.24736957366478218\n"
     ]
    }
   ],
   "source": [
    "def correlation(x, y):\n",
    "    stdev_x = standard_deviation(x)\n",
    "    stdev_y = standard_deviation(y)\n",
    "    if stdev_x > 0 and stdev_y > 0:\n",
    "        return covariance(x, y) / stdev_x / stdev_y\n",
    "    else:\n",
    "        return 0 # if no variation, correlation is zero\n",
    "print(\"correlation(num_friends, daily_minutes)\", correlation(num_friends, daily_minutes))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:19:15.761201Z",
     "start_time": "2023-11-24T07:19:15.231821Z"
    },
    "cell_style": "center",
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.set(style=\"ticks\", palette=\"pastel\")\n",
    "sns.boxplot(x=num_friends, y=daily_minutes)\n",
    "sns.despine(offset=10, trim=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:19:25.494546Z",
     "start_time": "2023-11-24T07:19:25.489780Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.24736957],\n",
       "       [0.24736957, 1.        ]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(num_friends, daily_minutes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:22:11.763322Z",
     "start_time": "2023-11-24T07:22:11.758760Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.2473695736647822, 0.0003610473973450684)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats.stats import pearsonr   \n",
    "  \n",
    "pearsonr(num_friends, daily_minutes) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:22:34.478093Z",
     "start_time": "2023-11-24T07:22:34.474171Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "correlation(num_friends_good, daily_minutes_good) 0.5736792115665573\n"
     ]
    }
   ],
   "source": [
    "outlier = num_friends.index(100) # index of outlier\n",
    "\n",
    "num_friends_good = [x\n",
    "                    for i, x in enumerate(num_friends)\n",
    "                    if i != outlier]\n",
    "\n",
    "daily_minutes_good = [x\n",
    "                      for i, x in enumerate(daily_minutes)\n",
    "                      if i != outlier]\n",
    "\n",
    "\n",
    "print(\"correlation(num_friends_good, daily_minutes_good)\", \\\n",
    "      correlation(num_friends_good, daily_minutes_good))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Regression Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-07T00:47:56.160422Z",
     "start_time": "2020-06-07T00:47:55.982068Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9038659456058652 22.947552413469026 0.5736792115665575 3.676825862770313e-19\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "slope, intercept, r_value, p_value, std_err = stats.linregress(num_friends_good,daily_minutes_good)\n",
    "print(slope, intercept, r_value, p_value)\n",
    "xi = range(1,np.max(num_friends_good)+1)\n",
    "# plotting the line\n",
    "matplotlib.style.use('ggplot')\n",
    "y_fit = slope*xi+intercept\n",
    "plt.scatter(num_friends,daily_minutes)\n",
    "plt.plot(xi,y_fit,'r-', label = '$Linear\\,Fit$')\n",
    "plt.xlabel('$x_i$', fontsize = 20)\n",
    "plt.ylabel('$y$', fontsize = 20)\n",
    "plt.legend(loc=0,numpoints=1,fontsize=13)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 比较均值：T检验\n",
    "\n",
    "![image.png](./images/end2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:31:27.892727Z",
     "start_time": "2023-11-24T07:31:27.886754Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2750.0 7100.0\n"
     ]
    }
   ],
   "source": [
    "income_male = [1000, 1500, 2000, 3000, 2500, 4000, 5000, 3500]\n",
    "income_female=[6000, 6200, 7000, 7100, 9000, 10000, 12000]\n",
    "income_male_median = np.median(income_male)\n",
    "income_female_median = np.median(income_female)\n",
    "print(income_male_median, income_female_median) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-07T00:48:07.483280Z",
     "start_time": "2020-06-07T00:48:07.340532Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the boxplot to see\n",
    "# minimum value, 25%,50%,75% percentile, maximum value\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.boxplot([income_male, income_female], # meanline=True,showmeans=True,\n",
    "            labels = ['$male$', '$female$'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![image.png](img/stats/t-test3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![](img/stats/t-test.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![](img/stats/t-test2.jpeg)\n",
    "\n",
