2.Sampling Size.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Impact of Large Sample Sizes\n",
    "\n",
    "When we increase our sample size, even the smallest of differences may seem significant. (ex, profit from A and B)   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "np.random.seed(1)\n",
    " \n",
    "coffee_full = pd.read_csv('C:/Users/Minkun/Desktop/classes_1/NanoDeg/1.Data_AN/L4/data/coffee_dataset.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`1.` In this case, imagine we are interested in testing if **the mean height of all individuals** in `full_data` is equal to 67.60 inches or **different** than 67.60.  First, use **quiz 1** below to identify the null and alternative hypotheses for these cases. \n",
    "\n",
    "$$H_0: \\mu = 67.60$$\n",
    "\n",
    "$$H_1: \\mu \\neq 67.60$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`2.` What is the population mean height?  What is the standard deviation of the population heights? What is the sample mean height? Simulate the sampling distribution for the mean of five values to see the shape and plot a histogram.  What is the standard deviation of the sampling distribution of the mean of five draws?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(67.59748697307937, 3.119433206550344)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# population height mean and standard deviation\n",
    "coffee_full.height.mean(), coffee_full.height.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "67.9754986070742"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sampling \n",
    "sample1 = coffee_full.sample(5)\n",
    "sample1.height.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAD8CAYAAACRkhiPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIEk9ZghIUo8ZApLUY4aAJPXY/wfnVJjrINVOsAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x215af055f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 10000 sampling and the distribution of their statistics - 'means' of 10000.\n",
    "sampling_dist_mean5 = []\n",
    "\n",
    "for _ in range(10000):\n",
    "    bootstrap_sample = sample1.sample(5, replace=True)\n",
    "    bootstrap_mean = bootstrap_sample.height.mean()\n",
    "    sampling_dist_mean5.append(bootstrap_mean)\n",
    "\n",
    "plt.hist(sampling_dist_mean5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1737458377805681"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std_sampling_dist = np.std(sampling_dist_mean5); std_sampling_dist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`3.` Using the null and alternative set up in question 1 and the results of your sampling distribution in question 2, simulate the mean values you would expect from the null hypothesis.  Use these simulated values to determine a p-value to make a decision about your null and alternative hypotheses.  \n",
    "\n",
    "**Hint:** Use the numpy documentation [here](https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.random.normal.html) to assist with your solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAD8CAYAAACRkhiPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nApLUMUNAkjpmCEhSxwwBSeqYISBJHfv/BkI2qV3wIK0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x215af97e7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "null_mean = 67.60\n",
    "null_vals = np.random.normal(null_mean, std_sampling_dist, 10000)\n",
    "\n",
    "plt.hist(null_vals);\n",
    "\n",
    "# where our sample mean falls on null distribution\n",
    "plt.axvline(x=sample1.height.mean(), color = 'red');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.74280000000000002"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# for a two sided hypothesis, we want to look at anything \n",
    "# more extreme from the null in both directions\n",
    "obs_mean = sample1.height.mean()\n",
    "\n",
    "prob_more_extreme_high = (null_vals > obs_mean).mean()\n",
    "prob_more_extreme_low = (null_vals < null_mean - (obs_mean - null_mean)).mean()\n",
    "\n",
    "pval = prob_more_extreme_low + prob_more_extreme_high; pval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAD8CAYAAACRkhiPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x215afa238d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's see where our sample mean falls on the null distribution\n",
    "lower_bound = null_mean - (obs_mean - null_mean)\n",
    "upper_bound = obs_mean\n",
    "\n",
    "plt.hist(null_vals);\n",
    "plt.axvline(x=lower_bound, color = 'red');\n",
    "plt.axvline(x=upper_bound, color = 'red');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.79190000000000005"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "null_mean = 67.60  \n",
    "\n",
    "# this is another way to compute the standard deviation of the sampling distribution theoretically  \n",
    "std_sampling_dist = coffee_full.height.std()/np.sqrt(5)  \n",
    "num_sims = 10000\n",
    "\n",
    "null_sims = np.random.normal(null_mean, std_sampling_dist, num_sims)  \n",
    "low_ext = (null_mean - (sample1.height.mean() - null_mean))  \n",
    "high_ext = sample1.height.mean()  \n",
    "\n",
    "(null_sims > high_ext).mean() + (null_sims < low_ext).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`4.` Now, imagine you received the same sample mean you calculated from the sample in question 2 above, but with a sample of 1000.  What would the new standard deviation be for your sampling distribution for the mean of 1000 values?  Additionally, what would your new p-value be for choosing between the null and alternative hypotheses you set up? Simulate the sampling distribution for the mean of five values to see the shape and plot a histogram.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.099515069810618501"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get standard deviation for a sample size of 1000\n",
    "sample2 = coffee_full.sample(1000)\n",
    "sampling_dist_mean1000 = []\n",
    "for _ in range(10000):\n",
    "    bootstrap_sample = sample2.sample(1000, replace=True)\n",
    "    bootstrap_mean = bootstrap_sample.height.mean()\n",
    "    sampling_dist_mean1000.append(bootstrap_mean)\n",
    "    \n",
    "std_sampling_dist1000 = np.std(sampling_dist_mean1000)\n",
    "std_sampling_dist1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAD8CAYAAACcjGjIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLbC70KMBFwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x215b0bcff98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "null_vals = np.random.normal(null_mean, std_sampling_dist1000, 10000)\n",
    "\n",
    "plt.hist(null_vals);\n",
    "plt.axvline(x=lower_bound, color = 'red');\n",
    "plt.axvline(x=upper_bound, color = 'red');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00020000000000000001"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# for a two sided hypothesis, we want to look at anything \n",
    "# more extreme from the null in both directions\n",
    "\n",
    "prob_more_extreme_low = (null_vals < lower_bound).mean()\n",
    "prob_more_extreme_high = (upper_bound < null_vals).mean()\n",
    "\n",
    "pval = prob_more_extreme_low + prob_more_extreme_high; pval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}