ch04_Statistical_Inference.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 4: Statistical Inference.\n",
    "\n",
    "In this notebook we will see how to infer predictions about a population. To\n",
    "this end we will explore the relationship between sample parameters and population parameters and we will propose some methods to assess the quality\n",
    "of parameter estimates of a sample.\n",
    "\n",
    "## Data description\n",
    "\n",
    "Let's consider a dataset of accidents in Barcelona in 2013. This dataset can\n",
    "be downloaded from OpenDataBCN website (http://opendata.bcn.cat/),\n",
    "Barcelona's City Hall open data service. Each register in the dataset represents an accident by a series of features: weekday, hour, address, number\n",
    "of dead and injured people, etc. This dataset will represent our population:\n",
    "the set of all reported traffic accidents in Barcelona during 2013.\n",
    "\n",
    "In https://dieguico.cartodb.com/viz/50b06d8c-13ab-11e5-8619-0e4fddd5de28/public_map you can visualize a map of accidents in the city of Barcelona by hour of day, and by day of week."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pylab as plt\n",
    "from matplotlib import cm\n",
    "import math\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random\n",
    "\n",
    "%matplotlib inline \n",
    "plt.style.use('seaborn-whitegrid')\n",
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='times')\n",
    "plt.rc('xtick', labelsize=10) \n",
    "plt.rc('ytick', labelsize=10) \n",
    "plt.rc('font', size=12) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['Número d'expedient', 'Codi districte', 'Nom districte', 'NK barri',\n",
      "       'Nom barri', 'Codi carrer', 'Nom carrer', 'Num postal caption',\n",
      "       'Descripció dia setmana', 'Dia de setmana', 'Descripció tipus dia',\n",
      "       'NK Any', 'Mes de any', 'Nom mes', 'Dia de mes', 'Hora de dia',\n",
      "       'Descripció torn', 'Descripció causa vianant', 'Número de morts',\n",
      "       'Número de lesionats lleus', 'Número de lesionats greus',\n",
      "       'Número de víctimes', 'Número de vehicles implicats',\n",
      "       'Coordenada UTM (Y)', 'Coordenada UTM (X)'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv(\"files/ch04/ACCIDENTS_GU_BCN_2013.csv\", encoding='latin-1')\n",
    "print(data.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will create a new data column which is the date and a list with the number of accidents for every day of the year:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 25.90958904109589\n"
     ]
    }
   ],
   "source": [
    "#Create a new column which is the date\n",
    "data['Date'] = '2013-'+data['Mes de any'].apply(lambda x : str(x)) + '-' +  data['Dia de mes'].apply(lambda x : str(x))\n",
    "data['Date'] = pd.to_datetime(data['Date'])\n",
    "accidents = data.groupby(['Date']).size()\n",
    "print(\"Mean:\", accidents.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's suppose that we are interested in describing the number of daily traffic\n",
    "accidents (**accident rate**) in the streets of Barcelona during 2013.  In order to get a first idea of the data, we can plot the number of accidents for each day of 2013:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12, 4))\n",
    "plt.ylabel('Number of accidents')\n",
    "plt.xlabel('Day')\n",
    "plt.plot(range(0, 365), np.array(accidents), 'b-+', lw=0.7, alpha=0.7)\n",
    "plt.plot(range(0, 365), [accidents.mean()]*365, 'r-', lw=0.7, alpha=0.9)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, we can plot the distribution of our variable of interest: the daily number of accidents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12, 3))\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Number of accidents')\n",
    "plt.hist(np.array(accidents), bins=20)\n",
    "ax.axvline(x=accidents.mean(), ymin=0, ymax=40, color=[1, 0, 0])\n",
    "plt.savefig(\"bootmean.png\",dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have access to the whole *population*, the computation of the **accident rate** in 2013 is a simple operation: the total number of accidents divided by 365. As a measure of quality of this parameter we can also compute the standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 25.90958904109589 ; STD: 9.108324962464705\n"