    "Welch's t-test: Equal or unequal sample sizes, unequal variances \n",
    "\n",
    "https://en.wikipedia.org/wiki/Student%27s_t-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:31:33.183837Z",
     "start_time": "2023-11-24T07:31:33.177319Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-5.757056463981614, pvalue=6.631425817426509e-05)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "stats.ttest_ind(income_male, income_female)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 单因素方差分析（one-way ANOVA）\n",
    "\n",
    "ANOVA: Analysis of Variance\n",
    "\n",
    "假设：有k组实验数据，彼此之间相互独立且服从正态分布，均值分别为$\\mu_1,\\mu_2,...\\mu_k$，方差都为$\\sigma^2$\n",
    "- H0:假设两组或者多组数据之间有相同的均值\n",
    "- H1:至少有两个均值不相等\n",
    "\n",
    "![image.png](./images/chi2.png)\n",
    "\n",
    "https://en.wikipedia.org/wiki/One-way_analysis_of_variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Consider an experiment to study the effect of three different levels of a factor on a response (e.g. three levels of a fertilizer on plant growth). If we had 6 observations for each level, we could write the outcome of the experiment in a table like this, where a1, a2, and a3 are the three levels of the factor being studied.\n",
    "\n",
    "```\n",
    "a1\ta2\ta3\n",
    "6\t8\t13\n",
    "8\t12\t9\n",
    "4\t9\t11\n",
    "5\t11\t8\n",
    "3\t6\t7\n",
    "4\t8\t12\n",
    "```\n",
    "\n",
    "The null hypothesis, denoted H0, for the overall F-test for this experiment would be that all three levels of the factor produce the same response, on average. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "To calculate the F-ratio:\n",
    "\n",
    "Step 1: Calculate the mean within each group:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}{\\overline {Y}}_{1}&={\\frac {1}{6}}\\sum Y_{1i}={\\frac {6+8+4+5+3+4}{6}}=5\\\\{\\overline {Y}}_{2}&={\\frac {1}{6}}\\sum Y_{2i}={\\frac {8+12+9+11+6+8}{6}}=9\\\\{\\overline {Y}}_{3}&={\\frac {1}{6}}\\sum Y_{3i}={\\frac {13+9+11+8+7+12}{6}}=10\\end{aligned}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "Step 2: Calculate the overall mean:\n",
    "\n",
    "$\\overline{Y}=\\frac{\\sum _{i} \\overline{Y_i}}{a}=\\frac {\\overline{Y_1}+\\overline{Y_2}+\\overline{Y_3}}{a}=\\frac {5+9+10}{3}=8$ \n",
    "\n",
    "where $a$ is the number of groups."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Step 3: Calculate the \"between-group\" sum of squared differences:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}S_{B}&=n({\\overline {Y}}_{1}-{\\overline {Y}})^{2}+n({\\overline {Y}}_{2}-{\\overline {Y}})^{2}+n({\\overline {Y}}_{3}-{\\overline {Y}})^{2}\\\\[8pt]&=6(5-8)^{2}+6(9-8)^{2}+6(10-8)^{2}=84\\end{aligned}\n",
    "$$\n",
    "\n",
    "where n is the number of data values per group.\n",
    "\n",
    "The between-group degrees of freedom is one less than the number of groups $f_{b}=3-1=2$\n",
    "\n",
    "The between-group mean square value is\n",
    "$MS_{B}=84/2=42$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Step 4: Calculate the \"within-group\" sum of squares. Begin by centering the data in each group\n",
    "\n",
    "```\n",
    "a1\ta2\ta3\n",
    "6−5=1\t8−9=−1\t13−10=3\n",
    "8−5=3\t12−9=3\t9−10=−1\n",
    "4−5=−1\t9−9=0\t11−10=1\n",
    "5−5=0\t11−9=2\t8−10=−2\n",
    "3−5=−2\t6−9=−3\t7−10=−3\n",
    "4−5=−1\t8−9=−1\t12−10=2\n",
    "```\n",
    "\n",
    "The within-group sum of squares:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}S_{W}=&(1)^{2}+(3)^{2}+(-1)^{2}+(0)^{2}+(-2)^{2}+(-1)^{2}+\\\\&(-1)^{2}+(3)^{2}+(0)^{2}+(2)^{2}+(-3)^{2}+(-1)^{2}+\\\\&(3)^{2}+(-1)^{2}+(1)^{2}+(-2)^{2}+(-3)^{2}+(2)^{2}= 68\\\\\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The within-group degrees of freedom is\n",
    "\n",
    "$f_{W}=a(n-1)=3(6-1)=15$\n",
    "\n",
    "Thus the within-group mean square value is\n",
    "\n",
    "$MS_{W}=S_{W}/f_{W}=68/15\\approx 4.5$\n",
    "\n",
    "Step 5: The F-ratio is\n",
    "\n",
    "$ F={\\frac {MS_{B}}{MS_{W}}}\\approx 42/4.5\\approx 9.3$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$F_{crit}(2,15) = 3.68$ at α = 0.05. The results are significant at the 5% significance level. \n",
    "\n",
    "![image.png](./images/anova.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:39:21.271142Z",
     "start_time": "2023-11-24T07:39:21.266703Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.264705882352942 0.0023987773293929083\n"
     ]
    }
   ],
   "source": [
    "a1 = [6, 8, 4, 5, 3, 4]\n",
    "a2 = [8, 12, 9, 11, 6, 8]\n",
