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.
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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…)
When you hear about multilevel models or mixed models, you very often think of a nested design. Level 1 units 
nested in Level 2 units, which are in turn possibly nested in Level 3 units. But these variables that define the units and that become random factors in the model can, in fact, be crossed with each other, not nested.
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Designing experiments would always be simple if we could just randomly assign subjects to different treatment conditions with no other restrictions. Unfortunately, that doesn’t always work.
For example, there are many experimental situations where the subjects aren’t independent of each other. The subjects that are related to each other are combined into clusters called “blocks.” It can happen due to practicalities of running an experiment efficiently or you can intentionally plan it as a way to reduce random variance.
In either case, this is a randomized complete block design. It’s a great design to become familiar with because it will greatly expand your ability to create and analyze experiments.
How It Works
When you have subjects that share characteristics with one another, it can sometimes be difficult to isolate those characteristics directly. This makes it hard to record them as additional variables. By identifying the subjects that are similar, you can still capture how those characteristics affect the outcome. Subjects that are similar are grouped into “blocks.”
From there, you can make treatment assignments so that you put subjects from the same block into different treatment groups.
Why different treatment groups? Suppose subjects from the same block were assigned to the same treatment group. (more…)
Some repeated measures designs make it quite challenging to specify within-subjects factors. Especially difficult is when the design contains two “levels” of repeat, but your interest is in testing just one.
Let’s look at a great example of what this looks like and how to deal with it in this question from a reader :
The Design:
I want to do a GLM (repeated measures ANOVA) with the valence of some actions of my test-subjects (valence = desirability of actions) as a within-subject factor. My subjects have to rate a number of actions/behaviours in a pre-set list of 20 actions from ‘very likely to do’ to ‘will never do this’ on a scale from 1 to 7, and some of these actions are desirable (e.g. help a blind man crossing the street) and therefore have a positive valence (in psychology) and some others are non-desirable (e.g. play loud music at night) and therefore have negative valence in psychology.
My question is how I can use valence as a within-subjects factor in GLM. Is there a way to tell SPSS some actions have positive valence and others have negative valence ? I assume assigning labels to the actions will not do it, as SPSS does not make analyses based on labels …
Please help. Thank you.
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One of the difficult decisions in mixed modeling is deciding which factors are fixed and which are random. And as difficult as it is, it’s also very important. Correctly specifying the fixed and random factors of the model is vital to obtain accurate analyses.
Now, you may be thinking of the fixed and random effects in the model, rather than the factors themselves, as fixed or random. If so, remember that each term in the model (factor, covariate, interaction or other multiplicative term) has an effect. We’ll come back to how the model measures the effects for fixed and random factors.
Sadly, the definitions in many texts don’t help much with decisions to specify factors as fixed or random. Textbook examples are often artificial and hard to apply to the real, messy data you’re working with.
Here’s the real kicker. The same factor can often be fixed or random, depending on the researcher’s objective. (more…)
