In many research fields, a common practice is to categorize continuous predictor variables so they work in an ANOVA. This is often done with median splits. This is a way of splitting the sample into two categories: the “high” values above the median and the “low” values below the median.
There are many reasons why this isn’t such a good idea: (more…)
I’ve talked a bit about the arbitrary nature of median splits and all the information they just throw away.
But I have found that as a data analyst, it is incredibly freeing to be able to choose whether to make a variable continuous or categorical and to make the switch easily. Essentially, this means you need to be (more…)
The way to follow up on a significant two-way interaction between two categorical variables is to check the simple effects. Most of the time the simple effects tests give a very clear picture about the interaction. Every so often, however, you have a significant interaction, but no significant simple effects. It is not a logical impossibility. They are testing two different, but related hypotheses.
Assume your two independent variables are A and B. Each has two values: 1 and 2. The interaction is testing if A1 – B1 = A2 – B2 (the null hypothesis). The simple effects are testing whether A1-B1=0 and A2-B2=0 (null) or not.
If you have a crossover interaction, you can have A1-B1 slightly positive and A2-B2 slightly negative. While neither is significantly different from 0, they are significantly different from each other.
And it is highly useful for answering many research questions to know if the differences in the means in one condition equal the differences in the means for the other. It might be true that it’s not testing a hypothesis you’re interested in, but in many studies, all the interesting effects are in the interactions.
Here’s a little reminder for those of you checking assumptions in regression and ANOVA:
The assumptions of normality and homogeneity of variance for linear models are not about Y, the dependent variable. (If you think I’m either stupid, crazy, or just plain nit-picking, read on. This distinction really is important). (more…)
If your graduate statistical training was anything like mine, you learned ANOVA in one class and Linear Regression in another. My professors would often say things like “ANOVA is just a special case of Regression,” but give vague answers when pressed.
It was not until I started consulting that I realized how closely related ANOVA and regression are. They’re not only related, they’re the same thing. Not a quarter and a nickel–different sides of the same coin.
So here is a very simple example that shows why. When someone showed me this, a light bulb went on, even though I already knew both ANOVA and multiple linear (more…)
In a Regression model, should you drop interaction terms if they’re not significant?
In an ANOVA, adding interaction terms still leaves the main effects as main effects. That is, as long as the data are balanced, the main effects and the interactions are independent. The main effect is still telling (more…)