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…)
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.
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:
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…)
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.
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.
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…)
The classic way to compare means in analysis of variance is examining pairwise differences in means after an F test.. It’s great for many problems, but sometimes your research question isn’t about pairwise differences.
Pairwise differences are not ideal if your research question is if, like the Sesame Street song, one of these groups is not like the others. Perhaps, you are trying to assure that groups conform to a common standard. Analysis of Means (ANOM) helps in all these settings. (more…)