1. Random Thoughts On Enhancing the Scientific Credibility of Single-Case Intervention Research: Randomization to the Rescue Thomas R. Kratochwill and Joel R. Levin (Psychological Methods, in press)

2. Why Random? Internal Validity Elevates the status of single-case research by increasing the scientific credibility of its methodology Statistical-Conclusion Validity Legitimizes the conduct of various statistical tests and one’s interpretation of results

3. Internal Validity in Single-Case Designs Inspired by Reichardt (2006)… …and an IES grant!

4. Internal Validity in Single-Case Designs But randomization ideas had been percolating within us for 30+ years… Levin, J. R., Marascuilo, L. A., & Hubert, L. J. (1978). N = nonparametric randomization tests. In T. R. Kratochwill (Ed.), Single subject research: Strategies for evaluating change (pp. 167-196). New York: Academic Press.

5. Traditional AB Design

6. Internal Validity in Single-Case Designs AB design “…[I]nstead of automatically administering the two phases in an AB order, one could randomly determine which phase should come first.” (Levin et al., 1978) problems include both time-related effects and carryover effects

7. Traditional ABAB Design

8. Internal Validity in Single-Case Designs ABAB design addresses time and carryover effects to some extent “…[H]owever, systematic assignment (A preceding B in each pair) is not the same as random assignment (either within each pair or within the entire experiment).” (Levin et al., 1978) – other problems include Hawthorne/novelty effects Edgington, E. S. (1992). Nonparametric tests for single-case experiments. In T. R. Kratochwill & J. R. Levin (Eds.), Single-case research design and analysis (pp.133- 157). Hillsdale, NJ: Erlbaum. Onghena, P. (1992). Randomization tests for extensions and variation of ABAB single- case experimental designs: A rejoinder. Behavioral Assessment, 14, 153-171.

12. Internal Validity in Single-Case Designs “[I]n certain ABAB designs, random assignment may indeed be possible. For example, in the baseline (A) versus treatment (B) situation an initial A phase could be designated as an adaptation or ‘warmup’ phase, not to be included in the analysis. It might then be possible to randomly assign two A and two B to four successive phases to constitute the analysis proper. In other instances A and B may represent two different experimental treatments…in which case random assignment may be more reasonable.” (Levin et al., 1978)

20. Marascuilo, L. A., & Busk, P. L. (1988). Combining statistics for multiple-baseline AB and replicated ABAB designs across subjects. Behavioral Assessment, 10, 1-28.

24. Statistical-Conclusion Validity Each of the randomized single-case designs described here can be associated with a valid “randomization” inferential statistical test. Investigating the statistical properties (viz., Type I error and power) of several such tests is one of the foci of our current IES grant.* *Special thanks to our research collaborators Venessa Lall and John Ferron.

25. Contact Information Thomas R. Kratochwill, PhD Educational and Psychological Training Center 1025 West Johnson Street University of Wisconsin-Madison Madison, Wisconsin 53706 E-Mail: tomkat@education.wisc.edutomkat@education.wisc.edu