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. […]

# StatLab Articles

## 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 […]

## Ask Better Code Questions (and Get Better Answers) With Reprex

Note: This article was written about version 2.0.0 of the reprex package. In the forums and Q&A sections of websites like Stack Overflow, GitHub, and community.rstudio.com, there is a volunteer force of data science detectives, code consultants, and error-fighting emissaries ready to offer assistance to programmers who find themselves staring down unhappy code that’s resisting […]

## Getting Started with Generalized Estimating Equations

Generalized Estimating Equations, or GEE, is a method for modeling longitudinal or clustered data. It is usually used with non-normal data such as binary or count data. The name refers to a set of equations that are solved to obtain parameter estimates (ie, model coefficients). If interested, see Agresti (2002) for the computational details. In […]

## Getting Started with Binomial Generalized Linear Mixed Models

Binomial Generalized Linear Mixed Models, or binomial GLMMs, are useful for modeling binary outcomes for repeated or clustered measures. For example, let’s say we design a study that tracks what college students eat over the course of 2 weeks, and we’re interested in whether or not they eat vegetables each day. For each student we’ll […]

## Getting Started with Web Scraping in Python

“Web scraping” or “data scraping” is simply the process of extracting data from a website. This can, of course, be done manually: you could go to a website, find the relevant data or information, and enter that information into some data file that you have stored locally. But imagine that you want to pull a […]

## A Brief on Brier Scores

Not all predictions are created equal, even if, in categorical terms, the predictions suggest the same outcome: “X will (or won’t) happen.” Say that I estimate that there’s a 60% chance that 100 million COVID-19 vaccines will be administered in the US during the first 100 days of Biden’s presidency, but my friend estimates that […]

## Getting Started with pandas in Python

The pandas package is an open-source software library written for data analysis in Python. Pandas allows users to import data from various file formats (comma-separated values, JSON, SQL, fits, etc.) and perform data manipulation operations, including cleaning and reshaping the data, summarizing observations, grouping data, and merging multiple datasets. In this article, we’ll explore briefly […]

## Understanding Multiple Comparisons and Simultaneous Inference

When it comes to confidence intervals and hypothesis testing there are two important limitations to keep in mind. The significance level1, \(\alpha\), or the confidence interval coverage, \(1 – \alpha\), only apply to one test or estimate, not to a series of tests or estimates. are only appropriate if the estimate or test was not […]