I'm designing a language-learning study with maybe 30 participants. My collaborators want each person to experience both of the methods we're using, so we are planning a crossover design. In addition to the "method" factor (and a random effect for each person's aptitude), we have two nuisance factors to block by. One is language: we'll use two different languages to reduce bleed-through (effects carrying from one round of treatment into the next in our crossover design). The other is order: half the people do method A followed by method B; half do the reverse.
We could have four types of people:
- Swedish Method 1 followed by Norwegian Method 2
- Swedish Method 2 followed by Norwegian Method 1
- Norwegian Method 1 followed by Swedish Method 2
- Norwegian Method 2 followed by Swedish Method 1
Or we could have just two types:
- Norwegian Method 1 followed by Swedish Method 2
- Norwegian Method 2 followed by Swedish Method 1
I have three related questions (sorry) (thanks).
- Can you help me conceptualize potential interactions here?
- Are either of these designs obviously bad for some reason?
- If not, then which one is more efficient?
In your answer, keep in mind that our goal is inference on which methods are "better," as measured by some yet-to-be-carefully-selected quantitative variables describing learning and learner preferences. I have looked through Gary Oehlert's experimental design textbook (pdf), especially ch. 13, and I read a few suggested questions here on CV.