     ]
    }
   ],
   "source": [
    "print(\"Mean:\", accidents.mean(), \"; STD:\", accidents.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But now, let's suppose that we have only access to a limited part of the data\n",
    "(the *sample*): the number of accidents during *some days* of 2013. Can we still\n",
    "give an approximation (an *estimate*) to this population mean?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variability in estimates.\n",
    "\n",
    "Estimates generally vary from one sample to another, and this sampling variation suggests our estimate may be close, but it will not be exactly equal to the parameter.\n",
    "\n",
    "This can be easily checked by generating 10 different samples (composed of 25% of the population) from our population and compute their accident rate estimates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample 0: Mean 24.91\n",
      "Sample 1: Mean 25.45\n",
      "Sample 2: Mean 26.25\n",
      "Sample 3: Mean 26.90\n",
      "Sample 4: Mean 25.82\n",
      "Sample 5: Mean 25.29\n",
      "Sample 6: Mean 26.79\n",
      "Sample 7: Mean 25.60\n",
      "Sample 8: Mean 24.37\n",
      "Sample 9: Mean 25.35\n"
     ]
    }
   ],
   "source": [
    "df = accidents.to_frame()\n",
    "m = []\n",
    "\n",
    "for i in range(10):\n",
    "    df['for_testing'] = False\n",
    "    # get a 25% sample \n",
    "    sampled_ids = np.random.choice(df.index,\n",
    "                                   size=np.int64(np.ceil(df.index.size * 0.25)),\n",
    "                                   replace=False)\n",
    "    df.loc[sampled_ids, 'for_testing'] = True\n",
    "    accidents_sample = df[df['for_testing'] == True]\n",
    "    m.append(accidents_sample[0].mean())\n",
    "    print('Sample '+str(i)+': Mean', '%.2f' % accidents_sample[0].mean())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Sample')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XL2WMiYN2GIZyHEdbW1v66aefJCl+D9/35XmejDFxb/ZZvdUAMG4mer1ez3YRAIAPb25uTr/99pvtMgDgk8MQCwAAACCBgAwAF1B/6IXv+7ZLAYBPDkMsAAAAgAR6kAEAAIAEAjIAAACQQEAGAAAAEgjIAAAAQAIBGQAAAEggIAMAAAAJ/w+g8QrZHkqhGwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12, 2))\n",
    "x = range(10)\n",
    "ax.step(x,m, where='mid')\n",
    "ax.set_ylabel('Mean')\n",
    "ax.set_xlabel('Sample')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accident rate estimates can range from 24 accident per day to 27 accidents per day, depending on the sample. How can we give a unique value for the estimate?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling distribution of point estimates\n",
    "\n",
    "The most intuitive way to go about giving a value for the estimate is to simply take the *sample\n",
    "mean*. The sample mean is a point estimate of the population mean. If we\n",
    "can only choose one value to estimate the population mean, this is our best\n",
    "guess.\n",
    "\n",
    "Let's computer the sample means for a set of 10000 samples, each one composed of 200 days:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample mean: 25.910944\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.autumn()\n",
    "\n",
    "# population\n",
    "df = accidents.to_frame()    \n",
    "N_test = 10000              \n",
    "elements = 200             \n",
    "\n",
    "# mean array of samples\n",
    "means = [0] * N_test             \n",
    "\n",
    "# sample generation\n",
    "for i in range(N_test):          \n",
    "    rows = np.random.choice(df.index.values, elements)\n",
    "    sampled_df = df.loc[rows]\n",
    "    means[i] = sampled_df.mean()\n",
    "    \n",
    "fig, ax = plt.subplots(1, 1, figsize=(12,3))\n",
    "\n",
    "plt.hist(np.array(means),bins=50)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Sample mean value')\n",
    "ax.axvline(x = np.array(means).mean(), \n",
    "           ymin = 0, \n",
    "           ymax = 700, \n",
    "           color = [1, 0, 0])\n",
    "plt.savefig(\"empiricalmean.png\",dpi=300, bbox_inches='tight')\n",
    "plt.show()\n",
    "plt.set_cmap(cmap=cm.Pastel2)\n",
    "\n",
