{
"cells": [
{
"cell_type": "code",
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"metadata": {
"tags": [
"remove_input"
]
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"outputs": [],
"source": [
"path_data = '../../data/'\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('fivethirtyeight')\n",
"\n",
"import warnings\n",
"warnings.filterwarnings('ignore')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Confidence Intervals\n",
"We have developed a method for estimating a parameter by using random sampling and the bootstrap. Our method produces an interval of estimates, to account for chance variability in the random sample. By providing an interval of estimates instead of just one estimate, we give ourselves some wiggle room.\n",
"\n",
"In the previous example we saw that our process of estimation produced a good interval about 95% of the time, a \"good\" interval being one that contains the parameter. We say that we are *95% confident* that the process results in a good interval. Our interval of estimates is called a *95% confidence interval* for the parameter, and 95% is called the *confidence level* of the interval.\n",
"\n",
"The situation in the previous example was a bit unusual. Because we happened to know the value of the parameter, we were able to check whether an interval was good or not so good, and this in turn helped us to see that our process of estimation captured the parameter about 95 out of every 100 times we used it.\n",
"\n",
"But usually, data scientists don't know the value of the parameter. That is the reason they want to estimate it in the first place. In such situations, they provide an interval of estimates for the unknown parameter by using methods like the one we have developed. Because of statistical theory and demonstrations like the one we have seen, data scientists can be confident that their process of generating the interval results in a good interval a known percent of the time."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Confidence Interval for a Population Median: Bootstrap Percentile Method ###\n",
"\n",
"We will now use the bootstrap method to estimate an unknown population median. The data come from a sample of newborns in a large hospital system; we will treat it as if it were a simple random sample though the sampling was done in multiple stages. [Stat Labs](https://www.stat.berkeley.edu/~statlabs/) by Deborah Nolan and Terry Speed has details about a larger dataset from which this set is drawn. \n",
"\n",
"The table `baby` contains the following variables for mother-baby pairs: the baby's birth weight in ounces, the number of gestational days, the mother's age in completed years, the mother's height in inches, pregnancy weight in pounds, and whether or not the mother smoked during pregnancy."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"baby = pd.read_csv(path_data + 'baby.csv')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
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" Birth Weight Gestational Days Maternal Age Maternal Height \\\n",
"0 120 284 27 62 \n",
"1 113 282 33 64 \n",
"2 128 279 28 64 \n",
"3 108 282 23 67 \n",
"4 136 286 25 62 \n",
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"\n",
" Maternal Pregnancy Weight Maternal Smoker \n",
"0 100 False \n",
"1 135 False \n",
"2 115 True \n",
"3 125 True \n",
"4 93 False \n",
"... ... ... \n",
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"\n",
"[1174 rows x 6 columns]"
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},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"baby"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Birth weight is an important factor in the health of a newborn infant – smaller babies tend to need more medical care in their first days than larger newborns. It is therefore helpful to have an estimate of birth weight before the baby is born. One way to do this is to examine the relationship between birth weight and the number of gestational days. \n",
"\n",
"A simple measure of this relationship is the ratio of birth weight to the number of gestational days. The table `ratios` contains the first two columns of `baby`, as well as a column of the ratios. The first entry in that column was calcualted as follows:\n",
"\n",
"$$\n",
