As evidence-based practice (EBP) continues gaining prominence in the professional literature, at least two overlapping challenges make it difficult for mainstream social workers to accept EBP as the primary mode for practice. Social workers need a robust pool of intervention research on which to base practice decisions. The research must remain current; be well formulated, for instance, conforming to the Consolidated Standards of ReportingTrials guidelines (the gold standard for reporting clear, transparent, and sufficiently detailed conference abstracts and journal articles); and be focused on ascertaining the most appropriate interventions that attain the desired outcomes for specific clients with specific problems (Hopewell et al., 2008; Thyer, 2001). Social workers also need research that values knowledge derived from clinical expertise or practice wisdom. Any apprehension social workers have with adopting the kind of transparent EBP put forward by Gambrill (2007) may be attributed in part to the lack of appreciation for practice wisdom that is hard to observe and quantify as a valid source of evidence.
Over the past few years, other professions have found Bayesian analysis useful across many disciplines where data collection is difficult or expensive, most notably medicine and pharmacology. The application of Bayesian analysis to adaptive designs in clinical trials has allowed trials to stop sooner, thus getting patients on an effective medicine or off of a harmful medicine much faster than in the past (see, for instance, Giles et al., 2003, and Krams, Lees, Hacke, & Grieve, 2003).
This article introduces Bayesian analysis as a statistical paradigm conducive to addressing the challenges of EBP in social work research and practice. In contrast to classical statistical methods, Bayesian analysis allows researchers to translate practice wisdom into evidence and incorporate data from past and present studies. The article begins with a brief introduction to Bayes's theorem, followed by a discussion and comparison of classical and Bayesian approaches. Finally, we provide a practical example of Bayesian analysis to assess the clinical improvement of youths receiving children's psychosocial rehabilitation (CPSR) from a mental health clinic that specializes in the treatment of youths with severe emotional disturbance (SED).
Classical Statistical Analysis
Most statistical analysis done in social work has tended to be in the classical (also called the "frequentist") paradigm. In the frequentist approach to statistics, parameters are assumed to be fixed, unknown quantities. A sample is taken from the population, and inference is generally accomplished through either hypothesis testing or confidence intervals. There are actually several difficulties with frequentist inference, but one problem in particular is that it relies on what is termed the "repeated sampling paradigm," which makes interpretation of results difficult and quite nonintuitive.
For instance, suppose interest lies in the proportion of clients therapeutically discharged from a state-supported intensive outpatient treatment program for mental health and substance abuse disorders. We denote this unknown proportion p. The frequentist confidence interval (CI) found in most introductory textbooks is of the form
[??] [+ or -] [z.sub.[alpha]/2 [square root of ([??](1 - [??]/n)],
where [??] is the estimated proportion of positive responses, found by taking the number of positive responses divided by the sample size n, and [z.sub.[alpha]/2] is the value of the standard normal distribution that leaves (1 - [alpha]/2) * 100 in the upper tail of the distribution. The common value for [alpha] is .05 which leads to a value [z.sub.[alpha]/2] = 1.96. The interpretation of this interval is not the desired one of the "probability" that p in the interval is 95%. Instead, we have to imagine repeating the experiment essentially an infinite number of times and interpreting the interval by saying that 95% of these "repeated sampling" intervals would contain the true parameter p. …