    "print(\"Sample mean:\", np.array(means).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the **sampling distribution of the mean**. From it we could estimate the most probable value of the mean and also its standard deviation, but in the real world we will not have access to this function!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard error of the mean\n",
    "\n",
    "Noe let's suppose that we have only one sample of the propulation. As comented before, the mean estimate from that sample may be close, but it will not be exactly equal to our parameter of interest (that can only be computed if we have access to the full population). For this reason it is interesting to measure its variability with respect to the sampling process. To this end we can use the *standard error of the mean*.\n",
    "\n",
    "It can be mathematically shown that given $n$ independent observations $\\{ x_i \\}_{i=1,..,n}$ from a population with a standard deviation $\\sigma_x$, the standard deviation of the sample mean $\\sigma_{\\bar{x}}$, or **standard error** is:\n",
    "\n",
    "$$ SE = \\frac{\\sigma_{x}}{\\sqrt{n}} $$\n",
    "\n",
    "This allows **to estimate the standard deviation of the sample mean** even if we cannot perform the simulation process (f.e. because we have no access to the population). Usually, $\\sigma_x$ is not known and it is substituted by its empirical estimate (that is sufficiently good of $n>30$ and the population distribution is not skewed):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Direct estimation of SE from one sample of 200 elements: 0.5867464160810184\n",
      "Estimation of the SE by simulating 10000 samples of 200 elements: 0.6411950318460056\n"
     ]
    }
   ],
   "source": [
    "rows = np.random.choice(df.index.values, 200)\n",
    "sampled_df = df.loc[rows]\n",
    "est_sigma_mean = sampled_df.std()/math.sqrt(200)\n",
    "\n",
    "print('Direct estimation of SE from one sample of 200 elements:', \\\n",
    "       est_sigma_mean[0])\n",
    "print('Estimation of the SE by simulating 10000 samples of 200 elements:',  \\\n",
    "       np.array(means).std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could be also interested in quantifying the standard deviation of other estimates: median, standard deviation, etc., but unlike in the case of the sample mean, there is no simple formula for the standard\n",
    "error of other interesting sample estimates, such as the median."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's consider from now the whole accidents dataset as a sample from an hypothetical population (this is the most common situation when analyzing real data!)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bootstrapping the standard error of the mean.\n",
    "\n",
    "A modern alternative to the traditional approach to statistical inference is\n",
    "the *bootstrapping method*. In the bootstrap, we draw $N$ observations with\n",
    "replacement from the original data to create a bootstrap sample or resample.\n",
    "Then, we can calculate the mean for this resample. By repeating this process\n",
    "a large number of times we can built a good approximation of the mean\n",
    "sampling distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean estimate: 25.915641643835617\n"
     ]
    }
   ],
   "source": [
    "def meanBootstrap(X,numberb):\n",
    "    import numpy as np\n",
    "    x = [0]*numberb\n",
    "    for i in range(numberb):\n",
    "        sample = [X[_] for _ in np.random.randint(len(X), size=len(X))]\n",
    "        x[i] = np.mean(sample)\n",
    "    return x\n",
    "\n",
    "m = meanBootstrap(accidents, 10000)\n",
    "print(\"Mean estimate:\", np.mean(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7f97165fd5e0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12, 3))\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Sample mean value')\n",
    "plt.hist(m, \n",
    "         bins = 50, \n",
    "         density = True)\n",
    "ax.axvline(x = np.mean(m), \n",
    "           ymin = 0.0, \n",
    "           ymax = 1.0, \n",
    "           color = [1, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The boostrapping method can be applied to other simple estimates such as\n",
