StatLab Articles

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 antigen tests for COVID-19. In these cases we might want to compare the two tests on the same subjects. This is known as a paired study design.

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.

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 sample size is too small to determine a normal distribution? That’s where the Kruskal-Wallis test comes in.

What are average marginal effects? 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 better handle on this topic.

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 upper lips like prop blood.

Or, at least, I felt that way.

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.

It is well documented that post hoc power calculations are not useful (Althouse, 2020; Goodman & Berlin, 1994; Hoenig & Heisey, 2001). 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 test failed to achieve significance because it wasn’t powerful enough. This allows researchers to entertain the notion that their hypothesized effect may actually exist; they just needed to use a bigger sample size.

Consider the following data from the text Design and Analysis of Experiments, 7th ed. (Montgomery, 2009, 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 per minute. (An Angstrom is one ten-billionth of a meter.) Of interest is how (or if) the power setting affects the etch rate.

Note: This article was written about version 2.0.0 of the reprex package.

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 (i.e., model coefficients). If interested, see Agresti (2002) for the computational details. In this article we simply aim to get you started with implementing and interpreting GEE using the R statistical computing environment.