Whether or not you run experiments, there are elements of experimental design that affect how you need to analyze many types of studies.
The most fundamental of these are replication, randomization, and blocking. These key design elements come up in studies under all sorts of names: trials, replicates, multi-level nesting, repeated measures. Any data set that requires mixed or multilevel models has some of these design elements. (more…)
One important yet difficult skill in statistics is choosing a type model for different data situations. One key consideration is the dependent variable.
For linear models, the dependent variable doesn’t have to be normally distributed, but it does have to be continuous, unbounded, and measured on an interval or ratio scale.
Percentages don’t fit these criteria. Yes, they’re continuous and ratio scale. The issue is the (more…)
When I was in graduate school, stat professors would say “ANOVA is just a special case of linear regression.” But they never explained why.
And I couldn’t figure it out.
The model notation is different.
The output looks different.
The vocabulary is different.
The focus of what we’re testing is completely different. How can they be the same model?
Most of the p-values we calculate are based on an assumption that our test statistic meets some distribution. These distributions are generally a good way to calculate p-values as long as assumptions are met.
But it’s not the only way to calculate a p-value.
Rather than come up with a theoretical probability based on a distribution, exact tests calculate a p-value empirically.
The simplest (and most common) exact test is a Fisher’s exact for a 2×2 table.
Remember calculating empirical probabilities from your intro stats course? All those red and white balls in urns? (more…)
Question: Can you talk more about categorical and repeated Time? If I have 5 waves at ages 0, 1 year, 3 years, 5 years, and 9 years, would that be categorical or repeated? Does mixed account for different spacing in time?
Mixed models can account for different spacing in time and you’re right, it entirely depends on whether you treat Time as categorical or continuous.
First let me mention that not all designs can treat time as either categorical or continuous. The reason it could go either way in your example is because time is measured discretely, yet there are enough numerical values that you could fit a line to it. (more…)
As mixed models are becoming more widespread, there is a lot of confusion about when to use these more flexible but complicated models and when to use the much simpler and easier-to-understand repeated measures ANOVA.
One thing that makes the decision harder is sometimes the results are exactly the same from the two models and sometimes the results are (more…)