    "the median or the variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median estimate: 26.3005\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7f9717281e80>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def medBootstrap(X,numberb):\n",
    "    import numpy as np\n",
    "    x = [0]*numberb\n",
    "    for i in range(numberb):\n",
    "        sample = [X[_] for _ in np.random.randint(len(X), size=len(X))]\n",
    "        x[i] = np.median(sample)\n",
    "    return x\n",
    "\n",
    "med = medBootstrap(accidents, 10000)\n",
    "print(\"Median estimate:\", np.mean(med) )\n",
    "fig, ax = plt.subplots(1, 1, figsize=(12, 3))\n",
    "plt.hist(med, bins=5, density=True)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Sample median value')\n",
    "ax.axvline(x = np.array(med).mean(), \n",
    "           ymin = 0, \n",
    "           ymax = 1.0, \n",
    "           color = [1, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confidence intervals.\n",
    "\n",
    "A point estimate provides a single plausible value for a parameter. However,\n",
    "as we have seen a point estimate is rarely perfect; usually there is some error\n",
    "in the estimate. That is why we have proposed to use the standard error as\n",
    "a measure of its variability.\n",
    "\n",
    "As an alternative, a next logical step would be to provide a **plausible range of\n",
    "values** for the parameter. A plausible range of values for the sample parameter\n",
    "is called a **confidence interval**.\n",
    "\n",
    "We will base the definition of confidence interval on two ideas:\n",
    "\n",
    "+ Our point estimate is the most plausible value of the parameter, so it makes sense to build the confidence interval around the point estimate.\n",
    "\n",
    "+ The plausability of a range of values can be defined from the sampling distribution of the estimate.\n",
    "\n",
    "In order to define an interval, we can make use of a well\n",
    "known result from probability that applies to normal distributions: roughly\n",
    "95% of the time our estimate will be within 1.96 standard errors of the true\n",
    "mean of the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence interval: [24.975156065800284, 26.8440220163915]\n"
     ]
    }
   ],
   "source": [
    "m = accidents.mean()\n",
    "se = accidents.std()/math.sqrt(len(accidents))\n",
    "ci = [m - se*1.96, m + se*1.96]\n",
    "print(\"Confidence interval:\", ci)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is how we would compute a 95% confidence interval of the sample mean by using bootstrapping:\n",
    "\n",
    "1. Repeat the following steps a large number $M$ of times: \n",
    "    + Draw $N$ observations with replacement from the original data to create a bootstrap sample or resample; \n",
    "    + Calculate the mean for the resample.\n",
    "2. Calculate the **mean** of your $M$ values of the sample statistic. This process gives you a “bootstrapped” estimate of the sample statistic.\n",
    "3. Calculate the **standard deviation** of your $M$ values of the sample statistic. This process gives you a “bootstrapped” estimate of the **SE** of the sample statistic.\n",
    "4. Obtain the 2.5th and 97.5th centiles of your $M$ values values of the sample statistic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean estimate: 25.910843561643837\n",
      "SE of the estimate: 0.47927070407886707\n",
      "Confidence interval: [24.958904109589042, 26.84931506849315]\n"
     ]
    }
   ],
   "source": [
    "m = meanBootstrap(accidents, 10000)\n",
    "sample_mean = np.mean(m)\n",
    "sample_se =  np.std(m)\n",
    "\n",
    "print(\"Mean estimate:\", sample_mean)\n",
    "print(\"SE of the estimate:\", sample_se)\n",
    "\n",
    "ci = [np.percentile(m,2.5), np.percentile(m,97.5)]\n",
    "print(\"Confidence interval:\", ci)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Waht is the real meaning of CI?\n",
    "\n",
    "The real meaning of \"confidence\" is not evident and it must be understood\n",
    "from the point of view of the generating process.\n",
    "\n",
    "Suppose we take many (infinite) samples from a population and built a\n",
