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Invited Columns: Clinicians' Guide to Research Methods and Statistics

Single-Subject Designs

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JEFFREY A. GLINER Ph.D., GEORGE A. MORGAN Ph.D., ROBERT J. HARMON M.D.

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In this article we describe a subcategory of quasi-experimental time-series designs that can be used with very few participants. These single-subject designs have many of the characteristics that govern traditional group-time-series designs, such as the numerous repeated measures on each participant and the initiation and withdrawal of treatment. Using very few participants increases the flexibility of the design but limits the generalizability of the results. For such designs, completely different methods of data analysis are used.

We define single-subject designs as time-series designs in which an intervention (active independent variable) is given to very few participants-4 or fewer-not necessarily to only a single subject. In most situations, the independent variable is initiated and withheld numerous times throughout the study. In multiple-baseline single-subject designs, however, the removal of the independent variable is not necessary. Single-subject designs are quasi-experimental designs because they must include an active independent variable. In addition, there is no random assignment of participants to treatments. Two major types of single-subject designs are ABAB (or reversal designs) and multiple-baseline designs.

Reversal Designs

In these designs (Fig. 1), the first A stands for the baseline period, during which the participant is usually observed for a number of time periods. In single-subject designs, the investigator plots the data for each measurement period on graph paper to determine whether the behavior during baseline (or treatment) is increasing, decreasing, or leveling off. The first B period refers to the first intervention period. After the baseline has leveled off, the investigator initiates the treatment or active independent variable. Once the treatment data appear to level off (relatively flat line), the investigator withdraws the treatment and initiates a second A phase. The investigator observes this phase for several periods (3 at the minimum) until the behavior levels off. Then the investigator initiates the second B or treatment phase. This completes the minimum reversal design, with 2 A or baseline phases and 2 B or treatment phases.

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Fig. 1

What should happen in a typical ABAB single-subject study? Figure 1 shows schematically that one would expect that during the initial baseline period (A) there may be some fluctuation of responding, but after the first few periods, the participant's responses (dependent variable) should habituate or level off. During the initial treatment period (B), behavior should increase (or decrease if the treatment is designed to reduce an undesirable behavior; e.g., aggression). One would expect this behavior to continue to increase up to a point and then level off. Next, during the withdrawal of the treatment (second A period), the expectation is that performance will decrease (although perhaps not as low as the first A period) and then begin to stabilize. When the stabilization has occurred, the reintroduction of the treatment (second B period) takes place and performance is expected to increase to at least that of the preceding treatment phase. Often this phase is the highest because the second treatment phase is added to any carryover effect from the first treatment phase.

The ABAB single-subject reversal design does not necessarily mean that there should only be 2 baseline phases and 2 intervention phases. Most ABAB designs use at least 3 A and 3 B phases, while many use quite a few more. More A and B phases make the study more convincing, and hence increase internal validity. In addition, the investigator is not limited to just the phases of A and B. Consider a situation in which after the initial A phase, the investigator initiates a treatment in the B phase. However, the treatment fails to increase performance above that observed during the baseline period. In a single-subject design, the investigator could modify the treatment and introduce it (as C) after the B phase. Thus the design might be something like ABCAC. The point to remember is that a strength of single-subject designs is that they are very flexible. The number of sessions making up any particular phase may be changed, and you are not limited to just an A and B phase.

Multiple-Baseline Designs

Multiple-baseline single-subject designs were introduced more recently. Multiple baseline designs were introduced because (1) in clinical situations the removal of treatment is often considered unethical, especially if the treatment appears successful; and (2) many of these studies were being performed in settings in which the patient was responsible for payment for the treatment. In multiple-baseline studies, in the initial stages of the study as many as 3 baselines may be recorded simultaneously. These baselines may represent the responses of 3 different participants, the responses of 3 different behaviors of the same participant, or the responses of the same participant in 3 different settings. The key to multiple-baseline single-subject studies is that the investigator intervenes at a randomly selected time and observes the effect on only one of the baselines while the other 2 baselines should be unchanged. This type of design eliminates the internal validity threat of history because one would expect that if some external event was altering behavior, it would affect all participants, settings, or behaviors, not just one. We will discuss the multiple-baseline across-subjects design because it is the most common. Its popularity is partially due to the ease of completing this type of study, especially in a clinical setting.

The procedure for carrying out the multiple-baseline across-subjects design is as follows. Initially, the investigator selects 3 (or perhaps 4) different participants for the study. All 3 participants are observed concurrently in a baseline phase, and their responses for each baseline period are plotted on a graph (see Fig. 2). Next, the investigator gives the intervention to one of the participants while continuing to obtain a baseline on the other 2 participants at the same time. After a given number of periods, the intervention is started with the second participant and continued with the first participant, while a baseline is continued for the third participant. Again, after a number of baseline periods, the intervention is started with the third participant and continued with the first 2 participants.