"\\frac{120~\\mbox{ounces}}{284~\\mbox{days}} ~\\approx ~ 0.4225~ \\mbox{ounces per day}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"ratios = baby[['Birth Weight', 'Gestational Days']]\n",
"\n",
"ratios['Ratio BW/GD'] = baby['Birth Weight']/baby['Gestational Days']"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
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"output_type": "display_data"
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"unit = ''\n",
"\n",
"fig, ax = plt.subplots(figsize=(8,6))\n",
"\n",
"ax.hist(ratios['Ratio BW/GD'], density=True, color='blue', alpha=0.8, ec='white')\n",
"\n",
"y_vals = ax.get_yticks()\n",
"\n",
"y_label = 'Percent per ' + (unit if unit else 'unit')\n",
"\n",
"x_label = 'Ratio BW/GD'\n",
"\n",
"ax.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
"\n",
"plt.ylabel(y_label)\n",
"\n",
"plt.xlabel(x_label)\n",
"\n",
"plt.xticks(rotation=90)\n",
"\n",
"plt.title('');\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At first glance the histogram looks quite symmetric, with the density at its maximum over the interval 4 ounces per day to 4.5 ounces per day. But a closer look reveals that some of the ratios were quite large by comparison. The maximum value of the ratios was just over 0.78 ounces per day, almost double the typical value."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
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"\n",
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Birth Weight
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Gestational Days
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Ratio BW/GD
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"source": [
"ratios_1 = ratios.sort_values(by=['Ratio BW/GD'], ascending=False)\n",
"\n",
"ratios_1.iloc[[0]]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The median gives a sense of the typical ratio because it is unaffected by the very large or very small ratios. The median ratio in the sample is about 0.429 ounces per day."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.42907801418439717"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.median(ratios.iloc[:,2])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But what was the median in the population? We don't know, so we will estimate it. \n",
"\n",
"Our method will be exactly the same as in the previous section. We will bootstrap the sample 5,000 times resulting in 5,000 estimates of the median. Our 95% confidence interval will be the \"middle 95%\" of all of our estimates.\n",
"\n",
"Recall the function `bootstrap_median` defined in the previous section. We will call this function and construct a 95% confidence interval for the median ratio in the population. Remember that the table `ratios` contains the relevant data from our original sample."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def bootstrap_median(original_sample, label, replications):\n",
" \n",
" \"\"\"Returns an array of bootstrapped sample medians:\n",
" original_sample: table containing the original sample\n",
" label: label of column containing the variable\n",
" replications: number of bootstrap samples\n",
" \"\"\"\n",
" just_one_column = original_sample[[label]]\n",
" medians = np.array([])\n",
" for i in np.arange(replications):\n",
" bootstrap_sample = just_one_column.sample(len(just_one_column), replace=True)\n",
" resampled_median = np.percentile(bootstrap_sample, 50)\n",
" medians = np.append(medians, resampled_median)\n",
" \n",
" return medians"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# Generate the medians from 5000 bootstrap samples\n",
"bstrap_medians = bootstrap_median(ratios, 'Ratio BW/GD', 5000)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.42545455, 0.43262411])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get the endpoints of the 95% confidence interval\n",
"left = np.percentile(bstrap_medians, 2.5, interpolation='nearest')\n",
"right = np.percentile(bstrap_medians, 97.5, interpolation='nearest')\n",
"\n",
"np.array([left, right])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The 95% confidence interval goes from about 0.425 ounces per day to about 0.433 ounces per day. We are estimating the median \"birth weight to gestational days\" ratio in the population is somewhere in the interval 0.425 ounces per day to 0.433 ounces per day.\n",
