The significance test is perhaps the most used statistical procedure in the world, though has never been without its detractors. This is the second of two posts exploring Neyman's frequentist arguments against the significance test; if you have not read Part 1, you should do so before continuing (“The frequentist case against the significance test, part 1”).Neyman offered two major arguments against the significance test:The significance test fails as an…
It is unfortunate that today, we tend to think about statistical theory in terms of Bayesianism vs frequentism. Modern practice is a blend of Fisher's and Neyman's ideas, with the characteristics of the blend driven by convenience rather than principle. Significance tests are lumped in as a “frequentist” technique by Bayesians in an unfortunate rhetorical shorthand.In recent years, the significance test has been critiqued on several grounds, but often these…
My colleagues Eric-Jan Wagenmakers and Jeff Rouder and I have a new manuscript in which we respond to Hoijtink, van Kooten, and Hulsker's in press manuscript Why Bayesian Psychologists Should Change the Way they Use the Bayes Factor. They sug...
A common problem in statistics is determining whether or not the means of 2 populations are equal. The independent 2-sample t-test is a popular parametric method to answer this question. (In an earlier Statistics Lesson of the Day, I discussed how data collected from a completely randomized design with 1 binary factor can be analyzed […]
In the previous post, I introduced the logic of Bayes factors for one-sample designs by means of a simple example. In this post, I will give more detail about the models and assumptions used by the BayesFactor package, and also how to do simple analyses of two- sample designs.See the previous posts for background:What is a Bayes factor?Bayes factor t tests, part 1This article will cover two-sample t tests.Bayesian t…
In my first post, I described the general logic of Bayes factors. I will continue discussing the general logic of Bayes factor, while introducing some of the basic functionality of the BayesFactor package.Recap: What is a Bayes factor?The Bayes factor is the relative evidence provided by the data for comparing two statistical models. It has two equivalent definitions:The Bayes factor is the relative predictive success between two hypotheses: it is…
The simplest experimental design is the completely randomized design with 1 factor. In this design, each experimental unit is randomly assigned to each factor level. This design is most useful for a homogeneous population (one that does not have major differences between any sub-populations). It is appealing because of its simplicity and flexibility – it can […]
I learned about Lord Rayleigh’s discovery of argon in my 2nd-year analytical chemistry class while reading “Quantitative Chemical Analysis” by Daniel Harris. (William Ramsay was also responsible for this discovery.) This is one of my favourite stories in chemistry; it illustrates how diligence in measurement can lead to an elegant and surprising discovery. I find […]
