## Simulation and Bootstrapping for Teaching Statistics

Citations: | 2 - 0 self |

### BibTeX

@MISC{Hesterberg_simulationand,

author = {Tim C. Hesterberg},

title = {Simulation and Bootstrapping for Teaching Statistics},

year = {}

}

### OpenURL

### Abstract

Some key ideas in statistics and probability are hard for students, including sampling distributions. Computer simulation lets students gain experience with and intuition for these concepts. Bootstrapping can reinforce that learning, and provide a way for students (and future practitioners!) to estimate sampling distributions when they have data but do not know the underlying distribution. Bootstrapping also frees us from the requirement to teach inference only for statistics for which simple formulas are available|we can bootstrap robust statistics like the median as easily as the mean. For the promise of simulation and bootstrapping to be realized, they must be available and easy to use in general-purpose statistical software, complete with the exploratory data analysis and inferential capabilities required in teaching and practice. We discuss some of the available software for simulation and bootstrapping, in particular software built on S-Plus. Key words: bootstrap, resampling, simulation,

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Citation Context ...limit theorem [19, 42, 22, 16, 8] sampling with and without replacement [41] confidence intervals and hypothesis tests [16, 41], ANOVA and regression [16], Bayesian methods [38, 2], and the bootstrap =-=[39, 34, 46, 44, 14]-=-. The basic idea in simulation is to emulate real life, where one collects a sample of random data (using a survey or an experiment), and summarizes the data graphically or numerically. In simulation ... |

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Citation Context ...nd will accelerate as young faculty who have been exposed to the bootstrap in their studies begin teaching (many of the books on the bootstrap and other resampling methods are quite recent, including =-=[11, 14, 15, 18, 21, 31, 40, 26, 25, 33, 35, 43]-=-). 2.2 Other resampling methods Many of the statistical and pedagogical advantages of the bootstrap hold for some other resampling methods, notably permutation tests. They also use simulation (or exac... |

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Citation Context ...nd will accelerate as young faculty who have been exposed to the bootstrap in their studies begin teaching (many of the books on the bootstrap and other resampling methods are quite recent, including =-=[11, 14, 15, 18, 21, 31, 40, 26, 25, 33, 35, 43]-=-). 2.2 Other resampling methods Many of the statistical and pedagogical advantages of the bootstrap hold for some other resampling methods, notably permutation tests. They also use simulation (or exac... |

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Citation Context ...nd will accelerate as young faculty who have been exposed to the bootstrap in their studies begin teaching (many of the books on the bootstrap and other resampling methods are quite recent, including =-=[11, 14, 15, 18, 21, 31, 40, 26, 25, 33, 35, 43]-=-). 2.2 Other resampling methods Many of the statistical and pedagogical advantages of the bootstrap hold for some other resampling methods, notably permutation tests. They also use simulation (or exac... |

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Citation Context ...e numbers, and the central limit theorem [19, 42, 22, 16, 8] sampling with and without replacement [41] confidence intervals and hypothesis tests [16, 41], ANOVA and regression [16], Bayesian methods =-=[38, 2]-=-, and the bootstrap [39, 34, 46, 44, 14]. The basic idea in simulation is to emulate real life, where one collects a sample of random data (using a survey or an experiment), and summarizes the data gr... |

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Citation Context ...work, particularly with missing data. 3.4 Resampling software Resampling Stats is a special purpose simulation and resampling program. that has been heavily promoted for teaching statistics using SAB =-=[8, 37, 35, 34]. It -=-is inadequate for teaching statistics. Its capabilities are extremely limited; it does not even do scatterplots, for instance. I believe Hinkley was thinking of this program when he wrote "We are... |

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Citation Context ...s plot is more effective in color.) The overwhelming sentiment in the literature is that simulation and bootstrapping (SAB) are valuable in teaching introductory students. Some controlled experiments =-=[36]-=- support this. Yet SAB have not yet realized their potential, particularly the bootstrap. Some reasons for this will become less important over time; for example, computers are becoming cheaper, more ... |

5 |
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Citation Context ... there are many newer articles. Writers have used simulation in a variety of ways, including simulations of random walks to help students understand the role of randomness in runs, streaks and slumps =-=[39, 42, 8]-=-, other probability problems [41, 8], sampling distributions, the law of large numbers, and the central limit theorem [19, 42, 22, 16, 8] sampling with and without replacement [41] confidence interval... |

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(Show Context)
Citation Context ...ctice and teaching of statistics : : : Good new ideas like the bootstrap, however, often infiltrate the curriculum very slowly. One reason for this delay can be the lack of software. Numerous authors =-=[24, 29, 7, 1, 47, 4, 6, 32, 17, 23, 10, 27, 28]-=- discuss software. They note that programs are ffl too hard to use, ffl too limited in their capabilities, ffl not flexible, ffl not suitable for use by students after graduation, ffl too expensive, o... |