"\n",
"The estimate of 0.429 based on the original sample happens to be exactly half-way in between the two ends of the interval, though that need not be true in general.\n",
"\n",
"To visualize our results, let us draw the empirical histogram of our bootstrapped medians and place the confidence interval on the horizontal axis."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"resampled_medians = pd.DataFrame({'Bootstrap Sample Median':bstrap_medians})\n",
"\n",
"unit = ''\n",
"\n",
"fig, ax = plt.subplots(figsize=(10,5))\n",
"\n",
"ax.hist(resampled_medians, bins=15, density=True, color='blue', alpha=0.8, ec='white', zorder=5)\n",
"\n",
"ax.plot(np.array([left, right]), np.array([0,0]), color='yellow', lw=8, zorder=10)\n",
"\n",
"y_vals = ax.get_yticks()\n",
"\n",
"y_label = 'Percent per ' + (unit if unit else 'unit')\n",
"\n",
"x_label = 'Bootstrap Sample Median'\n",
"\n",
"ax.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
"\n",
"plt.ylabel(y_label)\n",
"\n",
"plt.xlabel(x_label)\n",
"\n",
"plt.xticks(rotation=90)\n",
"\n",
"plt.title('');\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This histogram and interval resembles those we drew in the previous section, with one big difference – there is no red dot showing where the parameter is. We don't know where that dot should be, or whether it is even in the interval.\n",
"\n",
"We just have an interval of estimates. It is a 95% confidence interval of estimates, because the process that generates it produces a good interval about 95% of the time. That certainly beats guessing at random!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Keep in mind that this interval is an approximate 95% confidence interval. There are many approximations involved in its computation. The approximation is not bad, but it is not exact."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Confidence Interval for a Population Mean: Bootstrap Percentile Method ###\n",
"What we have done for medians can be done for means as well. Suppose we want to estimate the average age of the mothers in the population. A natural estimate is the average age of the mothers in the sample. Here is the distribution of their ages, and their average age which was about 27.2 years."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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lwmUsFouSkpJ8EhwAAFQtbpeS1NRUWSwWNWrUSJIKrx+xWq1q1KiRHA6HvvvuuyLLcO8SAADgLrdLyf79+32ZAwAABDi3rykBAADwJUoJAAAwBUoJAAAwBUoJAAAwBUoJAAAwBUoJAAAwBbdLSfv27bVly5ZSp2/dulXt27f3SigAABB43L5PyaFDh3T27NlSp589e1aHDx/2Sihc2vHjITp6tPIPdOXmNlFOTvGHMrojLy/Iy2kAAFWJ26VEKvsOrT/88INq1apV4UBwz9Gj1TR5cuV/yDscYbJay7fdadO8HAYAUKWUWUreeustvf3224Wv582bp+XLlxebLzs7WwcOHFDfvn29nxAAAASEMkvJ2bNnlZGRUfg6JydHTqezyDwWi0U1atTQmDFjNHXqVN+kBAAAVV6ZpWTcuHEaN26cJKldu3aaM2eObrvttkoJBgAAAovb15R88803vswBAAACnEcXukrSL7/8oiNHjuj06dNyuVzFpnfv3t0rwQAAQGBxu5ScPn1aU6ZM0fr161VQUFBsusvlksVi0alTp7waEAAABAa3S8mDDz6ozZs3a9y4cerevbtsNpsPYwEAgEDjdin56KOPNGHCBM2ePduXeQAAQIBy+5agISEhio6O9mUWAAAQwNwuJQMHDtS2bdt8mQUAAAQwt0vJfffdpxMnTujuu+/Wnj17dOLECf3888/F/gAAAJSH29eUdOzYURaLRSkpKUpKSip1Pne/ffPPf/5Tr7/+euFD/Fq2bKnJkydzq3oAAAKU26Xk0UcfLfOBfJ5q0KCBnnzySUVHR8vpdOrtt9/W6NGj9cknn+iaa67x2nYAAIB/cLuUTPPyI1779etX5PWMGTP02muvac+ePZQSAAACkNvXlFysoKBAp06d0oULF7wSoqCgQGvXrtXZs2d13XXXeWWdAADAv3h0m/kvv/xSs2bN0q5du3T+/HmtX79eN9xwg7KysnTPPfdo0qRJuuGGG9xe3//8z/8oLi5O586d02WXXaY333xTbdq0KXMZu93uSWS3+GKdvpab20QOR5gh23Y4HOVa7vz5IDkcxe8GbHYVzV3e8aoo/xzvIMPGqyJyc/Nkt6cbsm1/3H8ZifHyjC/GKyYmptRpbpeSL774QgMGDFBERIRGjhypFStWFE6rV6+ezpw5ozfeeMOjUhITE6NPP/1UOTk52rhxo+655x5t3rxZrVu3LnMZb7Lb7V5fZ2XIyQmV1RpU6dt1OByyWq3lWjY4WLJaPX7ckuEqkrsi41VR/jneFwwbr4qoXbu6IfsRf91/GYXx8owR4+X26ZunnnpK0dHR2r17t5544oli03v27Km9e/d6tPGQkBA1a9ZMHTp00MyZM9W2bVstWrTIo3UAAICqwe1S8uWXX+rPf/6zQkNDS/wWTsOGDZWRkVGhME6nU/n5+RVaBwAA8E9uH9utVq2aqlUrvcNkZGQoLMz9axz+/ve/Ky4uTg0bNtSZM2e0Zs0a7dixo8x7oAAAgKrL7VISGxurrVu3asKECcWm5efna/Xq1R59cyYjI0Pjx4/XyZMnVbt2bbVp00Zr1qxRnz593F4HAJiBxRKkvXtDK327ublNlJNTvu02bOhUZCRHpmEubpeShx56SEOHDtW9996rYcOGSZJOnDihjz76SPPmzdOPP/6ohQsXur3hxYsXe54WAEwoM1NKTDTiwvOwcl/wPm+eFBnp5UBABbldSm688UYtWbJEjzzyiN566y1J0j333COXy6XLL79cr776qjp37uyzoAAAoGrz6PuCQ4cO1W233abk5GQdPHhQTqdTTZs2VZ8+fVSzZk1fZQQAAAHA45sY1KhRo9gt4gEAACrK7a8Eb9myRY888kip0x955BFt3brVK6EAAEDgcbuUvPzyy/r1119LnX7u3Dm9+OKLXgkFAAACj9ul5MCBA4qNjS11evv27ZWamuqNTAAAIAC5XUouXLigvLy8Uqfn5eX55YO0AACAObhdSlq3bq2NGzfK6XQWm+Z0OrVx40a1bNnSq+EAAEDgcLuU3H333dq3b59GjRqllJQUORwOORwOpaSk6Pbbb9e+fftKvNsrAACAO9z+SvCQIUP0448/KjExUdu2bZMkWSwWuVwuWSwWTZkyRSNGjPBZUAAAULV5dJ+SyZMna+jQodq0aZPS09PlcrnUtGlTxcfHq0mTJj6KCAAAAoFbpSQvL0/Dhw/XiBEj9Oc//1n33Xefr3MBAIAA49Y1JWFhYfr6669VUFDg6zwAACBAuX2ha48ePfTZZ5/5MgsAAAhgbpeSuXPn6ssvv9SMGTOUnp5e4leDAQAAysvtC107d+4sl8ulhQsXauHChapWrZqCg4OLzGOxWHTs2DGvhwQAAFWf26Vk8ODBslgsvswCAAACmNulZPHixb7MAQAAApzb15QAAAD4kkel5NChQ/qv//ovxcbGKioqSjt27JAkZWVl6eGHH1ZKSoovMgIAgADg9umb7777TrfccoucTqc6deqkQ4cOFd63pF69etqzZ48cDocWLFjgs7AAAKDqcruUzJw5U7Vq1dJHH32koKAgNW/evMj0uLg4vfvuu97OBwAAAoTbp28+++wzjR07VuHh4SV+CycqKkrHjx/3ajgAABA43C4lFy5c0GWXXVbq9NOnTysoKMgroQAAQOBxu5S0bt1an376aYnTXC6XNm3apNjYWG/lAgAAAcbtUnLPPfdow4YNevbZZ3Xq1ClJktPp1Pfff6+//e1v+uqrr3h6MAAAKDe3L3QdMmSIDh8+rNmzZ2vOnDmF70lSUFCQnn76ad18882+SQkAAKo8t0uJJD3wwAMaOnSoNm7cqLS0NDmdTjVt2lQDBgzQVVdd5auMAAAgAFyylDgcDm3ZskXp6emqW7eu+vbtq4kTJ1ZGNgAAEEDKLCUZGRm67bbb9OOPP8rlckmSLrvsMq1atUrdu3evlIAAACAwlHmh69NPP6309HRNnDhRq1atUmJioqxWqx599NEKb3j+/Pm68cYbFRUVpejoaI0YMUIHDhyo8HoBAIB/KvNIyccff6xRo0bp6aefLnwvPDxcY8eO1dGjR9WwYcNyb3jHjh266667dO2118rlcumZZ57RoEGDtHv3btWpU6fc6wUAAP7pkqdvunTpUuS9rl27yuVy6ciRIxUqJevWrSvyesmSJWrcuLE+//xz3XrrreVeLwAA8E9lnr4pKChQaGhokfd+f33u3DmvBjlz5oycTqdsNptX1wsAAPzDJb99k56ern379hW+zs3NlSTZ7XbVrFmz2PwdO3YsV5CpU6eqbdu2uu6668qcz263l2v9lb1OX8vNbSKHI8yQbTscjnItd/58kByOAi+n8b2K5i7veFWUf453kGHjVRFGjnV5xys3N092e7p3w/gBf9zfG8kX4xUTE1PqtEuWksTERCUmJhZ7/48Xu7pcLlkslsK7vXriscce0+eff66tW7de8vk5Zf0w5WG3272+zsqQkxMqq7XynzXkcDhktVrLtWxwsGS1enRrHFOoSO6KjFdF+ed4XzBsvCrCqLGuyN+v2rWr++W+ryL8dX9vFCPGq8zfooULF/o8wLRp07Ru3Tpt2rRJTZo08fn2AACSxRKkvXtDLz2jyTRs6FRkZL7RMeAjZZaS22+/3acbnzJlitatW6fNmzfr6quv9um2AAD/kZkpJSb635Pd582TIiONTgFfMezY7uTJk7Vq1Sq9+eabstlsysjIkPTbzdlKulYFAABUbW4/JdjbXn31Vf3yyy8aOHCgWrRoUfjn5ZdfNioSAAAwkGFHSrKzs43aNAAAMCHDjpQAAABcjFICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMgVICAABMobrRAQAAcJfFEqS9e0PLtWxubhPl5JRv2Ypo2NCpyMj8St+uP6KUAAD8RmamlJgYVK5lHY4wWa3lW7Yi5s2TIiMrfbN+idM3AADAFCglAADAFCglAADAFCglAADAFCglAADAFCglAADAFCglAADAFCglAADAFAwtJTt37tTIkSPVqlUr2Ww2rVy50sg4AADAQIaWkrNnz6p169aaM2eOwsLCjIwCAAAMZuht5uPi4hQXFydJmjhxopFRAACAwbimBAAAmILfPZDPbrf7xTp9LTe3iRwOY055ORyOci13/nyQHI4CL6fxvYrmLu94VZR/jneQYeNVEUaONb+PnjHi71dubp7s9vRK3643+OLzMSYmptRpfldKyvphysNut3t9nZUhJyfUkKddOhwOWa3Wci0bHCxZrX73V65CuSsyXhXln+N9wbDxqgijxprfR88Y9ftYu3Z1v/ycMeLzkdM3AADAFCglAADAFAw9dnfmzBmlpaVJkpxOp44cOaJvvvlGderUUVRUlJHRAABAJTP0SMlXX32l66+/Xtdff73y8vKUmJio66+/Xs8884yRsQAAgAEMPVLSs2dPZWdnGxkBAACYBNeUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6CUAAAAU6hudAAAAKoyiyVIe/eGGh3DY6GhkZW+TUoJAAA+lJkpJSYGGR3DY088Ya30bXL6BgAAmAKlBAAAmELAn75xOCL98lxfXp7/HQoEAKAsAV9KTp60atYs//uAnzbN6AQAAHgXp28AAIApUEoAAIApUEoAAIApGF5KXn31VbVr104RERG64YYb9NlnnxkdCQAAGMDQUrJu3TpNnTpVDz/8sLZv367rrrtOw4YN0+HDh42MBQAADGBoKVm4cKFuv/12jRkzRi1atNBzzz2niIgILVu2zMhYAADAAIaVkvz8fKWkpKh3795F3u/du7d2795tUCoAAGAUw0pJVlaWCgoKVL9+/SLv169fXydPnqy0HLVr16q0bVUFVmvlPwvBnzFengkODvhbJ3mEv1+eYbw8Y8TnoyU7O9tV6VuVdPz4cbVq1UpbtmxRt27dCt+fM2eO1q5dqz179hgRCwAAGMSwIyX16tVTUFBQsaMimZmZxY6eAACAqs+wUhISEqLY2FglJycXeT85OVldunQxKBUAADCKoSdwJ02apAkTJqhjx47q0qWLli1bphMnTujOO+80MhYAADCAoaUkISFBp06d0nPPPaeMjAy1atVKSUlJaty4sZGxAACAAQy70BUAAOBifP8OpTp79qzWrFmj3bt36+TJk7JYLKpfv766du2qIUOG6LLLLjM6ommdP39eH3zwgdLS0hQREaH+/fszXkAlYv9VfkbuvwL6SAkfHKVLTU3V4MGDdebMGXXr1k3169eXy+VSZmamdu3apZo1a2rdunVq2bKl0VFNIS4uTklJSbLZbMrMzNSAAQNkt9vVoEEDHT9+XOHh4frwww/VoEEDo6OaBh8a5ce+q2zsvzxjpv1XQJUSMw282fXv31/169fX4sWLFRoaWmTauXPnNHHiRJ08eVKbN282KKG51KlTR99//73q16+v+++/X/v27dOaNWt05ZVXKisrS6NGjdLVV1+tBQsWGB3VFPjQ8Az7Ls+w//KMmfZfAVVKzDTwZhcZGank5ORSPxQOHDigPn366Pjx45WczJwu/rvVqVMnzZ49W3379i2c/umnn2rSpEn65ptvDExpHnxoeIZ9l2fYf3nGTPsvQx/IZ6SdO3dqxowZuvLKKyX9djO3GTNmaPv27QYnMwebzaYffvih1OkHDx6UzWarvEB+wGKxSJJycnKKfYPsqquuUkZGhhGxTGnfvn2aMmVKsUIiSaGhoZo8ebL27dtnQDLzY991aey/PGeW/VfAXehqloE3u7/+9a+aOHGi7Ha7brzxRtWvX18Wi0UnT55UcnKy/vGPf2jSpElGxzSV8ePHKyQkROfPn9dPP/2kVq1aFU7LyMjQ5ZdfbmA6c/n9Q6O0f8nyoVEc+y73sf/ynFn2XwFXSswy8GY3bdo0hYWF6ZVXXtGsWbMKd4gul0sRERF6+OGHdf/99xuc0jxGjRpV+P+33Xab8vLyikzfuHGj2rZtW9mxTIsPDc+x73If+y/PmGn/FVDXlEycOLHI65tvvlmDBw8ufD1jxgwdOHBAa9eurexoppaenl74jKLw8HA1adLE2EB+6OzZswoKCirxdEWgeuGFF/TKK68oIyOj2IfGPffcw4fGRdh3ld/F+6+6deuqefPmBifyH+fPn1dwcHCl7r8CqpRcCh8cQOWj9FYc+y731K9fXzt27FCLFi2MjuIXjBivgDt9U5bTp08rMTFRCxcuNDqKKWRnZ2v37t2y2Wy67rrrCv81K/22E1ywYIGmTJliYEJzYbw8c+DAAe3Zs0ddunTRddddp9TUVM2fP18Oh0MjRoxQ7969jY5oKhePV8uWLZWamqpFixYxXiV49NFHS3y/oKBAzz//fOH1Ss8++2wlpjIvM40XR0ousn//ft1www06deqU0VEM97//+78aNGiQMjMz5XQ61b59e61YsaLwAruTJ0+qZcuWjNX/Y7w88+GHH2r06NGqWbOmfv31V7355pu6++671bZtWzmdTu3cuVNr165Vr169jI5qCoyXZ+rUqaNrrrmm2HU2O3fuVIcOHVSjRg1ZLBZt2rTJoITmYqbxCqhS8vbbb5c5/ciRI0pMTOSDQ9LIkSNVvXp1LVmyRL/88oumTp2qL774Qps2bVJ0dDQfsn/AeHkmLi5O119/vR5//HGtXbtWDz/8sO666y7NmDFDkvTkk08qJSVF69evNzipOTBennn++ee1YsUKLViwQD179ix8/4orrtCOHTu4Kd8fmGm8AqqU1KlTp7DxlcTpdOrcuXN8cEhq3ry5Nm3aVOQK/8cee0zr16/Xpk2bVLt2bT5kL8J4eaZx48b65JNP1KxZMzmdToWHh+ujjz5SbGyspN9OVQwaNEjff/+9sUFNgvHy3J49ezR+/HgNHjxY06dPV1BQEKWkDGYZr4C6eVpkZKQWL16sI0eOlPhn69atRkc0jfz8/GLl7ZlnntGgQYPUr18/fffddwYlMyfGy3PVqlUr/G9oaGiR+5LUrFlTubm5BiUzJ8bLM507d9Ynn3yiH3/8UTfddFOZN1ODecYroEpJ+/bty7xNrsVikcsVMAeOytS8eXN99dVXxd5PTEzUoEGDNHr0aANSmRfj5ZmoqCgdPHiw8PWHH36oRo0aFb4+evSowsPDjYhmSoxX+Vx++eV6/fXXdccdd+iWW26R0+k0OpKpmWG8AqqU3HffferSpUup05s1a8aFT/+vf//+pd7zYO7cuRo+fDgF7iKMl2fuvPNO5efnF75u3bq1qlf/z5cBP/zwQ/Xo0cOIaKbEeFXMmDFjtHXrVi1YsICHFrrByPEKqGtKAACAeQXUkRIAAGBelBIAAGAKlBIAVYLNZlNiYqLRMQBUAKUE8DMrV66UzWaTzWbT9u3bS5ynd+/estls6ty5c7m2sWrVKi1atKgiMf1CbGysbDab3nnnHaOjABClBPBboaGhWr16dbH3Dx48qC+//LJCD2dLSkrS4sWLKxLP9D7//HOlp6ercePGSkpKMjoOAFFKAL8VFxenDRs2yOFwFHl/1apVCg8PV4cOHQxKVrpff/3V6AiFkpKSFB0drUcffVT//ve/lZGRYXQkIOBRSgA/NWTIEJ05c6bYnYjXrFmjhISEwjuAXmzlypUaOHCgrr76aoWHh6tjx4564YUXitwkqV+/fvrv//5vHT58uPA00cV3D3W5XFq6dKm6deumiIgINW3aVOPGjdPRo0eLbKtfv37q3Lmzvv32W8XHx6tBgwZ6+OGHJf12/ceDDz6obdu2qWfPnoqIiNC1116rNWvWFFnH6dOn9fjjj6tbt25q1KiRGjZsqP79++vzzz+v0Njl5+dr/fr1GjJkiOLj41W9evVi2/7drl271KdPH0VEROiaa67Riy++qDfffFM2m00//fRTkXmTk5PVv39/NWrUSA0aNFD//v21e/fuCmUFAkn1S88CwIwaNGig7t27a/Xq1Ro4cKAkae/evUpLS9Pw4cO1f//+Ysv885//VExMjG666SaFhYUpOTlZf//735Wbm6snnnhCkjR58mRlZ2frxIkTeuaZZ4qt46GHHtKKFSs0YsQIjR07VhkZGVq6dKl2796t7du3FykwOTk5SkhIUHx8vIYMGVLkKaR79uzRe++9pzvvvFN/+ctftGLFCo0fP15t27ZVixYtJEnp6enasGGDBg4cqGbNmiknJ0crVqzQwIEDlZycrNatW5dr7D788EOdPn26MNPNN9+spKQkTZo0qch8+/fvV0JCgurWratHHnlEISEhWr58uWrUqFFsnWvWrNH48ePVs2dPTZ8+XU6nUytXrtSAAQP03nvvqVOnTuXKCgQSSgngx4YNG1ZYImw2m1atWqXo6Ghde+21Jc6/ZcuWIh+oY8eO1X333aclS5ZoypQpslqtuvHGG3XllVcqNzdXI0aMKLL87t279frrr2vhwoVFbp0fHx+vXr16aenSpXr00UcL3z958qTmzJmju+++u1iW1NRU7dy5s7CADBo0SNdcc43efPNNPfXUU5J+u3NpSkqKgoKCCpe744471LlzZ73yyit66aWXyjFqv526adOmTeG2hw4dqjvuuEPfffdd4XvSb88vcjqdev/999W4cWNJ0ujRo9WxY8ci6zt79qwmT56sESNGFLkW584771TXrl01a9Ysbdy4sVxZgUDC6RvAjw0cOFAWi0UbNmzQhQsX9O6772rYsGGlzv97ISkoKFB2draysrLUo0cPnT17Vna7/ZLbW79+vWrWrKm4uDhlZWUV/omMjFR0dHSxbwNVr15dd9xxR4nr6tmzZ5ECEB4erpiYGKWnpxe+Z7VaCwvJ70/wdjqd6tixo1JSUi6ZtyTZ2dn64IMPNGTIkML3brnlFtWqVavIBa8FBQX65JNPdOuttxYWEkmqV69esTFOTk5Wdna2hg8fXmRc8vLy1KtXL+3atUvnz58vV14gkHCkBPBjl19+ueLi4pSUlKQGDRro559/LrOU7Nq1S7NmzdK+ffuKPEtF+u1Uy6UcPHhQZ86cUUxMTInT//ik5CuvvLLUbwFFRUUVe89ms+n06dOFr51Op1588UX961//Knb9xlVXXXXJvCX5/eLgTp06FVln9+7dlZSUpMcff1wWi0U///yz8vLyFB0dXWwdf3zv94flDR48uNTt5uTk6IorrihXZiBQUEoAPzds2DCNGTNGktSxY8cSP0Sl367PGDx4sJo1a6bExEQ1atRIVqtVX3/9tWbOnOnWE0GdTqfq1q2rZcuWlTj9j9dahIWFlbqui0/JXOziBxe+8MILmjVrlkaNGqXHH39cdevWVVBQkObPn68ff/zxknlLsmrVKknSgAEDSpy+a9cudevWrcx1/PHhir+P3aJFi0p9gFnt2rU9jQoEHEoJ4Of69u2r2rVra+fOnZozZ06p823ZskXnzp3TO++8U+R0xB+PQEjFj3j8rmnTpkpOTlbHjh1Vq1atioe/hHXr1qlHjx7F7plS3ju3Hj58WLt27dLYsWPVq1evYtPvv/9+JSUlqVu3bqpfv77CwsIKj4JcLC0trcjrpk2bSpKuuOKKEtcLwD1cUwL4OavVqueff15TpkzR0KFDS53v9yMTF/8r3+FwaOnSpcXmrVGjRomncxISEuR0OkssPy6XS1lZWeX5EUoVFBRU7KjE7t279cUXX5RrfUlJSXK5XJo0aZL69+9f7M/NN9+sd999V/n5+QoKClKvXr30/vvv69ChQ4XryMrKKnbTuj59+ujyyy/XvHnzit03RpIyMzPLlRcINBwpAaqAssrI7/r06aOQkBCNHDlSd9xxh/Lz8/XOO++UeD+TDh06aOPGjZoyZYo6deqkatWqaciQIerWrZsmTJighQsX6ttvv9VNN92kGjVq6KefftLmzZv1l7/8RQ8++KDXfq5bb71Vc+bM0YQJE9StWzcdPHhQ//rXv9SyZUudOXPG4/WtXr1aLVu2LDyyUdL23nnnHX3wwQeKj4/XtGnT9PHHH+vWW2/V3/72NwUHB2v58uVq3LixsrOzC48o1apVSy+++KLuuusu9ejRQ8OGDVNERISOHj2qTz/9VJdddlmp90EB8B+UEiBANG/eXCtXrtSsWbM0c+ZM1atXTyNHjlSPHj2KXaA5fvx4paamKikpSUuXLpXL5Sr8tsrcuXMVGxur1157TYmJiapWrZoaNGigPn36qH///l7N/NBDDykvL0+rV6/Whg0b1KpVKy1btkxr167Vjh07PFpXSkqKUlNTyyxNvXv3VkhIiJKSkhQfH6927dpp3bp1mjFjhubOnavw8HCNGzdOoaGh+uabb4pcxDto0CBFRkZq/vz5WrRokfLy8hQREaFOnTrpr3/9a7nHAAgkluzsbNelZwMA/G7KlClavny5jh49WuoFuwA8xzUlAFCGvLy8Iq8zMzO1atUqdevWjUICeBmnbwCgDO3atdPw4cMVExOj48eP64033tDZs2eL3LkWgHdQSgCgDHFxcdq0aZNOnjyp6tWrKzY2VkuXLlXXrl2NjgZUOVxTAgAATIFrSgAAgClQSgAAgClQSgAAgClQSgAAgClQSgAAgClQSgAAgCn8H5qawVWOToTGAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"unit = ''\n",
