A single-case alternating treatment design (Barlow & Hayes, 1979 (link)) without baseline was used to compare the effects of two conditions (i.e., silent and noise) of the modified FA on the dependent variables. The two conditions were alternated within each day for majority of the days when study sessions were implemented. To minimize potential sequence effects, the alternating sequence was randomly determined with no more than two consecutive sessions of the same condition. For each participant, an average of two modified FA sessions was implemented per day, across 3 to 5 days a week. On some of the days, one or three sessions were implemented based on the availability of the child participant and the clinic staff on a particular day. The alternation between conditions sometimes occurred across days instead of within a day if only one session was implemented on a day.
The purpose of the silent condition was to simulate a low-stimulation environment and evoke behavior maintained by automatic access to stimulation; the purpose of the noise condition was to simulate a high-stimulation environment and evoke behavior maintained by automatic escape from stimulation. If a participant engaged in higher levels of target repetitive behavior in the silent relative to the noise condition, the behavior was hypothesized to have an automatic positive reinforcement function. If a participant engaged in higher levels of target repetitive behavior in the noise relative to the silent condition, the behavior was hypothesized to have an automatic negative reinforcement function. If a participant engaged in similar levels of target repetitive behavior across the silent and noise conditions, the behavior was hypothesized to have a mixed automatic reinforcement function. If a participant engaged in minimal levels of target repetitive behavior in both conditions, the behavior was hypothesized to have a social reinforcement function instead of an automatic reinforcement function. An illustration of the study design and hypothesized subtypes based on the modified FA outcome is shown in Fig. 1.

Study design and hypothesized outcomes with corresponding functional subtypes