creases in desired behavior or decreases in undesirable behavior) that reliably occur when the treatment is implemented and withdrawn indicate a functional (i.e., causal) relationship between the treatment and outcome variables (Barlow and Hersen, 1984). This design is usually replicated with at least two or three participants.

In a multiple baseline design, three (or more) participants may be involved. Data are collected for all participants in an initial baseline phase, and then the treatment is begun with one participant while the others remain in the baseline phase of the study. When changes occur for the first participant, the treatment is introduced for the second participant, and when changes occur for the second participant, the treatment is introduced for the third participant. Variations on this design include multiple baselines across behaviors of single individuals and multiple baselines across settings. Again, the researcher infers a functional relationship when changes reliably occur only after the treatment is implemented across (usually three) participants, settings, or behaviors.

Single-subject designs differ from group designs in three ways. First, changes in the outcome variables are measured frequently (e.g., daily, weekly) rather than at the beginning and end of the treatment. The second is that visual analysis of differences in trends in the data (e.g., increases in social interaction or decreases in stereotypic behavior) is usually used to determine the effectiveness of treatment, rather than statistical analyses between groups. Third, unlike group designs, in which the treatments often represent a range of theoretical perspectives, treatments evaluated through single-subject designs tend to follow an applied behavior analysis theoretical orientation (Kazdin, 1982).

There are methodological problems and limitations when single-subject designs are applied to studying children with autistic spectrum disorders. The most obvious is that only a small number of children are involved in any single study, so the applicability of findings of a single study to other children is limited. Single-subject designs build their external validity on systematic replications across studies (Tawney and Gast, 1983). One set of current standards stipulates (Lonigan et al., 1998) that nine replications of studies with good experimental designs and treatment comparisons should be required for effectiveness of an intervention to be “well-established,” while three replications of studies with the acceptable methodological characteristics are necessary for an intervention to be identified as “probably efficacious.” These are arbitrary, though useful, designations.

The issue of inter- and intrasubject variability also exists for this methodology. Single-subject designs require that some level of stability in the participants’ performance be reached before another phase is implemented, and variability in participants’ behavior, as occurs for children with autistic spectrum disorders, may obscure comparisons across phases.

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