1. Randomized Single-Case Intervention Designs Joel R
Randomized Single-Case Intervention Designs Joel R. Levin University of Arizona
Adapted from Kratochwill, T. R., & Levin, J. R. (2010). Enhancing the scientific credibility of single-case intervention research: Randomization to the rescue. Psychological Methods, 15,

2. Major Purpose of this Presentation
To broaden your minds by introducing you to new and exciting, scientifically credible single-case intervention design possibilities. To let you know that these procedures are becoming increasingly acceptable to single-case intervention researchers and are beginning to appear in the SCD research literature. Whether YOU ever choose to adopt them in your own SCD research (after this week!) is entirely up to you.

3. 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 the results

4. Traditional Single-Case Designs
Basic design (AB)
Reversal (or withdrawal or “operant”) design (ABAB)
Alternating and simultaneous treatment designs
Multiple-probe design
Changing criterion design
Multiple-baseline design

5. Four Single-Case Design-and-Analysis Randomization Variations
Phase/Intervention Randomization (within cases)
2. Intervention Randomization (between
cases)
3. Start-Point Randomization
4. Case Randomization

6. Days/Weeks/Months/Sessions
Traditional Basic Design (AB)

7. 1. Phase/Intervention Randomization (Within Cases)
With phase randomization, the order in which the A and B phases are administered is randomly determined for each case (e.g., participant, pair, small group, classroom).

8. AB Design
“[I]nstead of automatically administering the two phases in an AB order, one could randomly determine which phase should come first.” (Levin, Marascuilo, & Hubert, 1978)
Problems with randomizing phases?
If A is a true baseline condition, logically it should be administered first.
Problems with not randomizing phases?
If A and B are two alternative intervention conditions, potential problems include both time-related effects and carryover effects.
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 ). New York: Academic Press.

9. Traditional (“Systematic”) ABAB Reversal Design With One Experimental Case

10. 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 and
expectancy 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 ). Hillsdale, NJ: Erlbaum.
Onghena, P. (1992). Randomization tests for extensions and variation of ABAB single-case experimental designs: A rejoinder. Behavioral Assessment, 14,

11. Randomized Phase Designs
For ABAB…AB and alternating-treatment designs, there are two basic types of phase randomization: simple and blocked. With simple randomization, the only constraint is that there be equal numbers of A and B phases in the design. With blocked randomization, additional constraints are imposed to control for order effects.

12. One Potentially Palatable Solution?
Prior to initiating the formal AB intervention study, include one or more mandatory baseline (adaptation, warmup) observations (A'). The administration order of the subsequent A and B phases is then randomly determined. The A' phase is not considered to be part of the actual study’s design or analysis.

13. Randomized Alternating Treatment Design (ATD) With One Case, Two Within-Case Conditions, and 13 Time Periods (Seven Mornings and Six Afternoons)

14. Randomized ABAB AB Design With One Case, Two Within-Case Conditions, and 10 Time Periods 5 A and 5 B)

15. Replicated Randomized ABAB
Replicated Randomized ABAB AB Design With Four Cases, Two Within-Case Conditions, and 10 Time Periods (5 A and 5 B)

16. 2. Intervention Randomization (Between Cases)
In some “between-case” multiple-intervention single-case designs, Treatment X (a control or intervention condition) is administered to one or more cases and Treatment Y (an alternative intervention condition) is administered to other cases. With intervention randomization, which cases receive Treatment X and which receive Treatment Y is randomly determined. [Examples of intervention randomization are presented in later slides.]

17. A Two-Intervention (Between Cases) Example

18. Time Out for an Introduction to “Intervention Start Points” (To Be Returned to Throughout the Institute)
The intervention start point [and subsequent transition points] is [are] “response guided” – preferred by many traditional SCD researchers
later discussion of adopting this approach with the assistance of a “masked visual analyst (MVA)”
The intervention start point [and subsequent transition points] is/are designated on an a priori basis by the researcher – preferred by traditional methodologists
The intervention start point [and subsequent transition points] is [are] randomly selected from a set of potential points that is designated as “acceptable” by the researcher – preferred by “new-age” SCD methodologists

19. 3. Start-Point Randomization
With start-point randomization, the actual A-to-B transition (“intervention start point”) is randomly selected from a set of researcher-designated “acceptable” (or “potential”) start points. This type of randomization can be implemented in single-case designs where A and B are either baseline and intervention conditions or two different intervention conditions.

20. AB Design With One Case (“Unit”), Two Within-Series Intervention Conditions, 20 Time Periods, and 13 Potential Intervention Start Points

21. Replicated AB Design With Three Cases (“Units”), Two Within-Series Intervention Conditions, 20 Time Periods, and 13 Potential Intervention Points for Each Case
Marascuilo, L. A., & Busk, P. L. (1988). Combining statistics for multiple-baseline AB and replicated ABAB designs across subjects. Behavioral Assessment, 10, 1-28.

