Power, Sample Size Estimation, and Early Stopping Rules
In 1962, Cohen published a seminal article pointing out that the majority of psychological studies were conducted with inadequate power. Subse quently, several other surveys of research literature in both psychology (Rossi, 1990; Sedlmeir & Girgenzer, 1989) and related fields (Daniel, 1993; Kawano, 1993; Kosciulek & Szymanski, 1993) reaffirmed the exis tence of this problem. Consequently, there is now increasing recognition of the need to design studies with adequate power. One indicator of this is the requirement of power analyses in any application for federal re search support, and a second indicator is the steady increase in the practice of reporting measures of effect in psychological research (Dar, Serlin, & Omer, 1994). It is ironic that during this time of increased (and appropriate) emphasis on statistical power, researchers, clinicians, social service agencies, and funding agencies are simultaneously under evertightening budgetary constraints. This means that it is essential to de sign studies with maximal efficiency; that is, studies that are both pow erful and minimize the consumption of resources (Allison, Allison,
Faith, Paultre, & Pi-Sunyer, submitted). In this chapter we consider pow er in the context of single-subject research design. To our knowledge, only one other discussion of power in single-case research has appeared in the literature (Johannessen & Fosstvedt, 1991).