Consider the following papers:
- Johnson, Marianne, and Eric Kuennen. "Basic math skills and performance in an introductory statistics course." Journal of Statistics Education 14.2 (2006).
- Lunsford, M. Leigh, and Phillip Poplin. "From research to practice: Basic mathematics skills and success in introductory statistics." Journal of Statistics Education 19.1 (2011).
These feature a multiple-choice diagnostic test used at the start of a statistics course, with various data and conclusions drawn from the results. The test is given in its entirety in each paper. The Johnson paper uses a 15-question test, and the Lunsford paper builds on it with an additional 5 questions. I've used this as the basis for a first-day diagnostic in my community-college elementary statistics course for several years. I find that it has a small amount of predictive power with regard to final exam scores (R^2 = 0.13, N = 238).
