ANOVA On Lmer: Valid Before Pairwise Comparisons?

Hey everyone! Let's dive into a common statistical conundrum: using ANOVA on an lmer model before doing pairwise comparisons, especially when you've got a dataset with missing data from some participants. This is a tricky area, and it’s awesome that you’re thinking critically about the right approach. You're just starting your stats journey, which is super exciting! Let’s break down whether your reasoning makes sense and what other things you should keep in mind.

Understanding the Study Design: A Fictional RCT

Imagine a randomized controlled trial (RCT) where we're testing a new intervention to improve, say, mood. We have several participants, and they're randomly assigned to different groups – maybe a treatment group, a placebo group, and a control group getting the usual care. We measure their mood at baseline (before the intervention), at several time points during the intervention, and then at follow-up points after the intervention ends. The goal is to see if our intervention has a significant effect on mood compared to the other groups. Sounds straightforward, right? But here's the catch: not everyone shows up for every measurement. Life happens, and we end up with missing data. This is where things get interesting – and a bit more complex.

Missing data is a common challenge in longitudinal studies and RCTs. Participants might drop out, miss appointments, or sometimes, data collection might be incomplete for various reasons. When dealing with such data, the choice of statistical analysis becomes crucial. A naive approach of simply removing participants with any missing data (complete-case analysis) can lead to biased results, especially if the missing data isn't completely random. This is why mixed-effects models, implemented with functions like lmer in R's lme4 package, are so valuable. They can handle missing data under certain assumptions, offering a more robust and efficient analysis.

Now, let's consider why you're thinking about using ANOVA on an lmer model. Often, the first step in analyzing data from a multi-group comparison is to check for an overall effect. Is there a significant difference somewhere among the groups? ANOVA is a classic tool for this, assessing whether the means of several groups are equal. However, when you're using mixed-effects models to account for repeated measures and individual variability, the standard ANOVA framework needs some adjustments. The anova() function, when applied to an lmer model, provides a way to conduct this overall test, taking into account the complexities of the mixed-effects structure. But, and this is a big but, interpreting the results and deciding on the next steps (like pairwise comparisons) requires careful consideration.

The decision to proceed with pairwise comparisons after a significant ANOVA result is a common practice, but it's not always a straightforward yes. It's like seeing a sign that says