Chapter14_Z_and_t_distributions.ipynb

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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\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",
    "%matplotlib inline\n",
    "filterwarnings('ignore')"
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   "source": [
    "# The Z and t distributions"
   ]
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   "source": [
    "## Introduction"
   ]
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   "cell_type": "markdown",
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   "source": [
    "<p>It is of utmost importance to understand the difference between the distribution of your dataset (per variable) as opposed to the two most common statistical distributions, the Z and t distributions.  Let's take white cell count (WCC) as an example.  Imagine for a moment that you could measure the WCC of 1 000 000 healthy individuals.  What would the ditribution of values look like?</p>\n",
    "<p>Fist of all, let's be clear that by distribution I refer to the fact that we start counting how many times a specific WCC value comes up.  Certainly some values will come up more commonly than others.  Something deeper is going on here.  You might have guessed it.  Yes, WCC is a continuous variable.  For all practical purposes, the WCC is infinitely divisible.  If we had a very powerful WCC counting apparatus, it could measure the WCC of an individual as 5.5 or 5.56 or 5.564, or 5.5648.  Would we count the occurence of all of these as seperate values?  Not at all.  They form part of a seemless mass.  We can only make sense of ranges of values, say lump (bin) all values between 5.50 and 5.55 in a group (called a bin).  To be sure, there are many, many possible individual values between these two bounds.</p>\n",
    "<p>Again, we would have to ask: Are all of these arbitrary range bins equally likely to occur?</p>\n",
    "<p>Random variables come in patterns, which we call distributions.  Most variables pertaining to healthcare come in the normal form.  This means if we were to get a histogram of the variables, it would be bell-shaped, or have a normal curve.  There are many other continous distributions and also discrete distributions.  The geometric distribution is and examples of a discrete random variable distribution.</p>\n",
    "<p>In the first section below I'll show you how python&#8482; (using the *scipy.stats* library can generate random variables for you to play with.  We'll use the plotting libraries of *pandas*, *matplotlib*, and *seaborn*, to image these variables.</p>"
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   "source": [
    "## Generating random normal variables"
   ]
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    "<p>In this first section I will create a computer variable called *rv1* and attach to it the normal distribution.  In actual fact, it will be the standard normal distribution.  The standard normal distribution has a mean of zero and a standard deviation of one.  It doesn't do much, but just to show you I'll call the *.mean()*, *.median()*, and *.std()* functions."
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   "source": [
    "rv1 = stats.norm()"
   ]
  },
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    "rv1.mean()"
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    "rv1.median()"
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    "rv1.std()"
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   "source": [
    "<p>Now that wasn't too exiting.  I can ask the *stats* library to generate a whole lot of random variables from the normal distribution.  Here I attach it to a *pandas Series* object and attach it to the computer variable name *rv1_set*.  I then use the *.describe()* function to find out a little more about my new dataset.</p>"
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   "execution_count": 7,
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       "count    2000.000000\n",
       "mean        0.005339\n",
       "std         1.001829\n",
       "min        -3.632323\n",
       "25%        -0.645921\n",
       "50%        -0.032196\n",
       "75%         0.658415\n",
       "max         4.241615\n",
       "dtype: float64"
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   "source": [
    "rv1_values = stats.norm.rvs(size = 2000) # I create 2000 values, all taken from a normal distribution\n",
    "rv1_set = pd.Series(rv1_values) # Making a pandas Series object\n",
    "rv1_set.describe() # Every time you run this cell, a new set of variables will be created"
   ]
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   "source": [
    "<p>Now for the really interesting bit.  Graphing (plotting) the dataset.  I'll use *seaborn*'s *distplot* plot.  It will generate a histogram, which will autogenerate (unless I give it a specific value in the arguments) a bunch of bins (each describes a range of values) and then gives the number of times that a value in my dataset occurs in that range, but expressing it as a probability.  You'll clearly see that we have a bell-shaped curve.</p>\n",
    "<p>The *displot* goes further and constructs what is called a kernel denisty estimate.  A mathematical equation is created to derive a smooth curve of the dataset.</p>"
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SAHaPIAWgadp99MFmowMhVS1bNxe4ew/A7hGkADRNffTBeJtv7Ukf9EmZkxmHKwHQSTxO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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108a77780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10, 8))\n",
    "sns.distplot(rv1_set)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The probability density function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The kernel density function above is a type of probability density function (see below for Z and t distributions). A probability density function stretches from negative infinity to infinity on the x-axis and includes all of the possible values in a set, with the probability of any value occuring on the y-axis.  The python&#8482; function that I use is *.cdf()*.  It calculates the area under the curve from the left up until a point on the x-axis that I want, which I add as an argument.  Say I want to ask the question: Hwo likely was it to get a value of *-2* or less from a standard normal distribution?  That would be the area under the curve from negative infinity (from the left) up until the *-2* mark.  Here we go!</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.022750131948179195"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv1.cdf(-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The value given is the probability of getting a value in your random dataset of less than *-2*.  Let's ask how likely it is to get a value of more than *0.7*.  Not so easy.  Remember that we calculate the area from the left, so if we plug in *0.7* as an argument, we will get the probability of getting a value of less than *0.7*.  To solve this little conundrum, remember that the total area under the curve is *1.0*.  So we can subtract the *0.7* area value from *1.0* and *voila!* we have the answer.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24196365222307303"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - rv1.cdf(0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other normal distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>I needn't be stuck with the standard normal distribution.  I can generate and play with a set of variables from a normal distribution, with any given mean and standard deviation.</p>\n",