    "95% confidence interval from each sample. Then about 95% of those intervals\n",
    "would contain the actual parameter.\n",
    "\n",
    "This can be easily showed by simulating a large number of samples and checking how many intervals contain the true parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = accidents   \n",
    "\n",
    "n = 100                                               # number of observations\n",
    "N_test = 100                                          # number of samples with n observations\n",
    "means = np.array([0.0] * N_test)                      # samples' mean\n",
    "s = np.array([0.0] * N_test)                          # samples' std\n",
    "ci = np.array([[0.0,0.0]] * N_test)\n",
    "tm = df.mean()                                        # \"true\" mean\n",
    "\n",
    "for i in range(N_test):                               # sample generation and CI computation\n",
    "    rows = np.random.choice(df.index.values, n)\n",
    "    sampled_df = df.loc[rows]\n",
    "    means[i] = sampled_df.mean()\n",
    "    s[i] = sampled_df.std()\n",
    "    ci[i] = means[i] + np.array([-s[i] *1.96/np.sqrt(n), s[i]*1.96/np.sqrt(n)])    \n",
    "\n",
    "out1 = ci[:,0] > tm                                   # CI that do not contain the \"true\" mean\n",
    "out2 = ci[:,1] < tm\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(12, 5))\n",
    "ind = np.arange(1, N_test+1)\n",
    "ax.axhline(y = tm, \n",
    "           xmin = 0, \n",
    "           xmax = N_test+1, \n",
    "           color = [0, 0, 0])\n",
    "ci = np.transpose(ci)\n",
    "ax.plot([ind,ind], \n",
    "        ci, \n",
    "        color = '0.75', \n",
    "        marker = '_', \n",
    "        ms = 0, \n",
    "        linewidth = 3)\n",
    "ax.plot([ind[out1],ind[out1]], \n",
    "        ci[:, out1], \n",
    "        color = [1, 0, 0, 0.8], \n",
    "        marker = '_', \n",
    "        ms = 0, \n",
    "        linewidth = 3)\n",
    "ax.plot([ind[out2],ind[out2]], \n",
    "        ci[:, out2], \n",
    "        color = [1, 0, 0, 0.8], \n",
    "        marker = '_',\n",
    "        ms = 0, \n",
    "        linewidth = 3)\n",
    "ax.plot(ind, \n",
    "        means, \n",
    "        color = [0, .8, .2, .8], \n",
    "        marker = '.',\n",
    "        ms = 10, \n",
    "        linestyle = '')\n",
    "ax.set_ylabel(\"Confidence interval for the samples' mean estimate\",\n",
    "              fontsize = 12)\n",
    "ax.set_xlabel('Samples (with %d observations). '  %n, \n",
    "              fontsize = 12)\n",
    "plt.savefig(\"confidence.png\",\n",
    "            dpi = 300, \n",
    "            bbox_inches = 'tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis testing\n",
    "\n",
    "To give a measure of variability of our estimates is a way of producing a\n",
    "statistical proposition about the population, but not the only one. R.A.Fisher\n",
    "(1890-1962) proposed an alternative, known as *hypothesis testing*, that is\n",
    "based on the concept of *statistical significance*.\n",
    "\n",
    "Let's suppose that a deeper analysis of traffic accidents in Barcelona results\n",
    "in a difference between 2010 and 2013. Of course, the diference could be caused only by chance, because of the variability of both estimates. But it\n",
    "could also be the case that traffic conditions are very diferent in Barcelona\n",
    "during these two periods and, because of this, data from these two periods can\n",
    "be considered as belonging to two diferent populations. Then, the relevant\n",
    "question is: Are the observed effects real or not?\n",
    "\n",
    "The process of determining the statistical significance of an effect is called\n",
    "**hypothesis testing**. This process starts by simplifying the options into two\n",
    "competing hypotheses:\n",
    "\n",
    "+ $H_0$: The mean number of daily traffic accidents is the same in 2013 and 2010 (there is only one population, one true mean, and 2010 and 2013 are just different samples from the same population).\n",
    "\n",
    "+ $H_A$: The mean number of daily traffic accidents for 2010 and for 2013 is different (2010 and 2013 are two samples from two different populations).\n",
    "\n",
