Statistical Evidence: A Likelihood Paradigm

"Richard Royall used to be a professor at Johns Hopkins University, but he retired before I joined. This book was actually given to me when I first arrived, and it revolutionized the way I think about data analysis and statistical thinking. It’s a very small book, quick to read, but I’ve gone through it probably twenty or thirty times. Every time, I get something new out of it. It’s a little technical and on the mathematical side; you do need some statistical background to read it. It talks about the distinction between what the data gives you and what happens when you combine the data with outside things. He explains the different inferential paradigms in statistics, including frequentist and Bayesian, and he presents this middle road that he calls ‘likelihood’. His main point is that there are things that we do that we can trace back to the data, but other inferential tools that we use only depend on our assumptions about the world. We need to separate those two things, establish what the data says, and then decide what we’re going to use it for (like making a decision, enrolling patients in a trial, etc.). Support Five Books Five Books interviews are expensive to produce. If you're enjoying this interview, please support us by donating a small amount . We often make decisions by combining data with outside elements, and we need to be conscious of this. Many tools try to wrap those things together and they make things very confusing. P-values are an example of this in frequentist statistics: they become confusing because they combine results coming from the data with assumptions about the world. Royall’s way of thinking was new to me, and it had a profound effect on how I approached data analysis. A lot of the discussion about data analysis tends to lump things together, but many steps have nothing to do with the data specifically—they’re ‘data-adjacent’, for lack of a better word. The role of the data analyst is important, but the role of the scientist or policy-maker is different, and we need to think of them separately. It assumes that the reader knows statistics up to an introductory course. You don’t have to know calculus, but you should be comfortable with seeing some mathematical symbols."