    "a3 = [13, 9, 11, 8, 7, 12]\n",
    "\n",
    "f,p = stats.f_oneway(a1, a2, a3)\n",
    "print(f,p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:39:49.789760Z",
     "start_time": "2023-11-24T07:39:49.785997Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# 5个地方的蚌壳长度的均值是否都一样呢？\n",
    "from scipy import stats\n",
    "tillamook = [0.0571, 0.0813, 0.0831, 0.0976, 0.0817, 0.0859, 0.0735, 0.0659, 0.0923, 0.0836]\n",
    "newport = [0.0873, 0.0662, 0.0672, 0.0819, 0.0749, 0.0649, 0.0835,0.0725]\n",
    "petersburg = [0.0974, 0.1352, 0.0817, 0.1016, 0.0968, 0.1064, 0.105]\n",
    "magadan = [0.1033, 0.0915, 0.0781, 0.0685, 0.0677, 0.0697, 0.0764, 0.0689]\n",
    "tvarminne = [0.0703, 0.1026, 0.0956, 0.0973, 0.1039, 0.1045]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:39:53.694538Z",
     "start_time": "2023-11-24T07:39:53.547187Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot([tillamook, newport, petersburg, magadan, tvarminne], # meanline=True,showmeans=True,\n",
    "            labels = ['tillamook', 'newport', 'petersburg', 'magadan', 'tvarminne'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:40:06.023471Z",
     "start_time": "2023-11-24T07:40:06.019795Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.121019471642447 0.0002812242314534544\n"
     ]
    }
   ],
   "source": [
    "f,p = stats.f_oneway(tillamook, newport, petersburg, magadan, tvarminne)\n",
    "print(f,p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:43:45.728256Z",
     "start_time": "2023-11-24T07:43:45.661307Z"
    },
    "code_folding": [],
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                df    sum_sq   mean_sq         F    PR(>F)\n",
      "C(treatment)   4.0  0.004520  0.001130  7.121019  0.000281\n",
      "Residual      34.0  0.005395  0.000159       NaN       NaN\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "from statsmodels.stats.anova import anova_lm\n",
    "import pandas as pd\n",
    "\n",
    "df = []\n",
    "labels = ['tillamook', 'newport', 'petersburg', 'magadan', 'tvarminne']\n",
    "for k, i in enumerate([tillamook, newport, petersburg, magadan, tvarminne]):\n",
    "    for j in i:\n",
    "        df.append([labels[k],j])\n",
    "        \n",
    "df = pd.DataFrame(df, columns = ['treatment', 'value'])\n",
    "model = ols('value ~ C(treatment)', df).fit()\n",
    "print(anova_lm(model)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-08T12:39:53.488586Z",
     "start_time": "2020-05-08T12:39:53.478902Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Two-way ANOVA\n",
    "ANOVA with interaction\n",
    "\n",
    "Measurement of fetal head circumference **hs**, by four observers in three fetuses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:44:05.783333Z",
     "start_time": "2023-11-24T07:44:05.774234Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\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>hs</th>\n",
       "      <th>fetus</th>\n",
       "      <th>observer</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14.3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14.8</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.6</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.6</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     hs  fetus  observer\n",
       "0  14.3      1         1\n",
       "1  14.0      1         1\n",
       "2  14.8      1         1\n",
       "3  13.6      1         2\n",
       "4  13.6      1         2"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# https://raw.githubusercontent.com/thomas-haslwanter/statsintro_python/master/ipynb/Data/data_altman/altman_12_6.txt\n",
    "import pandas as pd\n",
    "df = pd.read_csv('./data/altman_12_6.txt', names=['hs', 'fetus', 'observer'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:44:06.602725Z",
     "start_time": "2023-11-24T07:44:06.435009Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.api import interaction_plot\n",
    "plt.figure(figsize=(8,6))\n",
    "fig = interaction_plot(df['fetus'], df['observer'], df['hs'],\n",
    "        ms=10, ax=plt.gca())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-11-24T07:44:08.948297Z",
     "start_time": "2023-11-24T07:44:08.931736Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                        df      sum_sq     mean_sq            F        PR(>F)\n",
      "C(fetus)               2.0  324.008889  162.004444  2113.101449  1.051039e-27\n",