    "<p>Here I take 200 random sample from a normal distribution with a mean of *10* and a standard deviation of *4* and construct the sample values as a *pandas Series* object that I attach to the computer variable *rv2_set*.  I'll then desribe and plot the dataset.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rv2_set = pd.Series(stats.norm.rvs(loc = 10, scale = 4, size = 200)) # The argument loc is the eman and scale is the standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    200.000000\n",
       "mean      10.066117\n",
       "std        3.717157\n",
       "min       -1.600347\n",
       "25%        7.651339\n",
       "50%       10.059294\n",
       "75%       12.793162\n",
       "max       19.223572\n",
       "dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv2_set.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AxRifWVAqnVNPW1huhhDfwud1q6s1rPh8RtMxhhKBYqJsAagYPx1CrO6FTG9m1/ICp5eZ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\nVfR//kLcbCl3h0YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108bf1550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10, 8))\n",
    "sns.distplot(rv2_set)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A completely random set of values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Just to be clear, I can use the *numpy* library to generate a set of random variables, not from any know distribution.  It is never realy, really random, but that's another topic.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108eb67f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_variables = np.random.random(size = 2000)\n",
    "\n",
    "plt.figure(figsize = (10, 8))\n",
    "plt.hist(random_variables, bins = 50)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Z distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From the lecture on the central limit theorem (CLT) you'll remember that we talked about the mean of all the possible means (remember combination?).  When we plot a histogram of this, we note that it is bell-shaped, or normal.  It also has a probability density function and we can ask the same questions of it.  What is the probability (area under the curve) for getting a value larger than such or such?</p>\n",
    "<p>Now, when we talk about the Z distribution, we are no longer talking about the data from you actual sample set.  It is a distribution of all the possible means.  We use the equation for the Z distribution when we know (or can accurately estimate) population standard deviation and mean.  This happends very rarely.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The equation for the probability desnity function of the Z distribuition (normal distribution) is:</p>\n",
    "$$ \\frac { 1 }{ \\sigma \\sqrt { 2\\pi  }  } { e }^{ -{ \\frac { { \\left( x-\\mu  \\right)  }^{ 2 } }{ { 2\\sigma  }^{ 2 } }  } } $$\n",
    "<p>Below is a bit of code to construct a plot from this equation.  You'll note that it is indeed bell-shaped.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rnXB+fkKP+Oxi+rx/+nxzHnmkfn360/dmfn7vjs61kz6/5ZbkS19K5ubmct11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\nIFQBALRAqAIAaIFQBQDQgv8fvXDwWbq4r5MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10918a1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-30, 30, 1000)\n",
    "sigma = 1\n",
    "mu =0\n",
    "pdf_z = (1 / sigma * np.sqrt(2 * np.pi)) * np.exp(-((x - mu) ** 2 / (2 * sigma ** 2)))\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.plot(x, pdf_z, 'b-')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The t distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>It is much more common for us to know **nothing** about the population standard deviation.  In this case we have to construct a bell-shaped curve from the data we have at our disposal (our sample data).  The mathematics of this is quite spectacular as you'll see in the equation below.  In essence it construct for us a histogram of all the possible means.</p>\n",
    "<p>It is from this distribution that we calculate probability (area under the curve) for any question we would like answered.  For instance, consider that we have a set of values for a variable for each of two groups.  We calculate the means of each group and want to know if the difference in means is significant.  We could to a t-test for this.  When we do this t-test using the equation below, we (well actually python&#8482;) will calculate a t-distribution for the difference between the means of the two groups that we have in our study.  From this bell-shaped distribution (as guarenteed from the CLT) we can now ask: What was the probability (*p*-value or area under the curve) for finding our specific difference in means?</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The equation for the probability density function of the t-distribution is:</p>\n",
    "$$ \\frac { \\Gamma \\left( \\frac { \\nu +1 }{ 2 }  \\right)  }{ \\sqrt { \\nu \\pi  } \\Gamma \\left( \\frac { \\nu  }{ 2 }  \\right)  } { \\left( 1+\\frac { { t }^{ 2 } }{ \\nu  }  \\right)  }^{ -\\frac { \\nu +1 }{ 2 }  } $$\n",
    "<p>...where:</p>\n",
    "$$ \\Gamma $$\n",
    "<p>...is the gamma function and</p>\n",
    "$$ \\nu $$\n",
    "<p>...is the degrees of freedom.  I told you it was spectacular!</p>\n",
    "<p>In the example below I will generate *1000* examples from a t distribution and show you what the plot looks like.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = 10 # the distribution will loook different for each value given as the degrees of freedom\n",
    "r = stats.t.rvs(df, size = 1000) # Generating 1000 values and attaching it to the computer variable r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Fm/cOwq2iIZ+SXUFNLeS0UlhzuxwALYCABaCh0rmiFtMFHRyIuV3KnmzWOz7L3YQAKiNg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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109223390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,8))\n",
    "sns.distplot(r)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>PLEASE note that I only include this last example to illustrate the bell-shaped nature of the curve.  A plot of the t-distribution is not a plot of your actual variable values.  It uses your data (or the difference between you means (and other parameters) to construct a plot (probability density function) of the means of all possible means you could have gotten had you been able to do your study over and over and over again!  Combinations rule!</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
}