# Elementary Probability

• ### Probabilistic Risk Assessment Procedures Guide for NASA Managers and Practitioners

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.

• ### Statistics: Basic Concepts 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: Calculators

Our online calculators and converters can help you in many daily tasks that require calculations to complete.

• ### 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.

• ### Log-linear Models for Multidimensional Contingency Tables

This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: partial/conditional tables, confounding, types of independence (mutual, joint, marginal, and conditional), identifiability constraints, partial odds ratios, hierarchical log-linear model, pairwise interaction log-linear model, conditional independence log-linear model, goodness of fit, and model building.

• ### Introduction to Log-linear Models

This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: conditional independence, log-linear models for 2x2 tables, expected counts, logistic regression, odds ratio, parameters of interest for different designs and the MLEs, poisson log-linear model, double dichotomy, the multinomial, and the multinomial log-linear model.

• ### Partitioning Chi Squares and Residual Analysis

This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: Pearson's residuals and rules for partitioning an I x J contingency tables as ways to determine association between variables.

• ### 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,

• ### Summary Measures

This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: uncertainty coefficient, ordinal trends, the gamma statistic and linear association, conditional independence, marginal independence, and Simpson's Paradox.

• ### Song: It Might Not Be That Bad

A song for use in helping students to apply Bayes Theorem and examine marginal and conditional proportions in a table to see how, for rare conditions, most positive test results may be false positives.  Lyrics and music by Tom Toce copyright 2015.  This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smiles for the interactive version of the song, a short reading covering the topic, and an assessment item).