      "C(observer)            3.0    1.198611    0.399537     5.211353  6.497055e-03\n",
      "C(fetus):C(observer)   6.0    0.562222    0.093704     1.222222  3.295509e-01\n",
      "Residual              24.0    1.840000    0.076667          NaN           NaN\n"
     ]
    }
   ],
   "source": [
    "formula = 'hs ~ C(fetus) + C(observer) + C(fetus):C(observer)'\n",
    "lm = ols(formula, df).fit() \n",
    "print(anova_lm(lm))  "
   ]
  },
  {
   "cell_type": "markdown",
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    "\n",
    "###  卡方检验 A chi-squared test\n",
    "\n",
    "https://en.wikipedia.org/wiki/Chi-squared_test\n",
    "\n",
    "\n",
    "Suppose we look at the House of Representatives for the 113th Congress. This data is taken from [www.senate.gov](https://www.senate.gov).\n",
    "\n",
    "|        | Republican | Democrat | Total |\n",
    "| :----- | :--------: | :------: | :---: |\n",
    "| Male   |    215     |   143    |  358  |\n",
    "| Female |     19     |    64    |  83   |\n",
    "| Total  |    234     |   207    |  441  |"
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    "\n",
    "- also referred to as χ² test (or chi-square test), is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is true.\n",
    "- A chi-squared test can then be used to reject the null hypothesis that the data are independent.\n",
    "- Test statistics that follow a chi-squared distribution arise from an assumption of independent normally distributed data, which is valid in many cases due to the central limit theorem.\n",
    "- Chi-squared tests are often constructed from a sum of squared errors, or through the sample variance.\n"
   ]
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    "### Chi-Square Formula\n",
    "\n",
    "$Χ^2 = \\frac{\\sum (O − E)^2}{E} $\n",
    "\n",
    "- $\\sum$ means to sum up (see Sigma Notation)\n",
    "- O = each Observed (actual) value\n",
    "- E = each Expected value\n",
    "\n",
    "So we calculate  $(O−E)^2/E$ for each pair of observed and expected values then sum them all up.\n",
    "\n",
    " "
   ]
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     "text": [
      "189.9591836734694 168.04081632653063 \n",
      " 44.04081632653061 38.95918367346939\n"
     ]
    }
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   "source": [
    "total = 441\n",
    "republican_prob = 234.0/441\n",
    "democrat_prob = 207.0/441\n",
    "\n",
    "male_prob = 358.0/441\n",
    "female_prob = 83.0/441\n",
    "male_republican_expected = republican_prob * male_prob * total\n",
    "male_democrat_expected = democrat_prob * male_prob * total\n",
    "female_republican_expected = republican_prob * female_prob * total\n",
    "female_democrat_expected = democrat_prob * female_prob * total\n",
    "print(male_republican_expected, male_democrat_expected,'\\n', \n",
    "      female_republican_expected, female_democrat_expected)"
   ]
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    "Under the null hypothesis, it has approximately a chi-square distribution whose number of degrees of freedom are\n",
    "\n",
    "(number of rows−1)(number of columns−1)=(2−1)(2−1)=1.\n",
    "\n",
    "Then in that \"cell\" of the table, we have\n",
    "\n",
    "$$\\frac{(observed−expected)^2}{expected}=\\frac{(215−189.9)^2}{189.9} = 3.3$$\n",
    "\n",
    "The sum of these quantities over all of the cells is the Chi-square statistic.\n",
    "\n",
    "3.30093271 + 13.12279349 + 222.36009343 + 277.84184475 = 37.37\n",
    "\n"
   ]
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    "Observed\n",
    "\n",
    "|        | Republican | Democrat |\n",
    "| :----- | :--------: | :------: | \n",
    "| Male   |    215     |   143    | \n",
    "| Female |     19     |    64    |  \n",
    "\n",
    "\n",
    "Expected\n",
    "\n",
    "|        | Republican | Democrat | \n",
    "| :----- | :--------: | :------: | \n",
    "| Male   |    189.9     |   168.0    | \n",
    "| Female |     44.0     |    38.9    | \n",
    "\n",
    "\n",
    "Chi Square\n",
    "\n",
    "|        | Republican   |     Democrat   | \n",
    "| :------- | :-------: | :-----------: | \n",
    "| Male   |     $\\frac{(215-189.9)^2}{189.9} $     |   $\\frac{(143-168.0)^2}{168.0}$ | \n",
    "| Female |     $\\frac{(19-44.0)^2}{44.0}$         |    $\\frac{(64-38.9)^2}{38.9}$   | \n"
   ]
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     "text": [
      "37.365036593000426\n"
     ]
    }