    "We call $H_0$ the *null hypothesis* and it represents a skeptical point of view:\n",
    "the effect we have observed is due to chance (due to the specific sample bias).\n",
    "\n",
    "$H_A$ is the *alternative hypothesis* and it represents the other point of view:\n",
    "the effect is real.\n",
    "\n",
    "The general rule of frequentist hypothesis testing is: We will not discard $H_0$\n",
    "(and hence we will not consider $H_A$) unless the observed effect is implausible\n",
    "under $H_0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing hypotheses using confidence intervals.\n",
    "\n",
    "We can use the concept represented by confidence intervals to measure the\n",
    "plausibility of an hypothesis.\n",
    "\n",
    "We can illustrate the evaluation of the hypotheses setup by comparing the\n",
    "mean rate of traffic accidents in Barcelona during 2010 and 2013 using a point estimate from the 2013 sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2010: Mean 24.81095890410959\n",
      "2013: Mean 25.90958904109589\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv(\"files/ch04/ACCIDENTS_GU_BCN_2010.csv\", encoding='latin-1')\n",
    "#Create a new column which is the date\n",
    "data['Date'] = data['Dia de mes'].apply(lambda x : str(x)) + '-' +  \\\n",
    "               data['Mes de any'].apply(lambda x : str(x))\n",
    "data2 = data['Date']\n",
    "counts2010 =data['Date'].value_counts()\n",
    "print('2010: Mean', counts2010.mean())\n",
    "\n",
    "data = pd.read_csv(\"files/ch04/ACCIDENTS_GU_BCN_2013.csv\", encoding='latin-1')\n",
    "#Create a new column which is the date\n",
    "data['Date'] = data['Dia de mes'].apply(lambda x : str(x)) + '-' +  \\\n",
    "               data['Mes de any'].apply(lambda x : str(x))\n",
    "data2 = data['Date']\n",
    "counts2013 = data['Date'].value_counts()\n",
    "print('2013: Mean', counts2013.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This estimate suggests that during 2013 the mean rate of\n",
    "traffic accidents in Barcelona **was higher** than 2010. But is this effect statistically significant?\n",
    "\n",
    "Based on our sample, the 95% confidence interval for the mean rate of\n",
    "traffic accidents in Barcelona during 2013 can be calculated as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2010 accident rate estimate: 24.81095890410959\n",
      "2013 accident rate estimate: 25.90958904109589\n",
      "CI for 2013: [24.975156065800284, 26.8440220163915]\n"
     ]
    }
   ],
   "source": [
    "n = len(counts2013)\n",
    "mean = counts2013.mean()\n",
    "s = counts2013.std()\n",
    "ci = [mean - s*1.96/np.sqrt(n),  mean + s*1.96/np.sqrt(n)] \n",
    "print('2010 accident rate estimate:', counts2010.mean())\n",
    "print('2013 accident rate estimate:', counts2013.mean())\n",
    "print('CI for 2013:',ci)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because 2010 accident rate estimate does not fall in the range of plausible values of 2013, we say the\n",
    "alternative hypothesis cannot be discarted. That is, it can not be discarted that during 2013 the mean rate of traffic accidents in Barcelona was higher than during 2010."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing hypotheses using P-values.\n",
    "\n",
    "A more advanced notion of statistical significance was developed by R.A.Fisher\n",
    "in the 1920's when looking for a test to decide whether variation in crop yields\n",
    "were due to some specific intervention or merely randon factors beyond experimental control.\n",
    "Fisher first assumed that fertilizer caused no difference (null hypothesis)\n",
    "and then calculated $P$, the probability that an observed yield in a fertilized\n",
    "field would occur if fertilizer had no real effect. This probability is called\n",
    "p-value.\n",
    "\n",
    "The p-value is the probability of observing data at least as favorable to\n",
    "the alternative hypothesis as our current data set, if the null hypothesis is\n",
    "true.\n",
    "\n",
    "To apply a test of hypotheses to our problem, the first step is to quantify the size of the apparent effect by choosing a test statistic. In our case, the apparent effect is a difference in accident\n",
