A song to teach various concepts in probability. Written by Mary Pat Campbell for Mathcamp 2002 at Colorado College. May be sung to the tune of "Take a Chance on Me" by ABBA. Musical accompaniment realization by Joshua Lintz and vocals by Mariana Sandoval from University of Texas at El Paso.
January 26, 2010 webinar presented by Alicia Gram, Smith College, and hosted by Leigh Slauson, Capital University. This webinar describes an activity that uses data collected from an experiment looking at the relationship between two categorical variables: whether a cotton plant was exposed to spider mites; and did the plant contract Wilt disease? The activity uses randomization to explore whether there is a difference between the occurrence of the disease with and without the mites. The webinar includes a discussion of the learning goals of the activity, followed by an implementation of the activity then suggestions for assessment. The implementation first uses a physical simulation, then a simulation using technology. (Extra materials, including Fathom instructions for the simulation, available for download free of charge).
How can we accurately model the unpredictable world around us? How can we reason precisely about randomness? This course will guide you through the most important and enjoyable ideas in probability to help you cultivate a more quantitative worldview.
By the end of this course, you’ll master the fundamentals of probability and random variables, and you’ll apply them to a wide array of problems, from games and sports to economics and science. This course includes 62 interactive quizzes and more than 400 probabilty-based problems with solutions. Access to this course requires users to sign up for a free account.
This general, introductory tutorial on mathematical modeling (in pdf format) is intended to provide an introduction to the correct analysis of data. It addresses, in an elementary way, those ideas that are important to the effort of distinguishing information from error. This distinction constitutes the central theme of the material described herein. Both deterministic modeling (univariate regression) as well as the (stochastic) modeling of random variables are considered, with emphasis on the latter. No attempt is made to cover every topic of relevance. Instead, attention is focussed on elucidating and illustrating core concepts as they apply to empirical data.
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).
Statistics and probability concepts are included in K–12 curriculum standards—particularly the Common Core State Standards—and on state and national exams. STEW provides free peer-reviewed teaching materials in a standard format for K–12 math and science teachers who teach statistics concepts in their classrooms.
STEW lesson plans identify both the statistical concepts being developed and the age range appropriate for their use. The statistical concepts follow the recommendations of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework, Common Core State Standards for Mathematics, and NCTM Principles and Standards for School Mathematics. The lessons are organized around the statistical problemsolving process in the GAISE guidelines: formulate a statistical question, design and implement a plan to collect data, analyze the data by measures and graphs, and interpret the data in the context of the original question. Teachers can navigate the STEW lessons by grade level and statistical topic.
Here one finds a collection of applets and famous problems in probability (as well as other areas of mathematics such as calculus and geometry). Some of the topics/problems include: Bertrand's Paradox, Birthday Coincidence, Buffon's Needle (Noodle), Lewis Carroll's Problem, Monty Hall Dilemma, Parrondo Paradox, and Three pancakes problem.
The BUGS (Bayesian inference Using Gibbs Sampling) project is concerned with flexible software for the Bayesian analysis of complex statistical models using Markov chain Monte Carlo (MCMC) methods. This site is primarily concerned with the stand-alone WinBUGS 1.4.1 package, which has a graphical user interface and on-line monitoring and convergence diagnostics. This program can be downloaded for free from the site.
BrightStat is a free online application for statistical analyses. Besides many non-parametric tests, BrightStat offers multiple linear regression, logistic regression, ANOVA and repeated measurements ANOVA as well as Kaplan Meier Survival analysis. BrightStat has an easy to use GUI and supports the creation of mostly used scientifc graphs such as line-, bar-, scatter- and box-plots as well as histograms.