research hypotheses or establish the boundaries of parameter estimates. Perhaps the strongest suggestion for change that we can make is that researchers should collect a greater number of observations.
No psychologist would debate the notion that behavior changes over time, nor that behaviors are influenced by many interacting variables. Unfortunately, when investigators assess whether a systematic intervention influenced a given behavior that continued over time, there are many uncontrolled variables that can confound research findings. Among these confounds are carryover effects, cyclic behavior (see Beasley , Allison, & Gorman, chap. 9, this volume), and other time-varying events. By randomly assigning treatments to occasions, the effects of these serially dependent events may be reduced or even eliminated. Whenever possible, researchers should consider designs that include random assignments.
As we have seen, every statistical technique is affected by autocorrelated residuals. Because human behaviors typically occur in an ongoing temporal stream, autocorrelation is at least as likely as not. It is well established that statistical test values are overestimated by positive autocorrelation and underestimated in the presence of negative autocorrelation. It seems obligatory for researchers to choose designs, such as those that use randomization, to reduce the influence of autocorrelated effects. Additionally, they should examine results for autocorrelation and, if autocorrelations are present, they should choose statistical techniques that control for them.
When we started to work on this project several years ago, we were far more optimistic about the ease with which we could draw valid conclusions from single-case designs. We thought that if we had sufficient numbers of observations and state-of-the-art statistical techniques, single-case designs should present no more, and possibly even fewer problems, than should multisubject designs. More than 275 years ago, Alexander Pope ( 1711) penned the phrase, "For fools rush in where angels fear to tread." Somewhat foolishly and, definitely not angelic, we rushed to develop a compendium of techniques. We are more cautious now but we are not pessimistic. Rather, we believe that with better research designs and with the discovery of new statistical techniques, we can profit from the rich sources of information provided by single- case data.
Allison D. B., Faith M. S., & Gorman B. S. ( 1995, August). Type-I error in autocorrelated time series analyzed by randomization tests. Paper presented at the American Psychological Convention, New York.