    "rates, so a natural choice for the test statistic is the difference in means\n",
    "between the two periods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m: 365 n: 365\n",
      "mean difference:  1.0986301369863014\n"
     ]
    }
   ],
   "source": [
    "m = len(counts2010)\n",
    "n = len(counts2013)\n",
    "p = (counts2013.mean() - counts2010.mean())\n",
    "print('m:',m, 'n:', n)\n",
    "print('mean difference: ', p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second step is to define a null hypothesis, which is a model of the\n",
    "system based on the assumption that the apparent effect is not real. In\n",
    "our case the null hypothesis is that there is no diference between the two\n",
    "periods. The alternative hypothesis is that during 2013 the mean rate of traffic accidents in Barcelona was higher than 2010.\n",
    "\n",
    "The third step is to compute a p-value, which is the probability of seeing\n",
    "the apparent effect if the null hypothesis is true. In our case, we would\n",
    "compute the absolute difference in means, then compute the probability\n",
    "of seeing a difference as big, or bigger, under the null hypothesis.\n",
    "\n",
    "Usually, if P is less than 0.05 (the chance of a \n",
    "fluke is less than 5%) the\n",
    "result is declared statistically significant.\n",
    "\n",
    "To approximate the p-value, we can follow the following procedure:\n",
    "1. Pool the distributions, generate samples with size $n$ and compute the difference in the mean.\n",
    "2. Generate samples with size $n$ and compute the difference in the mean.\n",
    "3. Count how many differences are larger than the observed one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Pooled distribution')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = counts2010\n",
    "y = counts2013\n",
    "pool = np.concatenate([x,y])\n",
    "np.random.shuffle(pool)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(12, 3))\n",
    "plt.hist(pool, \n",
    "         bins = 25, \n",
    "         density = True)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Number of accidents')\n",
    "plt.title(\"Pooled distribution\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Difference in the mean')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10000 # number of samples\n",
    "diff = np.arange(N)\n",
    "for i in np.arange(N):\n",
    "    p1 = [random.choice(pool) for _ in np.arange(n)]\n",
    "    p2 = [random.choice(pool) for _ in np.arange(n)]\n",
    "    diff[i] = (np.mean(p1)-np.mean(p2))\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(12, 3))\n",
    "plt.hist(diff, bins = 50, density = True)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Difference in the mean')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# counting how many differences are larger than the observed one\n",
    "diff2 = np.array(diff)\n",
    "w1 = np.where(diff2 > p)[0]      \n",
    "len(w1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If there are $k$ sample pairs where the difference in mean is as big as or bigger than 0.05, the p-value is approximately $k/N$. In or case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value (Simulation)= 0.0013 ( 0.13 %) Difference = 1.0986301369863014\n",
      "The effect is likely\n"
     ]
    }
   ],
   "source": [
    "print('p-value (Simulation)=', len(w1)/float(N), '(', len(w1)/float(N)*100 ,'%)', 'Difference =', p)\n",
    "if len(w1)/float(N)<0.05:\n",
    "    print('The effect is likely')\n",
    "else:\n",
    "    print('The effect is not likely')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have defined the effect as a difference in mean as\n",
    "big or bigger than the observed difference, taking into account the sign. A test like this is called *one-sided*.\n",
    "\n",
    "If the relevant question is whether accident rates are different, then it\n",
    "makes sense to test the absolute difference in means. This kind of test is called *two-sided*\n",
    "because it  counts both sides of the distribution of differences."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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