{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "remove-input" ] }, "outputs": [], "source": [ "from datascience import *\n", "%matplotlib inline\n", "path_data = 'https://raw.githubusercontent.com/ChemeketaCS/datasci-textbook/main/assets/data/'\n", "import matplotlib.pyplot as plots\n", "plots.style.use('fivethirtyeight')\n", "import numpy as np" ] }, { "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 2019 are in the table `sf2019`." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "sf2019 = Table.read_table(path_data + 'san_francisco_2019.csv')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
Organization Group | Department | Job Family | Job | Salary | Overtime | Benefits | Total Compensation | \n", "
---|---|---|---|---|---|---|---|
Public Protection | Adult Probation | Information Systems | IS Trainer-Journey | 91332 | 0 | 40059 | 131391 | \n", "
Public Protection | Adult Probation | Information Systems | IS Engineer-Assistant | 123241 | 0 | 49279 | 172520 | \n", "
Public Protection | Adult Probation | Information Systems | IS Business Analyst-Senior | 115715 | 0 | 46752 | 162468 | \n", "
... (44522 rows omitted)
" ], "text/plain": [ "Organization Group | Department | Job Family | Job | Salary | Overtime | Benefits | Total Compensation | \n", "
---|---|---|---|---|---|---|---|
General Administration & Finance | Mayor | Administrative & Mgmt (Unrep) | Mayor | 342974 | 0 | 98012 | 440987 | \n", "
Organization Group | Department | Job Family | Job | Salary | Overtime | Benefits | Total Compensation | \n", "
---|---|---|---|---|---|---|---|
Public Protection | Adult Probation | Probation & Parole | Deputy Probation Officer | 0 | 0 | 0 | 0 | \n", "
Public Protection | Fire Department | Clerical, Secretarial & Steno | Senior Clerk Typist | 0 | 0 | 0 | 0 | \n", "
Public Protection | Juvenile Court | Correction & Detention | Counselor, Juvenile Hall PERS | 0 | 0 | 0 | 0 | \n", "
Public Protection | Police | Clerical, Secretarial & Steno | Clerk Typist | 0 | 0 | 0 | 0 | \n", "
Public Protection | Sheriff | Correction & Detention | Deputy Sheriff | 0 | 0 | 0 | 0 | \n", "
Public Works, Transportation & Commerce | Airport Commission | Sub-Professional Engineering | StdntDsgn Train2/Arch/Eng/Plng | 0 | 0 | 0 | 0 | \n", "
Public Works, Transportation & Commerce | Airport Commission | Clerical, Secretarial & Steno | Executive Secretary 1 | 0 | 0 | 0 | 0 | \n", "
Public Works, Transportation & Commerce | Airport Commission | Payroll, Billing & Accounting | Senior Account Clerk | 0 | 0 | 0 | 0 | \n", "
Public Works, Transportation & Commerce | Airport Commission | Housekeeping & Laundry | Custodian | 0 | 0 | 0 | 0 | \n", "
Public Works, Transportation & Commerce | Airport Commission | Housekeeping & Laundry | Custodian | 0 | 0 | 0 | 0 | \n", "
... (44515 rows omitted)
" ], "text/plain": [ "Organization Group | Department | Job Family | Job | Salary | Overtime | Benefits | Total Compensation\n", "Public Protection | Adult Probation | Probation & Parole | Deputy Probation Officer | 0 | 0 | 0 | 0\n", "Public Protection | Fire Department | Clerical, Secretarial & Steno | Senior Clerk Typist | 0 | 0 | 0 | 0\n", "Public Protection | Juvenile Court | Correction & Detention | Counselor, Juvenile Hall PERS | 0 | 0 | 0 | 0\n", "Public Protection | Police | Clerical, Secretarial & Steno | Clerk Typist | 0 | 0 | 0 | 0\n", "Public Protection | Sheriff | Correction & Detention | Deputy Sheriff | 0 | 0 | 0 | 0\n", "Public Works, Transportation & Commerce | Airport Commission | Sub-Professional Engineering | StdntDsgn Train2/Arch/Eng/Plng | 0 | 0 | 0 | 0\n", "Public Works, Transportation & Commerce | Airport Commission | Clerical, Secretarial & Steno | Executive Secretary 1 | 0 | 0 | 0 | 0\n", "Public Works, Transportation & Commerce | Airport Commission | Payroll, Billing & Accounting | Senior Account Clerk | 0 | 0 | 0 | 0\n", "Public Works, Transportation & Commerce | Airport Commission | Housekeeping & Laundry | Custodian | 0 | 0 | 0 | 0\n", "Public Works, Transportation & Commerce | Airport Commission | Housekeeping & Laundry | Custodian | 0 | 0 | 0 | 0\n", "... (44515 rows omitted)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sf2019.sort('Total Compensation')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For clarity of interpretation, we will focus our attention on those who had roughly the equivalent of a half-time job or more for the whole year. At a minimum wage of about 15 dollars per hour, and 20 hours per week for 52 weeks, that's a salary of over 15,000 dollars." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "sf2019 = sf2019.where('Salary', are.above(15000))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "37103" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sf2019.num_rows" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Population and Parameter\n", "Let this table of just over 37,000 rows be our population. Here is a histogram of the total compensations for the employees in this table." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Organization Group | Department | Job Family | Job | Salary | Overtime | Benefits | Total Compensation | \n", "
---|---|---|---|---|---|---|---|
General Administration & Finance | Retirement Services | Administrative & Mgmt (Unrep) | Chief Investment Officer | 577633 | 0 | 146398 | 724031 | \n", "
General Administration & Finance | Retirement Services | Unassigned | Managing Director | 483072 | 0 | 134879 | 617951 | \n", "
... (37101 rows omitted)
" ], "text/plain": [ "Left | Right | \n", "
---|---|
125093 | 139379 | \n", "
129925 | 140757 | \n", "
133955 | 146369 | \n", "
129335 | 140847 | \n", "
132756 | 145429 | \n", "
130167 | 143200 | \n", "
125935 | 138491 | \n", "
131092 | 142472 | \n", "
128509 | 140462 | \n", "
131270 | 145998 | \n", "
... (90 rows omitted)
" ], "text/plain": [ "Left | Right\n", "125093 | 139379\n", "129925 | 140757\n", "133955 | 146369\n", "129335 | 140847\n", "132756 | 145429\n", "130167 | 143200\n", "125935 | 138491\n", "131092 | 142472\n", "128509 | 140462\n", "131270 | 145998\n", "... (90 rows omitted)" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "intervals" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The good intervals are those that contain the parameter we are trying to estimate. Typically the parameter is unknown, but in this section we happen to know what the parameter is." ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "135747.0" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pop_median" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How many of the 100 intervals contain the population median? That's the number of intervals where the left end is below the population median and the right end is above." ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "93" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "intervals.where(\n", " 'Left', are.below(pop_median)).where(\n", " 'Right', are.above(pop_median)).num_rows" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It takes many minutes to construct all the intervals, but try it again if you have the patience. Most likely, about 95 of the 100 intervals will be good ones: they will contain the parameter.\n", "\n", "It's hard to show you all the intervals on the horizontal axis as they have large overlaps – after all, they are all trying to estimate the same parameter. The graphic below shows each interval on the same axes by stacking them vertically. The vertical axis is simply the number of the replication from which the interval was generated.\n", "\n", "The green line is where the parameter is. It has a fixed position since the parameter is fixed.\n", "\n", "Good intervals cover the parameter. There are approximately 95 of these, typically. \n", "\n", "If an interval doesn't cover the parameter, it's a dud. The duds are the ones where you can see \"daylight\" around the green line. There are very few of them – about 5 out of 100, typically – but they do happen. \n", "\n", "Any method based on sampling has the possibility of being off. The beauty of methods based on random sampling is that we can quantify how often they are likely to be off." ] }, { "cell_type": "code", "execution_count": 122, "metadata": { "tags": [ "remove-input" ] }, "outputs": [ { "data": { "image/png": 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\n", 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