"\n",
"fig, ax = plt.subplots(figsize=(8,5))\n",
"\n",
"ax.hist(baby['Maternal Age'], density=True, color='blue', alpha=0.8, ec='white', zorder=5)\n",
"\n",
"y_vals = ax.get_yticks()\n",
"\n",
"y_label = 'Percent per ' + (unit if unit else 'unit')\n",
"\n",
"x_label = 'Maternal Age'\n",
"\n",
"ax.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
"\n",
"plt.ylabel(y_label)\n",
"\n",
"plt.xlabel(x_label)\n",
"\n",
"plt.xticks(rotation=90)\n",
"\n",
"plt.title('');\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"27.228279386712096"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.mean(baby['Maternal Age'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What was the average age of the mothers in the population? We don't know the value of this parameter.\n",
"\n",
"Let's estimate the unknown parameter by the bootstrap method. To do this, we will edit the code for `bootstrap_median` to instead define the function `bootstrap_mean`. The code is the same except that the statistics are means instead of medians, and are collected in an array called `means` instead of `medians`"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"def bootstrap_mean(original_sample, label, replications):\n",
" \n",
" \"\"\"Returns an array of bootstrapped sample means:\n",
" original_sample: table containing the original sample\n",
" label: label of column containing the variable\n",
" replications: number of bootstrap samples\n",
" \"\"\"\n",
" \n",
" just_one_column = original_sample[[label]]\n",
" means = np.array([])\n",
" for i in np.arange(replications):\n",
" bootstrap_sample = just_one_column.sample(len(just_one_column), replace=True)\n",
" resampled_mean = np.mean(bootstrap_sample.iloc[:,0])\n",
" means = np.append(means, resampled_mean)\n",
" \n",
" return means\n"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([26.89437819, 27.57410562])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Generate the means from 5000 bootstrap samples\n",
"bstrap_means = bootstrap_mean(baby, 'Maternal Age', 5000)\n",
"\n",
"# Get the endpoints of the 95% confidence interval\n",
"left = np.percentile(bstrap_means, 2.5, interpolation='nearest')\n",
"right = np.percentile(bstrap_means, 97.5, interpolation='nearest')\n",
"\n",
"np.array([left, right])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The 95% confidence interval goes from about 26.9 years to about 27.6 years. That is, we are estimating that the average age of the mothers in the population is somewhere in the interval 26.9 years to 27.6 years. \n",
"\n",
"Notice how close the two ends are to the average of about 27.2 years in the original sample. The sample size is very large – 1,174 mothers – and so the sample averages don't vary much. We will explore this observation further in the next chapter.\n",
"\n",
"The empirical histogram of the 5,000 bootstrapped means is shown below, along with the 95% confidence interval for the population mean."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"resampled_means = pd.DataFrame({'Bootstrap Sample Mean':bstrap_means})\n",
"\n",
"unit = ''\n",
"\n",
"fig, ax = plt.subplots(figsize=(10,5))\n",
"\n",
"ax.hist(resampled_means, bins=15, density=True, color='blue', alpha=0.8, ec='white', zorder=5)\n",
"\n",
"ax.plot(np.array([left, right]), np.array([0,0]), color='yellow', lw=8, zorder=10)\n",
"\n",
"y_vals = ax.get_yticks()\n",
"\n",
"y_label = 'Percent per ' + (unit if unit else 'unit')\n",
"\n",
"x_label = 'Bootstrap Sample Median'\n",
"\n",
"ax.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
"\n",
"plt.ylabel(y_label)\n",
"\n",
"plt.xlabel(x_label)\n",
"\n",
"plt.xticks(rotation=90)\n",
"\n",
"plt.title('');\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Once again, the average of the original sample (27.23 years) is close to the center of the interval. That's not very surprising, because each bootstrapped sample is drawn from that same original sample. The averages of the bootstrapped samples are about symmetrically distributed on either side of the average of the sample from which they were drawn."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice also that the empirical histogram of the resampled means has roughly a symmetric bell shape, even though the histogram of the sampled ages was not symmetric at all:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"unit = ''\n",