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   "source": [
    "observed = [215, 143, 19, 64]\n",
    "expected = [male_republican_expected, male_democrat_expected,\n",
    "            female_republican_expected, female_democrat_expected]\n",
    "# The sum of these quantities over all of the cells is the test statistic.\n",
    "chi_square = np.sum( [(observed[k] - i)**2/i for k, i in enumerate(expected)] )\n",
    "print(chi_square)"
   ]
  },
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     "text": [
      "Test Statistic: 37.36503659300042\n",
      "p-value: 9.796267016333982e-10\n",
      "Degrees of Freedom: 1\n",
      "\n",
      "[[189.95918367 168.04081633]\n",
      " [ 44.04081633  38.95918367]]\n"
     ]
    }
   ],
   "source": [
    "import scipy\n",
    "house = [ [ 215, 143 ], [ 19, 64 ] ]\n",
    "chi2, p, ddof, expected = scipy.stats.chi2_contingency( house, correction = False)\n",
    "msg = \"Test Statistic: {}\\np-value: {}\\nDegrees of Freedom: {}\\n\"\n",
    "print( msg.format( chi2, p, ddof ) ) \n",
    "print( expected )"
   ]
  },
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     "slide_type": "skip"
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   "source": [
    "scipy.stats.chi2_contingency?"
   ]
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    "- Suppose there is a city of 1 million residents with four neighborhoods: A, B, C, and D.\n",
    "- A random sample of 650 residents of the city is taken and their occupation is recorded as \"blue collar\", \"white collar\", or \"no collar\".\n",
    "- The null hypothesis is that each person's neighborhood of residence is independent of the person's occupational classification. The data are tabulated as:\n",
    "\n",
    "|              |  A   |  B   |  C   |    D | Total |\n",
    "| :----------- | :--: | :--: | :--: | ---: | ----: |\n",
    "| White collar |  90  |  60  | 104  |   95 |   349 |\n",
    "| Blue collar  |  30  |  50  |  51  |   20 |   151 |\n",
    "| No coloar    |  30  |  40  |  45  |   35 |   150 |\n",
    "| Total        | 150  | 150  | 200  |  150 |   650 |\n"
   ]
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    "- 住在A社区的概率：Let us take the sample living in neighborhood A, 150/650, to estimate what proportion of the whole 1 million people live in neighborhood A.\n",
    "- 白领的概率：Similarly we take 349/650 to estimate what proportion of the 1 million people are white-collar workers.\n",
    "- 住在A社区的白领的数量：By the assumption of independence under the hypothesis we should \"expect\" the number of white-collar workers in neighborhood A to be\n",
    "\n",
    "$$\\frac{150}{650}\\frac{349}{650}650=80.54$$\n",
    "\n"
   ]
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   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "Then in that \"cell\" of the table, we have\n",
    "\n",
    "$$\\frac{(observed−expected)^2}{expected}=\\frac{(90−80.54)^2}{80.54} = 1.11$$\n",
    "\n",
    "The sum of these quantities over all of the cells is the test statistic.\n",
    "\n",
    "Under the null hypothesis, it has approximately a chi-square distribution whose number of degrees of freedom are\n",
    "\n",
    "(number of rows−1)(number of columns−1)=(3−1)(4−1)=6."
   ]
  },
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   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
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     "name": "stdout",
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     "text": [
      "Test Statistic: 24.5712028585826\n",
      " p-value: 0.0004098425861096696\n",
      " Degrees of Freedom: 6\n",
      "\n",
      "[[ 80.53846154  80.53846154 107.38461538  80.53846154]\n",
      " [ 34.84615385  34.84615385  46.46153846  34.84615385]\n",
      " [ 34.61538462  34.61538462  46.15384615  34.61538462]]\n"
     ]
    }
   ],
   "source": [
    "house = [ [ 90, 60, 104, 95 ], [ 30, 50, 51, 20 ], [30, 40, 45, 35] ]\n",
    "chi2, p, ddof, expected = scipy.stats.chi2_contingency( house )\n",
    "msg = \"Test Statistic: {}\\n p-value: {}\\n Degrees of Freedom: {}\\n\"\n",
    "print( msg.format( chi2, p, ddof ) )\n",
    "print( expected )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
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   "source": [
    "![image.png](./images/statistics.png)"
   ]
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   "source": [
    "![image.png](./images/end.png)"
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