# ANOVA

### An Introduction to Repeated Measures Designs

May 23rd, 2024 by

There are many designs that could be considered Repeated Measures design, and they all have one key feature: you measure the outcome variable for each subject on several occasions, treatments, or locations.

Understanding this design is important for avoiding analysis mistakes. For example, you can’t treat multiple observations on the same subject as independent observations.

### Example

Suppose that you recruit 10 subjects (more…)

### Assumptions of Linear Models are about Errors, not the Response Variable

March 19th, 2024 by

I recently received a great question in a comment about whether the assumptions of normality, constant variance, and independence in linear models are about the errors, εi, or the response variable, Yi.

The asker had a situation where Y, the response, was not normally distributed, but the residuals were.

Quick Answer:  It’s just the errors.

In fact, if you look at any (good) statistics textbook on linear models, you’ll see below the model, stating the assumptions: (more…)

### The Difference Between Crossed and Nested Factors

December 18th, 2023 by

One of those tricky, but necessary, concepts in statistics is the difference between crossed and nested factors.

As a reminder, a factor is any categorical independent variable. In experiments, or any randomized designs, these factors are often manipulated. Experimental manipulations (like Treatment vs. Control) are factors.

Observational categorical predictors, such as gender, time point, poverty status, etc., are also factors. Whether the factor is observational or manipulated won’t affect the analysis, but it will affect the conclusions you draw from the results.

### The Wide and Long Data Format for Repeated Measures Data

December 2nd, 2023 by

One issue in data analysis that feels like it should be obvious, but often isn’t, is setting up your data.

The kinds of issues involved include:

• What is a variable?
• What is a unit of observation?
• Which data should go in each row of the data matrix?

Answering these practical questions is one of those skills that comes with experience, especially in complicated data sets.

Even so, it’s extremely important. If the data isn’t set up right, the software won’t be able to run any of your analyses.

And in many data situations, you will need to set up the data different ways for different parts of the analyses. (more…)

### Concepts in Linear Regression to know before learning Multilevel Models

November 21st, 2023 by

Are you learning Multilevel Models? Do you feel ready? Or in over your head?

It’s a very common analysis to need to use. I have to say, learning it is not so easy on your own. The concepts of random effects are hard to wrap your head around and there is a ton of new vocabulary and notation. Sadly, this vocabulary and notation is not consistent across articles, books, and software, so you end up having to do a lot of translating.

### Six Common Types of Statistical Contrasts

September 18th, 2023 by

When you learned analysis of variance (ANOVA), it’s likely that the emphasis was on the ANOVA table, with its Sums of Squares and F tests, followed by a post-hoc test. But ANOVA is quite flexible in how it can compare means. A large part of that flexibility comes from its ability to perform many types of statistical contrast.

That F test  can tell you if there is evidence your categories are different from each other, which is a start. It is, however, only a start. Once you know at least some categories’ means are different, your next question is “How are they different?” This is what a statistical contrast can tell you.

### What is a Statistical Contrast?

A statistical contrast is a comparison of a combination of the means of two or more categories. In practice, they are usually performed as a follow up to the ANOVA F test. Most statistical programs include contrasts as an optional part of ANOVA analysis. (more…)