"\n",
"fig, ax = plt.subplots(figsize=(8,5))\n",
"\n",
"ax.hist(baby['Maternal Age'], density=True, color='blue', alpha=0.8, ec='white', zorder=5)\n",
"\n",
"y_vals = ax.get_yticks()\n",
"\n",
"y_label = 'Percent per ' + (unit if unit else 'unit')\n",
"\n",
"x_label = 'Maternal Age'\n",
"\n",
"ax.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
"\n",
"plt.ylabel(y_label)\n",
"\n",
"plt.xlabel(x_label)\n",
"\n",
"plt.title('');\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a consequence of the Central Limit Theorem of probability and statistics. In later sections, we will see what the theorem says."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### An 80% Confidence Interval\n",
"You can use the bootstrapped sample means to construct an interval of any level of confidence. For example, to construct an 80% confidence interval for the mean age in the population, you would take the \"middle 80%\" of the resampled means. So you would want 10% of the distribution in each of the two tails, and hence the endpoints would be the 10th and 90th percentiles of the resampled means."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([27.01192504, 27.45059625])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"left_80 = np.percentile(bstrap_means, 10, interpolation='nearest')\n",
"right_80 = np.percentile(bstrap_means, 90, interpolation='nearest')\n",
"np.array([left_80, right_80])"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"unit = ''\n",
"\n",
"fig, ax = plt.subplots(figsize=(10,5))\n",
"\n",
"ax.hist(resampled_means, bins=15, density=True, color='blue', alpha=0.8, ec='white', zorder=5)\n",
"\n",
"ax.plot(np.array([left_80, right_80]), np.array([0,0]), color='yellow', lw=8, zorder=10)\n",
"\n",
"y_vals = ax.get_yticks()\n",
"\n",
"y_label = 'Percent per ' + (unit if unit else 'unit')\n",
"\n",
"x_label = 'Bootstrap Sample Mean'\n",
"\n",
"ax.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
"\n",
"plt.ylabel(y_label)\n",
"\n",
"plt.xlabel(x_label)\n",
"\n",
"plt.xticks(rotation=90)\n",
"\n",
"plt.title('');\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This 80% confidence interval is much shorter than the 95% confidence interval. It only goes from about 27.0 years to about 27.4 years. While that's a tight set of estimates, you know that this process only produces a good interval about 80% of the time. \n",
"\n",
"The earlier process produced a wider interval but we had more confidence in the process that generated it.\n",
"\n",
"To get a narrow confidence interval at a high level of confidence, you'll have to start with a larger sample. We'll see why in the next chapter."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Confidence Interval for a Population Proportion: Bootstrap Percentile Method\n",
"In the sample, 39% of the mothers smoked during pregnancy."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.3909710391822828"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"len(baby[baby['Maternal Smoker'] == True]) / len(baby)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For what follows, it is useful to observe that this proportion can also be calculated by an array operation:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.3909710391822828"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"smoking = baby['Maternal Smoker']\n",
"np.count_nonzero(smoking)/len(smoking)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What percent of mothers in the population smoked during pregnancy? This is an unknown parameter which we can estimate by a bootstrap confidence interval. The steps in the process are analogous to those we took to estimate the population mean and median.\n",
"\n",
"We will start by defining a function `bootstrap_proportion` that returns an array of bootstrapped sampled proportions. Once again, we will achieve this by editing our definition of `bootstrap_median`. The only change in computation is in replacing the median of the resample by the proportion of smokers in it. The code assumes that the column of data consists of Boolean values. The other changes are only to the names of arrays, to help us read and understand our code."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"def bootstrap_proportion(original_sample, label, replications):\n",
