# Significance Testing Principles

• ### Song: Simulation!

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. Audio of the parody was produced and sung by students in the commercial music program of The University of Teas at El Paso.

• ### Joke: Another Light Bulb

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.

• ### Using the Bootstrap Method for a Statistical Significance Test of Differences Between Summary Histograms

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. "

• ### Statistics: Model Hypothesis Testing for Astronomers

This presentation was given by Aneta Siemiginowska at the 4th International X-ray Astronomy School (2005), held at the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA.

• ### Collection: Statistical Calculators

Free statistical calculators online.  Our basic statistical calculators will help you in common tasks you might encounter and deal mostly with simple distributions.

• ### Maintaining Bone Mineral Density (NASA Activity)

One health concern that arises when shifting from an environment with gravity to microgravity is the loss of bone mass density. This Math and Science @ Work advanced statistics activity has students analyze two different exercise countermeasures and construct null and alternative hypotheses to determine their relative effectiveness in maintaining bone mineral density.

NASA's Math and Science @ Work project provides challenging supplemental problems for students in advanced science, technology, engineering and mathematics, or STEM classes including Physics, Calculus, Biology, Chemistry and Statistics, along with problems for advanced courses in U.S. History and Human Geography.

• ### Display Design: A Human Factor of Spaceflight (NASA Activity)

NASA's Math and Science @ Work presents a free-response-styled question for advanced high school statistics. Students will evaluate the data from an experiment about astronaut response time. They then will perform hypothesis tests to see if a difference in response times indicates whether one control panel display is preferable to another.

NASA's Math and Science @ Work project provides challenging supplemental problems for students in advanced science, technology, engineering and mathematics, or STEM classes including Physics, Calculus, Biology, Chemistry and Statistics, along with problems for advanced courses in U.S. History and Human Geography.

• ### Generalized Linear Model Estimation and Logistic Regression

This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: iterative solutions to non-linear equations, score equations for exponential class variables, Newton-Raphson vs. Fisher’s Scoring, Logistic Regression for an R × 2 tables, saturated model, odds ratios when rows are not ordinal, goodness of fit, likelihood ratio statistic for nested models, and residuals.

• ### Ordinal Associations of I × J Contingency Tables

This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: linear association, correlation coefficient, ridits/modified ridits, nonparametric methods, Cochran-Armitage Trend test,

• ### Inference for Multinomial Parameters

This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: multinomial distribution, LaGrange multipliers, Exact Multinomial Test (EMT), the Pearson statistic, and goodness of fit.