A few years ago, at a meeting of the American Psychological Association ( August, 1993), I was asked to be the discussant for a series of papers on new research designs for the analysis of single subject data. Some of these papers now appear as chapters in this book. For me, this was an unusual request for two reasons. First, I am a terrible discussant, often drifting far afield from the main topic of the papers at hand. Second, most of my previous research has centered on latent variable structural equation modeling of cognitive abilities using large population based sample ( McArdle, 1994). However, as these presenters soon found out, I also advocate the use of more basic models using single subjects. This apparent contradiction on my part requires some further explanation.
The statistical features of the "law of large numbers" are well-known to the contemporary psychologists. In my first college level stats class (circa 1969), I learned the dictum, "odd things happen more often in small samples." Even though this principle is often misunderstood (see Nisbett, 1983), I was sure psychologists were mainly concerned with finding reliable and replicable results, so this was essential knowledge. In later classes on experimental design I learned that the surest way to achieve significant results was to have a very large sample (N); I think this early training accounts for much of my behavior today.
But then I went to graduate school (circa 1973), and things became more complicated. In my very first class I learned that some people had actually written papers on the benefits of what they called N = 1 designs. I was outspoken at this statistical heresy and I paid the price: I was forced (by Dr. Harold Yuker) to read and write about papers by Dukes ( 1965) and Shapiro ( 1964), a really difficult article by Rozeboom ( 1971), and something fairly new by Gottman ( 1973). I became aware of the importance of the "idiographic versus nomothetic" approaches to construct validation, and I began to understand the central concerns of "generalization" ( Crunbach et al., 1972). Although I was respectful of clinical practice, I thought that people were so different