" \n",
" \"\"\"Returns an array of bootstrapped sample proportions:\n",
" original_sample: table containing the original sample\n",
" label: label of column containing the Boolean variable\n",
" replications: number of bootstrap samples\n",
" \"\"\"\n",
" \n",
" just_one_column = original_sample[[label]]\n",
" proportions = np.array([])\n",
" for i in np.arange(replications):\n",
" bootstrap_sample = just_one_column.sample(len(just_one_column), replace=True)\n",
" resample_array = bootstrap_sample.iloc[:,0]\n",
" resampled_proportion = np.count_nonzero(resample_array)/len(resample_array)\n",
" proportions = np.append(proportions, resampled_proportion)\n",
" \n",
" return proportions\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us use `bootstrap_proportion` to construct an approximate 95% confidence interval for the percent of smokers among the mothers in the population. The code is analogous to the corresponding code for the mean and median."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.36286201, 0.41993186])"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Generate the proportions from 5000 bootstrap samples\n",
"bstrap_props = bootstrap_proportion(baby, 'Maternal Smoker', 5000)\n",
"\n",
"# Get the endpoints of the 95% confidence interval\n",
"left = np.percentile(bstrap_props, 2.5, interpolation='nearest')\n",
"right = np.percentile(bstrap_props, 97.5, interpolation='nearest')\n",
"\n",
"np.array([left, right])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The confidence interval goes from about 36% to about 42%. The original sample percent of 39% is very close to the center of the interval, as you can see below."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"resampled_proportions = pd.DataFrame({'Bootstrap Sample Proportion':bstrap_props})\n",
"\n",
"unit = ''\n",
"\n",
"fig, ax = plt.subplots(figsize=(10,5))\n",
"\n",
"ax.hist(resampled_proportions, bins=15, density=True, color='blue', alpha=0.8, ec='white', zorder=5)\n",
"\n",
"ax.plot(np.array([left, right]), np.array([0,0]), color='yellow', lw=8, zorder=10)\n",
"\n",
"y_vals = ax.get_yticks()\n",
"\n",
"y_label = 'Percent per ' + (unit if unit else 'unit')\n",
"\n",
"x_label = 'Bootstrap Sample Proportion'\n",
"\n",
"ax.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
"\n",
"plt.ylabel(y_label)\n",
"\n",
"plt.xlabel(x_label)\n",
"\n",
"plt.xticks(rotation=90)\n",
"\n",
"plt.title('');\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Care in Using the Bootstrap\n",
"The bootstrap is an elegant and powerful method. Before using it, it is important to keep some points in mind.\n",
"\n",
"- Start with a large random sample. If you don't, the method might not work. Its success is based on large random samples (and hence also resamples from the sample) resembling the population. The Law of Averages says that this is likely to be true provided the random sample is large.\n",
"\n",
"- To approximate the probability distribution of a statistic, it is a good idea to replicate the resampling procedure as many times as possible. A few thousand replications will result in decent approximations to the distribution of sample median, especially if the distribution of the population has one peak and is not very asymmetric. We used 5,000 replications in our examples but would recommend 10,000 in general.\n",
"\n",
"- The bootstrap percentile method works well for estimating the population median or mean based on a large random sample. However, it has limitations, as do all methods of estimation. For example, it is not expected to do well in the following situations.\n",
" - The goal is to estimate the minimum or maximum value in the population, or a very low or very high percentile, or parameters that are greatly influenced by rare elements of the population.\n",
" - The probability distribution of the statistic is not roughly bell shaped.\n",
" - The original sample is very small, say less than 10 or 15.\n",
"\n"
]
}
],
"metadata": {
"anaconda-cloud": {},
"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": "3.6.12"
}
},
"nbformat": 4,
"nbformat_minor": 1
}