{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "remove_input" ] }, "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": [ "### The Bootstrap ###\n", "A data scientist is using the data in a random sample to estimate an unknown parameter. She uses the sample to calculate the value of a statistic that she will use as her estimate. \n", "\n", "Once she has calculated the observed value of her statistic, she could just present it as her estimate and go on her merry way. But she's a data scientist. She knows that her random sample is just one of numerous possible random samples, and thus her estimate is just one of numerous plausible estimates. \n", "\n", "By how much could those estimates vary? To answer this, it appears as though she needs to draw another sample from the population, and compute a new estimate based on the new sample. But she doesn't have the resources to go back to the population and draw another sample.\n", "\n", "It looks as though the data scientist is stuck.\n", "\n", "Fortunately, a brilliant idea called *the bootstrap* can help her out. Since it is not feasible to generate new samples from the population, the bootstrap generates new random samples by a method called *resampling*: the new samples are drawn at random *from the original sample*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section, we will see how and why the bootstrap works. In the rest of the chapter, we will use the bootstrap for inference.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Employee Compensation in the City of San Francisco ###\n", "[SF OpenData](https://data.sfgov.org) is a website where the City and County of San Francisco make some of their data publicly available. One of the data sets contains compensation data for employees of the City. These include medical professionals at City-run hospitals, police officers, fire fighters, transportation workers, elected officials, and all other employees of the City. \n", "\n", "Compensation data for the calendar year 2015 are in the table `sf2015`." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "sf2015 = pd.read_csv(path_data + 'san_francisco_2015.csv')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | \n", "Calendar | \n", "2015 | \n", "2 | \n", "Public Works, Transportation & Commerce | \n", "WTR | \n", "PUC Water Department | \n", "21.0 | \n", "Prof & Tech Engineers - Miscellaneous, Local 21 | \n", "2400 | \n", "Lab, Pharmacy & Med Techs | \n", "... | \n", "21538 | \n", "82146.04 | \n", "0.00 | \n", "0.00 | \n", "82146.04 | \n", "16942.21 | \n", "12340.88 | \n", "6337.73 | \n", "35620.82 | \n", "117766.86 | \n", "
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---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
33383 | \n", "Calendar | \n", "2015 | \n", "4 | \n", "Community Health | \n", "DPH | \n", "Public Health | \n", "535.0 | \n", "SEIU - Human Services, Local 1021 | \n", "2900 | \n", "Human Services | \n", "... | \n", "40421 | \n", "57057.01 | \n", "0.00 | \n", "1729.89 | \n", "58786.90 | \n", "11746.85 | \n", "9178.06 | \n", "4903.86 | \n", "25828.77 | \n", "84615.67 | \n", "
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30419 | \n", "Calendar | \n", "2015 | \n", "5 | \n", "Culture & Recreation | \n", "LIB | \n", "Public Library | \n", "790.0 | \n", "SEIU - Miscellaneous, Local 1021 | \n", "3600 | \n", "Library | \n", "... | \n", "24606 | \n", "84599.01 | \n", "0.00 | \n", "2847.82 | \n", "87446.83 | \n", "18021.03 | \n", "12424.50 | \n", "7104.73 | \n", "37550.26 | \n", "124997.09 | \n", "
26544 | \n", "Calendar | \n", "2015 | \n", "2 | \n", "Public Works, Transportation & Commerce | \n", "HHP | \n", "PUC Hetch Hetchy | \n", "130.0 | \n", "Automotive Machinists, Local 1414 | \n", "7300 | \n", "Journeyman Trade | \n", "... | \n", "13291 | \n", "82350.50 | \n", "2270.19 | \n", "8014.64 | \n", "92635.33 | \n", "12874.06 | \n", "11707.71 | \n", "6648.82 | \n", "31230.59 | \n", "123865.92 | \n", "
34880 | \n", "Calendar | \n", "2015 | \n", "2 | \n", "Public Works, Transportation & Commerce | \n", "MTA | \n", "Municipal Transportation Agency | \n", "39.0 | \n", "Stationary Engineers, Local 39 | \n", "7300 | \n", "Journeyman Trade | \n", "... | \n", "44202 | \n", "31515.30 | \n", "5991.38 | \n", "7851.21 | \n", "45357.89 | \n", "7681.06 | \n", "4635.30 | \n", "3603.83 | \n", "15920.19 | \n", "61278.08 | \n", "
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... | \n", "... | \n", "
42983 | \n", "61349.71 | \n", "
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42988 | \n", "55812.90 | \n", "
36569 rows × 1 columns
\n", "\n", " | Left | \n", "Right | \n", "
---|---|---|
0 | \n", "105058.200375 | \n", "116182.540 | \n", "
1 | \n", "100979.960875 | \n", "113625.510 | \n", "
2 | \n", "111035.515375 | \n", "120036.350 | \n", "
3 | \n", "99386.440000 | \n", "114225.030 | \n", "
4 | \n", "105193.600000 | \n", "114084.070 | \n", "
... | \n", "... | \n", "... | \n", "
95 | \n", "103185.999875 | \n", "112283.220 | \n", "
96 | \n", "105153.655000 | \n", "116289.460 | \n", "
97 | \n", "105750.350000 | \n", "116475.370 | \n", "
98 | \n", "100902.910000 | \n", "114809.415 | \n", "
99 | \n", "98734.180000 | \n", "110230.570 | \n", "
100 rows × 2 columns
\n", "