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Fig. 2

Measurement Periods and Instruments

In a reversal design, the number of measurement periods may change between one phase and another. One should wait until each phase is stable before starting or withdrawing treatment. This adds to the flexibility of the design. On the other hand, within each measurement period (session), the length of time must be the same.

A second measurement issue to consider when performing single-subject designs is that the type of instrument selected could seriously compromise the study. Each session must yield a score or a number of responses. If there are a limited number of responses per session, then your instrument may not be sensitive enough for the study. There are 2 types of measures (dependent variables) used in single-subject designs: paper-pencil tests and behavioral observations (which are the most common). Certain rules should be followed when using observation.

· 1. It is best for the observer not to be the teacher, parent, or therapist.

· 2. It is best to have the observers be as discreet as possible (i.e., another student or students in the classroom or observers watching through a one-way mirror.).

· 3. The critical responses to be observed should be well defined before the study.

· 4. More than one observer should be used to record the responses.

· 5. Interrater reliability should be established among observers before the study.

Evaluation of the Results of Single-Subject Designs

Many early single-subject studies with animals did not use statistical analysis. Instead, the investigators believed that the graphic displays were convincing. However, single-subject studies with humans, especially reversal designs, usually have fewer baseline and intervention periods than animal studies. In addition, single-subject designs often have a problem of serial dependency (responses within the same individual are correlated, and thus future responses are partially predictable). Therefore, an increasing emphasis has been given to using some form of statistical analysis in addition to visual analysis.

Visual Analysis of Single-Subject Designs. When evaluating a single-subject graph visually, the key is to look for patterns in the data, especially as the phases change from baseline to intervention and back to baseline. Kazdin (1982) discussed the use of certain criteria for visual inspection of single-subject designs. One criterion is level, which is the change from the last measurement in a phase to the first measurement in the next phase. Sometimes, just examining change in level can be misleading. Because the criterion of level does not always reflect the pattern of a particular phase, one could use mean level as a second, more stable criterion. Mean level refers to the average of the points in one phase compared with the average of the points in the next phase. A third criterion for visual analysis (also suggested by Kazdin) was that of trend, which indicates a direction of the points within a phase. The trend could be positive, negative, or flat. An additional criterion for visual analysis recommended by Ottenbacher (1986) is slope, which refers to the angle of increase or decrease of the measurement points.

Statistical Analysis of Single-Subject Designs. While visual analysis has been one of the strengths of single-subject designs, sometimes the graphs from these studies are not convincing. Therefore, investigators using these designs have used statistical tests to determine whether interventions have made a difference. There is a disagreement, however, about the best statistical methods. Kazdin (1982) discussed the use of traditional parametric statistical tests, such as an analysis of variance, to compare all phases of an ABAB design. Nonparametric tests are discussed in some detail by Kratochwill and Levin (1992).

Considerations of Internal and External Validity of Single-Subject Designs

Internal validity problems relate to problems in random assignment. With only one participant, there cannot be random assignment of participants to treatments. More important, the order of the treatment phases also cannot be randomly assigned. A third problem is possible carryover effects from one phase to another. On the other hand, the ABAB design reduces the threats of confounding.

The problems in external validity for single-subject designs are even more obvious. The random selection of one participant, or even a small number of participants, is unusual because the participants are usually selected because of some particular behavioral or physical problem. What eventually works for one client/participant may not work for another. Of course, some of the unsuccessful treatments may work for another person.

REFERENCES

· Kazdin, 1982

· A Kazdin

· Single-Case Research Designs, Oxford University Press, New York (1982)

· Google Scholar

· Kratochwill and Levin, 1992

· T Kratochwill, J Levin (Eds.), Single-Case Research Design and Analysis, Erlbaum, Hillsdale, NJ (1992)

· Ottenbacher, 1986

· K Ottenbacher

· Evaluating Clinical Change, Williams & Wilkins, Baltimore (1986)

· Google Scholar

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The authors thank Helena Chmura Kraemer for a helpful critique and Nancy Plummer for manuscript preparation. Parts of the column are adapted, with permission from the publisher and the authors, from Gliner JA and Morgan GA (2000), Research Methods in Applied Settings: An Integrated Approach to Design and Analysis. Mahwah, NJ: Erlbaum. Permission to reprint or adapt any part of this column must be obtained from Erlbaum.

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Copyright © 2000 The American Academy of Child and Adolescent Psychiatry. Published by Elsevier Inc. All rights reserved.