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Statistical Inference & Techniques

  • A cartoon suitable for use in teaching about model fitting techniques. The cartoon is number 2048 from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a creative commons attribution-non-commercial 2.5 license.

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  • A cartoon suitable for use in teaching about the idea of a falsifiable hypothesis. The cartoon is number 2078 from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a creative commons attribution-non-commercial 2.5 license.

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  • A song to introduce the basic idea of using simulation to calculate a P-value for a randomization test (by simulating lots of group assignments and seeing what proportion of them give more extreme test statistics than observed with the actual group assignments).  The lyrics were written in November 2018 by Larry Lesser from The University of Texas at El Paso and Dennis Pearl from Penn State University. May be sung to the tune of the 1980 number #1 song “Celebration” by Kool and the Gang.

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  • A Cartoon to illustrate the idea of interaction (cell means) plots for a two factor ANOVA.  The cartoon was created in October 2018 by Larry Lesser from The University of Texas at El Paso.  

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  • A light bulb joke that can be used in discussing how the choice of model might affect the conclusions drawn.  The joke was submitted to AmStat News by Robert Weiss from UCLA and appeared on page 48 of the October, 2018 edition.

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  • A joke that could be used in introducing simulation-based inference.  The joke was written in 2018 by Larry Lesser from The University of Texas at El Paso.

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  • Explore the Hubble Deep Fields from a statistical point of view.  Watch out for the booby traps of bias, the vagueness of variability, and the shiftiness of sample size as we travel on a photo safari through the Hubble Deep Fields (HDFs).

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  • Probabilistic Risk Assessment (PRA) is a comprehensive, structured, and logical analysis method aimed at identifying and assessing risks in complex technological systems for the purpose of cost-effectively improving their safety and performance. NASA’s objective is to better understand and effectively manage risk, and thus more effectively ensure mission and programmatic success, and to achieve and maintain high safety standards at NASA. This PRA Procedures Guide, in the present second edition, is neither a textbook nor an exhaustive sourcebook of PRA methods and techniques. It provides a set of recommended procedures, based on the experience of the authors, that are applicable to different levels and types of PRA that are performed for aerospace applications. 

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  • This NASA-HANDBOOK is published by the National Aeronautics and Space Administration (NASA) to provide a Bayesian foundation for framing probabilistic problems and performing inference on these problems. It is aimed at scientists and engineers and provides an analytical structure for combining data and information from various sources to generate estimates of the parameters of uncertainty distributions used in risk and reliability models. The overall approach taken in this document is to give both a broad perspective on data analysis issues and a narrow focus on the methods required to implement a comprehensive database repository.

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  • Dr. Kuan-Man Xu from the NASA Langley Reserach Center writes, "A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries-Matusita distance and the Kuiper distance. "

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