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Citation Context ...stimating standard errors and obtaining rough con dence intervals, and are best for initial pedagogical purposes. However, more accurate procedures are available, such as the BC-a con dence intervals =-=[12]-=-. These are more complicated to program. Similarly, somevariance reduction procedures can dramatically improve the simulation accuracy of the bootstrap, for a given number of replications, but are mor... |

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Citation Context ...ctice and teaching of statistics : : : Good new ideas like the bootstrap, however, often infiltrate the curriculum very slowly. One reason for this delay can be the lack of software. Numerous authors =-=[24, 29, 7, 1, 47, 4, 6, 32, 17, 23, 10, 27, 28]-=- discuss software. They note that programs are ffl too hard to use, ffl too limited in their capabilities, ffl not flexible, ffl not suitable for use by students after graduation, ffl too expensive, o... |

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Citation Context ...ctice and teaching of statistics : : : Good new ideas like the bootstrap, however, often infiltrate the curriculum very slowly. One reason for this delay can be the lack of software. Numerous authors =-=[24, 29, 7, 1, 47, 4, 6, 32, 17, 23, 10, 27, 28]-=- discuss software. They note that programs are ffl too hard to use, ffl too limited in their capabilities, ffl not flexible, ffl not suitable for use by students after graduation, ffl too expensive, o... |

3 |
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2 |
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(Show Context)
Citation Context ...ica, and Systat, or an interactive high-level language such as S-Plus, Lisp-Stat, R, Matlab, and Mathematica. For SAB, the languages win, in particular S-Plus. Efron, inventor of the bootstrap, noted =-=[13]-=- that my bootstrapping has increased considerably with the switch to S, a modern interactive computing language. : : : My guess is that the bootstrap (and other computer-intensive methods) will really... |

2 |
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Citation Context ...students understand the role of randomness in runs, streaks and slumps [39, 42, 8], other probability problems [41, 8], sampling distributions, the law of large numbers, and the central limit theorem =-=[19, 42, 22, 16, 8]-=- sampling with and without replacement [41] confidence intervals and hypothesis tests [16, 41], ANOVA and regression [16], Bayesian methods [38, 2], and the bootstrap [39, 34, 46, 44, 14]. The basic i... |

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Citation Context ...ensive methods) will really come into its own only as more statisticians are freed from the constraints of batch-mentality processing systems like SAS. (S-Plus is built on the underlying S language). =-=[30]-=- adds The S language may continue to provide the simplest bootstrap programming in the future. Disadvantages of packages for SAB include: ffl lack of programming capabilities, in particularly looping ... |

2 |
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Citation Context ...and the Central Limit Theorem come alive before one's eyes through computer graphics. Direct experience and actual experimentation is the best way the student can obtain a feeling for these concepts. =-=[42]-=- Figure 1 shows a typical demonstration of the Central Limit Theorem. Normal probability plots can be included to provide better visual indications of departures from normality. The value of this demo... |

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Citation Context ...limit theorem [19, 42, 22, 16, 8] sampling with and without replacement [41] confidence intervals and hypothesis tests [16, 41], ANOVA and regression [16], Bayesian methods [38, 2], and the bootstrap =-=[39, 34, 46, 44, 14]-=-. The basic idea in simulation is to emulate real life, where one collects a sample of random data (using a survey or an experiment), and summarizes the data graphically or numerically. In simulation ... |

2 |
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(Show Context)
Citation Context ...istica, and Systat,oraninteractive high-level language such as S-Plus, Lisp-Stat, R, Matlab, and Mathematica. For SAB, the languages win, in particular S-Plus. Efron, inventor of the bootstrap, noted =-=[13]-=- that my bootstrapping has increased considerably with the switch to S, a modern interactive computing language. ::: My guess is that the bootstrap (and other computer-intensive methods) will really c... |

2 |
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(Show Context)
Citation Context ...ensive methods) will really come into its own only as more statisticians are freed from the constraints of batch-mentality processing systems like SAS. (S-Plus is built on the underlying S language). =-=[30]-=- adds The S language may continue to provide the simplest bootstrap programming in the future. Disadvantages of packages for SAB include: lack of programming capabilities, in particularly looping and ... |

1 |
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(Show Context)
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1 |
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Citation Context ... routines are not provided. 3.2 S-Plus S-Plus is a flexible data analysis environment built on the S language originally developed at Bell Labs [9]. The design of S-Plus is well-suited for education; =-=[3]-=- notes that it has several advantages over computer packages (such as SPSS, BMDP, and SAS) for use in statistics classes. S creates an environment in which the student can exercise creativity. : : : F... |

