StatLab Articles

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 […]

Power and Sample Size Analysis using Simulation

The power of a test is the probability of correctly rejecting a null hypothesis. For example, let’s say we suspect a coin is not fair and lands heads 65% of the time. The null hypothesis is the coin is not biased to land heads. The alternative hypothesis is the coin is biased to land heads. […]

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 […]

Understanding Ordered Factors in a Linear Model

Consider the following data from the text Design and Analysis of Experiments, 7 ed (Montgomery, Table 3.1). It has two variables: power and rate. Power is a discrete setting on a tool used to etch circuits into a silicon wafer. There are four levels to choose from. Rate is the distance etched measured in Angstroms […]