StatLab Articles

ROC Curves and AUC for Models Used for Binary Classification

This article assumes basic familiarity with the use and interpretation of logistic regression, odds and probabilities, and true/false positives/negatives. The examples are coded in R. ROC curves and AUC have important limitations, and I encourage reading through the section at the end of the article to get a sense of when and why the tools […]

Comparing the accuracy of two binary diagnostic tests in a paired study design

There are many medical tests for detecting the presence of a disease or condition. Some examples include tests for lesions, cancer, pregnancy, or COVID-19. While these tests are usually accurate, they’re not perfect. In addition, some tests are designed to detect the same condition, but use a different method. A recent example are PCR and […]

Correlation of Fixed Effects in lme4

If you have ever used the R package lme4 to perform mixed-effect modeling you may have noticed the “Correlation of Fixed Effects” section at the bottom of the summary output. This article intends to shed some light on what this section means and how you might interpret it. To begin, let’s simulate some data. Below […]

List Comprehensions in Python

List comprehensions are a topic a lot of new Python users struggle with. This article seeks to explain the benefits of list comprehensions and how list comprehensions work in a digestible manner. Single for loop list comprehension The following code uses a traditional for loop to change each string in a for loop from upper […]

Getting Started with the Kruskal-Wallis Test

What is it? One of the most well-known statistical tests to analyze the differences between means of given groups is the ANOVA (analysis of variance) test. While ANOVA is a great tool, it assumes that the data in question follows a normal distribution. What if your data doesn’t follow a normal distribution or if your […]

A Beginner’s Guide to Marginal Effects

What are average marginal effects? (If you’re reading this, chances are you just asked this question.) If we unpack the phrase, it looks like we have effects that are marginal to something, all of which we average. So let’s look at each piece of this phrase and see if we can help you get a […]

The Intuition Behind Confidence Intervals

Say it with me: An X% confidence interval captures the population parameter in X% of repeated samples. In the course of our statistical educations, many of us had that line (or some variant of it) crammed, wedged, stuffed, and shoved into our skulls until definitional precision was leaking out of noses and pooling on our […]

Post Hoc Power Calculations are Not Useful

It is well documented that post hoc power calculations are not useful (Goodman and Berlin 1994, Hoenig and Heisey 2001, Althouse 2020). Also known as observed power or retrospective power, post hoc power purports to estimate the power of a test given an observed effect size. The idea is to show that a “non-significant” hypothesis […]