Teaspoons, Tablespoons, and a new analogy for family-wise error.

This blog post contains one small analogy for explaining family-wise error to your students.

I was making French toast for dinner the other night. While I was measuring out cinnamon, I realized using one tablespoon instead of three teaspoons to avoid measuring errors is sort of like using a one-way ANOVA with three levels instead of doing three t tests to avoid Type I error. 

Stick with me here. If I were to use three teaspoons to measure out an ingredient, there is a chance I could make a mistake three times. Three opportunities for air pockets. Three opportunities to not perfectly level out my ingredient. Meanwhile, if I just use one tablespoon, I will only risk the error associated with using a measuring spoon once. 

Similarly, every time we use NHST, we accept 5% Type I error (well, if you are a psychologist and using the 5% gold standard, but I digress). Using three tests (t tests) when we could use one (ANOVA) will increase the risk of a false positive.

I don't know about you, but I never know which explanation for a statisitcal phenomena will stick in my students' brains. You can talk about, like, measuring whatever you want to use this analogy, but I like that the 3 to 1 ratio that applies teaspoons and tablespoons as well three t tests versus an one-way ANOVA and three t tests.