1 |
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Citation Context ...parameters the joint distribution of parameters can be viewed in using statistical graphical methods for viewing high-dimensional data, including brushing, rotating scatterplots, and Trellis graphics =-=[5]-=-. 3 Software A major cause for the delay in using SAB in teaching involves software. An apt summary of the situation is provided by [44]: Efron's (1982) bootstrap is an effective statistical tool that... |

1 |
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Citation Context ... there are many newer articles. Writers have used simulation in a variety of ways, including simulations of random walks to help students understand the role of randomness in runs, streaks and slumps =-=[39, 42, 8]-=-, other probability problems [41, 8], sampling distributions, the law of large numbers, and the central limit theorem [19, 42, 22, 16, 8] sampling with and without replacement [41] confidence interval... |

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Citation Context ...students understand the role of randomness in runs, streaks and slumps [39, 42, 8], other probability problems [41, 8], sampling distributions, the law of large numbers, and the central limit theorem =-=[19, 42, 22, 16, 8]-=- sampling with and without replacement [41] confidence intervals and hypothesis tests [16, 41], ANOVA and regression [16], Bayesian methods [38, 2], and the bootstrap [39, 34, 46, 44, 14]. The basic i... |

1 |
discussion of "Bootstrap: More than a stab in the dark
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(Show Context)
Citation Context ...eve Hinkley was thinking of this program when he wrote "We are also beginning to see the first wave of software products which claim to do bootstrap analysis: some of these are embarrassingly nai=-=ve." [20]-=-. [7] give a critical discussion of this program and the claims made for its value. LogXact and StatXact do permutation tests. I have not used them. 3.5 Spreadsheets Spreadsheets can be used for simul... |

1 |
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Citation Context ...students understand the role of randomness in runs, streaks and slumps [39, 42, 8], other probability problems [41, 8], sampling distributions, the law of large numbers, and the central limit theorem =-=[19, 42, 22, 16, 8]-=- sampling with and without replacement [41] confidence intervals and hypothesis tests [16, 41], ANOVA and regression [16], Bayesian methods [38, 2], and the bootstrap [39, 34, 46, 44, 14]. The basic i... |

1 |
PC-based simulation of statistical power with business law applications
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(Show Context)
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1 |
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(Show Context)
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(Show Context)
Citation Context ...re it is useful. In Section 3 we discuss software. 2 Applications of Simulation and Bootstrapping The idea of using simulation methods in teaching has engendered considerable interest over the years; =-=[29]-=- collected 175 references on the topic, and there are many newer articles. Writers have used simulation in a variety of ways, including simulations of random walks to help students understand the role... |

1 |
Statistical education via simulation
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(Show Context)
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1 |
Resampling and the ability to do statistics
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(Show Context)
Citation Context ...limit theorem [19, 42, 22, 16, 8] sampling with and without replacement [41] confidence intervals and hypothesis tests [16, 41], ANOVA and regression [16], Bayesian methods [38, 2], and the bootstrap =-=[39, 34, 46, 44, 14]-=-. The basic idea in simulation is to emulate real life, where one collects a sample of random data (using a survey or an experiment), and summarizes the data graphically or numerically. In simulation ... |

1 |
Computer simulations to motivate understanding
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(Show Context)
Citation Context ...have used simulation in a variety of ways, including simulations of random walks to help students understand the role of randomness in runs, streaks and slumps [39, 42, 8], other probability problems =-=[41, 8]-=-, sampling distributions, the law of large numbers, and the central limit theorem [19, 42, 22, 16, 8] sampling with and without replacement [41] confidence intervals and hypothesis tests [16, 41], ANO... |

1 |
Providing a statistical "model": Teaching applied statistics using real-world data
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(Show Context)
Citation Context ...ion There is an enormous opportunity to improve statistics teaching in the United States. Statistical methods are required by many disciplines, and dissatisfaction with current courses is widespread; =-=[45]-=- summarizes: Service courses in applied statistics abound in college and graduate school curricula around the world : : : The clear consensus, among students and professors alike, is that too many of ... |

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More foolproof teaching using resampling
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(Show Context)
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1 |
Review of \Resampling Stats (Version 3.14
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(Show Context)
Citation Context ...practice and teaching of statistics ::: Good new ideas like the bootstrap, however, often in ltrate the curriculum very slowly. One reason for this delay can be the lack of software. Numerous authors =-=[24, 29,7,1,47,4,6,32,17,23, 10, 27, 28]-=- discuss software. They note that programs are too hard to use, too limited in their capabilities, not exible, not suitable for use by students after graduation, too expensive, or not widely available... |