Analyzing Single-Subject Design Data Using Statistical Process Control Charts

Single-subject designs (SSDs) are advocated widely (for example, Bloom, Fischer, & Orme, 1999; Blythe, Tripodi, & Briar, 1994; Jayaratne & Levy, 1979; Kazi, 1998), although debate exists concerning their use in practice evaluation (for example, Kirk, 1996). One area of contention and ongoing development is the statistical analysis of data from these designs. Many of the available statistical methods are controversial, complicated, or misunderstood (for example, Bloom et al., 1999; Franklin, Allison, & Gorman, 1997; Kratochwill & Levin, 1992; Orme, 1991; Rubin & Knox, 1996). Additional methods are needed, as is a clear understanding of the strengths and limitations of existing methods. The two-standard-deviation-band method, also known as a "Shewhart" chart, is a statistical method that is well known to social workers familiar with SSDs. It has been described and illustrated in a number of social work texts (for example, Bloom & Fischer, 1982; Bloom, Fischer, & Orme, 1995, 1999; Blythe & Tripodi, 1989; Rubin & Babbie, 1989, 1997). What has not been discussed in the social work literature, or in well-known texts on SSDs outside of social work (Barlow & Hersen, 1984; Barlow, Hayes, & Nelson, 1984; Kazdin, 1982; Kratochwill, 1978; Kratochwill & Levin, 1992), is that there are many different types of Shewhart charts, known more generally as "statistical process control charts," or simply "control charts." Statistical process control (SPC) charts date back to the 1920s, and they are at the heart of SPC, a large and versatile body of industrial quality control techniques (for example, Doty, 1996; Ostle, Turner, Hicks, & McElrath, 1996; Wheeler & Chambers, 1992). SPC itself is a key part of an overall management system known as "total quality management" (TQM), which originally was implemented in U.S. manufacturing environments and is now being used in social work settings (Berman, 1995; Boettcher, 1998; Martin, 1993; Moore & Kelly, 1996). However, in a critique of TQM Gummer (1996) noted the frequent failure to incorporate SPC into TQM. SPC charts increasingly are being adapted to diverse areas, including human services (Brannen & Streeter, 1995), health care, and other service industries (for example, Albin, 1992; Blumenthal, 1993; Carey & Lloyd, 1995), program evaluation (for example, Posavac, 1995), and organizational behavior management (for example, Mawhinney, 1988). However, there has been limited discussion of the use of SPC charts to analyze SSD data (Hopkins, 1995; Pfadt, Cohen, Sudhalter, Romanczyk, & Wheeler, 1992; Pfadt & Wheeler, 1995; Sideridis & Greenwood, 1996). Not only has there been limited discussion of the use of SPC charts to analyze SSD data, but the only method for constructing an SPC chart described in the social work literature is incorrect (for example, Bloom & Fischer, 1982; Bloom et al., 1995, 1999; Blythe & Tripodi, 1989; Rubin & Babbie, 1989, 1997). This article describes and illustrates the correct method for constructing this particular type of chart, discusses it more fully than has been done in the social work literature, and places it in the context of SPC. A major advantage of SPC charts is the simplicity of the computations. Computations for most SPC charts can be done easily with a calculator or spreadsheet program. However, there is a wealth of computer software that can simplify the construction of SPC charts (Institute of Industrial Engineers Solutions, 1997). Thus, this article discusses briefly the microcomputer software available to construct SPC charts. SPC CHARTS SPC charts were developed by industrial quality control engineers to ensure the consistent delivery of quality products. Specifically, SPC charts are used to detect systematic changes in manufacturing processes through the identification of unusual product samples (for example, a sample of a part that is distinctly larger or smaller than other samples of this part). …