22. 4. Case Randomization
With case randomization, cases are randomly assigned to the different replication positions within the design. Multiple-baseline designs, with their systematically staggered intervention start points, are uniquely suited to this type of randomization.

23. Traditional Multiple-Baseline Design Across Participants

24. Randomized Multiple-Baseline Design Across Cases (“Units”) With 5 Randomized Cases, Two Within-Series Intervention Conditions (A and B), 10 Time Periods, and a Staggered Intervention Introduction of One Time Period
Kratochwill, T. R., & Levin, J. R. (1978). What time-series designs may have to offer educational researchers. Contemporary Educational Psychology, 3,
Wampold, B. E., & Worsham, N. L. (1986). Randomization tests for multiple-baseline designs. Behavioral Assessment, 8,

25. “Fascinating” Issue to Contemplate This Week
I will argue that the previously illustrated Marascuilo and Busk (1988) replicated AB design, with randomly determined intervention start points for each case, should be considered very nearly equivalent (in terms of its scientific credibility) to the just-presented multiple-baseline design, with random assignment of cases to the different multiple-baseline positions.

26. Other Randomized Start-Point Possibilities and Combinations
Random Assignment of Interventions (Between Cases, Intervention Orders (Within Cases), and/or Intervention Start Points
when multiple interventions are included in the study
Note: The designs in the following three slides incorporate both intervention randomization and start-point randomization.

27. Multiple-Baseline Design With 4 Randomized Cases (“Units”), Two Within-Series Conditions, 15 Time Periods, 3, 3, 2, and 2 Potential Intervention Start Points for Cases 1, 3, 2, and 4, Respectively, and a Staggered Intervention Introduction of at Least One Time Period

28. Levin & Wampold’s (1999) Simultaneous Start-Point Model
Time Period
Pair 1X A A A A A A A A A A A B* B B B B B B B B
Pair 1Y A A A A A A A A A A A B* B B B B B B B B
Note: X and Y are two different intervention conditions, randomly assigned to one of which is assigned to a pair member. Potential intervention start points are between Time Periods 5 and 17 inclusive.
*Randomly selected intervention start point for the pair of units
Levin, J. R., & Wampold, B. E. (1999). Generalized single-case randomization tests: Flexible analyses for a variety of situations. School Psychology Quarterly, 14, 59–93.

29. Levin & Wampold’s (1999) Replicated Simultaneous Start-Point Model
Time Period
Pair 1X A A A A A A A A A A A B* B B B B B B B B
Pair 1Y A A A A A A A A A A A B* B B B B B B B B
Pair 2X A A A A A A A A A B* B B B B B B B B B B
Pair 2Y A A A A A A A A A B* B B B B B B B B B B
Note: X and Y are two different intervention conditions, one of which is randomly assigned to a pair member in each pair. Potential intervention start points are between Time Periods 5 and 17 inclusive.
*Randomly selected intervention start point for each pair of units

30. In Addition… Two interesting adaptations of the preceding design:
1. One can incorporate a mixture of a randomized component (start-point randomization) and a nonrandomized component (pair member classifications) to address either individual or group interaction/moderation hypotheses.
In that situation, the X and Y members of each pair would represent different variable classifications of interest (e.g., gender, developmental level, classroom achievement).

31. In Addition…
2. X and Y could be two different outcome measures, associated either with a single intervention or with two different interventions. For example, X could be a reading performance measure and Y an arithmetic performance measure.
With a single intervention (e.g., a reading intervention), one could test the hypothesis that the intervention has comparable effects on the two measures.
With two different interventions (e.g., a reading intervention and a math intervention), one could test the hypothesis that the two interventions have comparable effects on their respective outcome measures. (This particular application is illustrated in a later session.) .

32. Extension of Marascuilo & Busk’s (1988) Replicated AB Design
Single-case analog to the conventional group crossover design (to be discussed later in the Institute):
Suppose that A and B consist of two different interventions that all cases are to receive. Cases would be assigned randomly to one of the two intervention orders (AB or BA) and each case would receive a randomly selected intervention start point. So, with N = 2 cases and 20 observations, with an a priori specification of at least 7 observations for each intervention:
Case 1 B B B B B B B B │A A A A A A A A A A A A
Case 2 A A A A A A A A A A A A │B B B B B B B B
One can test the hypothesis that the two interventions are equally effective – come back soon to see how, along with other proposed new comparative treatment designs!

33. Take-Home Message (to be Returned to Later in this Institute)
Through various randomization schemes, it is possible to design single-case intervention studies that possess the same or similar scientific credibility characteristics as those of conventional randomized group intervention studies.
With the additional inclusion of a sufficient number of replication components, who’s to say that a superbly implemented randomized single-case intervention study is less “valued” than a superbly implemented conventional randomized group intervention study?
…only our Swami knows