Chapter13_The_central_limit_theorem.ipynb

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   "source": [
    "import numpy as np\n",
    "#from scipy.stats import bayes_mvs\n",
    "from math import factorial\n",
    "#import scikits.bootstrap as bs\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from warnings import filterwarnings\n",
    "\n",
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   "source": [
    "# The central limit theorem"
   ]
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    "The central limit theorem (CLT) very simply stated:\n",
    "\n",
    "* Take a large population\n",
    "* Let each member of that population have a known random value for a certain variable \n",
    "* Repetatively take a random sample from that population\n",
    "* Calculate the mean of each sample\n",
    "\n",
    "The CLT now guarentees that a histogram of the sample means will be normally distributed."
   ]
  },
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   "metadata": {},
   "source": [
    "## Understanding combinations"
   ]
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    "Suppose there are five patients, named (for privacy sake), patients *A* through *E*.  How many distinct combinations can you make choosing only a pair of two patients (with, for example, choosing patients *A* and *C*, being the same as choosing *C* and *A*)?\n",
    "Let's have a look:\n",
    "\n",
    "* A and B\n",
    "* A and C\n",
    "* A and D\n",
    "* A and E\n",
    "* B and C\n",
    "* B and D\n",
    "* B and E\n",
    "* C and D\n",
    "* C and E\n",
    "* D and E\n",
    "\n",
    "<p>I count 10.</p>\n",
    "<p>There's a mathematical equation for this.  No need to panic, it's easy.  Suppose the number of patients is *n* and the number you have to choose is *r*.</p>\n",
    "<p>The equation is simply:</p>\n",
    "$$ \\frac { n! }{ r!\\left( n-r \\right) ! }  $$\n",
    "<p>**Factorial** requires simple multiplication.  *Factorial(4)* is expressed as 'four factorial' and is 4 times 3 times 2 times 1, which is 24.  Start with the number given and work your way back to 1.  Just remember *factorial(0) = 1*.</p>\n",
    "<p>The code is easy:</p>"
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     "text": [
      "The number of possible combinations choosing  2  patients from a possible  5  is  10.0\n"
     ]
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   ],
   "source": [
    "n = 5\n",
    "r = 2\n",
    "\n",
    "combinations = factorial(n) / (factorial(r) * factorial(n - r))\n",
    "print('The number of possible combinations choosing ', r, ' patients from a possible ', n, ' is ', combinations)"
   ]
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   "source": [
    "<p>Why is this important to know?  Thought-experiment time.  Suppose there are 1000 patients with acute appendicitis in your town over a given time period.  Now, suppose for your research project you needed to pick 30 of those.  Essentially, the time that you start your project is random.  The 30 you pick is just one combination of many, many combinations (plug in the values in the cell above and see for yourself).  If you calculate the mean of a given variable of your sample, that is just one mean of the many, many you could have had.  Pilling up a histogram of all those means, will end up with a normal distribution.</p>\n",
    "<p>Don't believe me?  Carry on and see below!</p>"
   ]
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   "source": [
    "## The central limit theorem"
   ]
  },
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   "source": [
    "<p>It's now time to bring some knowledge together.  You know that we can represent probabilities as an area.  This is especially elegant if we can represent it with a function, whose area under the curve is one.  In essence, we are saying that the sum of all possibilities (probabilities) is one.</p>\n",
    "<p>If all those possible means are plotted as a histogram, the mean of your research project falls somewhere on that graph.  Now, because the CLT states that this curve will represent a normal distribution, some means will occur much more commonly, whilst others will occur less commonly.</p>\n",
    "<p>Converting your study's mean to an area on this graph will allow you to state a likelihood of having found your particular result.  The CLT allows us to do the mathematics for this conversion.</p>\n",
    "<p>Let's play with the code below.</p>"
   ]
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II4+gsbERhw4dwqlTp2A0GnHvvffiH/7hH6BWJ+cPeqJUFImI6OofQ4VJD1mS3YqckKGQ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10415b668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "i = 0 # Introducing computer variable and setting its value to 0\n",
    "ave = [] # Introducing an empty array\n",
    "\n",
    "while i < 10000: # Starting a simple loop which will continue until the statement is no longer true\n",
    "    x = 10 * np.random.random(40) # Choose 40 random values between 0 and 10\n",
    "    # np.random.random() actually chooses random values between 0 and 1 (multiplying by 10 gives 0 to 10)\n",
    "    ave.append(np.mean(x)) # Populate the ave array with the mean of each of your samples of 40\n",
    "    i += 1 # Add 1 to i, which means this will carry on for the size set for the loop\n",
    "\n",
    "\n",
    "sns.distplot(ave, bins = 20); # Make is distribution plot spreading the mean values in bins\n",
    "# Just look at the magic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Indeed, plotting a historgram of 10 000 means is bell-shaped.  This is irrespective of whether the actual variable (*x* above) was normally distributed.  Just look at the plot below.  It shows a distribution of the actual randomly selected values.   Also, watch the lecture on Z and t distributions.  It will tell you a lot more about distributions.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4YERXX9xmdkkwAZcgcVYe/X/75XJY9XvXdJldCoBTYAZf8fJ77Opq8Wl/d1jx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\nZPb/VvgXPvPSbrMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103f69cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.random(10000)\n",
    "\n",
    "sns.distplot(x, bins = 50, kde = True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>So even if the original said variable in the population takes on random values, taking repetative samples and calculating the mean of each sample, and finally plotting a histogram (frequency distribution) of the means (how many times each specific mean occurs) will result in a normal (bell-shaped) distribution.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}