Approximating a normal distribution with a binomial distribution
Approximating a normal distribution with a binomial distribution
This compendium facilitates the creation of good graphs by presenting a set of concrete examples, ranging from the trivial to the advanced. The graphs can all be reproduced and adjusted by copy-pasting code into the R console. Almost every example in this compendium is driven by the same philosophy: A good graph is a simple graph, in the Einsteinian sense that a graph should be made as simple as possible, but not simpler. A note for R fans: the majority of our plots have been created in base R, but you will encounter some examples in ggplot.
This page supports an in-class exercise that highlights several key Bayesian concepts. The scenario is as follows: a large paper bag contains pieces of candy with wrappings of different color, and we are interested in learning about the unknown proportion of yellow-wrapped pieces of candy. After completing the exercises, we will be familiar with the following concepts and ideas: probability distributions can quantify degree of belief, prior distribution, posterior distribution, sequential updating, conjugacy, Cromwell’s Rule (http://en.wikipedia.org/wiki/Cromwell's_rule), the data overwhelm the prior, Bayes factors, Savage-Dickey density ratio, sensitivity analysis, coherence.
Find the best linear fit for a given set of data points and residuals (or let this app show you how it is done).
Adjust regression parameters to bend and shift a two-dimensional polynomial surface.
Check how your Bayes factor conclusion depends on the r-scale parameter.
This Shiny app implements the p-curve (Simonsohn, Nelson, & Simmons, 2014; see http://www.p-curve.com) in its previous ("app2") and the current version ("app3"), the R-Index and the Test of Insufficient Variance, TIVA (Schimmack, 2014; see http://www.r-index.org/), and tests whether p values are reported correctly.
When does a significant p-value indicate a true effect? This app will help with understanding the Positive Predictive Value (PPV) of a p-value.
This app is based on Ioannidis, J. P. A. (2005). Why most published research findings are false. PLoS Medicine, 2(8), e124. http://doi.org/10.1371/journal.pmed.0020124
The app allows you to see the trade-offs on various types of outlier/anomaly detection algorithms. Outliers are marked with a star and cluster centers with an X.
Can you "see" a group mean difference, just by eyeballing the data? Is your gut feeling aligned to the formal index of evidence, the Bayes factor?