Meaningful, interpretable and comparable estimates

Based on ideas from Ian Dworkin

Introduction

Getting the computer to fit a linear model is relatively straightforward. Spending the time and making sure what you plan to do is meaningful with respect to the measurements you have used, making your model estimates (coefficients) interpretable to help you understand the model output, and determining the best measures of effect to make your results comparable within your model, and to other estimates in the scientific literature is a key part of this.

In some sense the whole week is to get you to focus on the question “What is the difference?” (or “what are the differences?”), and to make sure the differences (and their associated uncertainties) are meaningful, interpretable and comparable. This is generally much better than asking questions like “Is there a difference?” (“are there differences?”). These latter questions are often much less useful, and more likely to result in bad habits in terms of data modeling, statistical inference and using these to answer biological questions.

Goals for this week

Class materials

Resources

Assignment

Describe your data and one or more of your questions from the point of view of measurement theory, guided by the steps in Voje et al. 2023 Figure 1 (note that this is not the same as Figure I). That is: describe the theoretical context, relevant attributes, what you will measure on what kind of scale, and how this will affect your statistical analyses.

Also, for at least one comparison discuss how you will decide whether a difference is “important” – you could specify a cutoff level, or describe how you will investigate this question further.