Single subject design and analysis is an ideal. The primary advantage is maximal congruence between observation and phenomenon, that is, between the level of Measurement and the levels of Behavior and Phenomena in the Experimental Pyramid of Chapter 1. In addition, single subjects can be more readily studied over many sessions, which may reveal phenomena never seen in the common one-session experiments.
Two classes of designs have been used in single subject research. One class is treatment randomization design, in which the various treatments are presented to the subject in random order. Treatment randomization has the priceless advantage that it can yield independence of scores. All the methods of previous chapters then become applicable.
The other class is serial observation design, which involves repeated presentation of one treatment at a time to the subject. In the simple A–B design, for example, a series of trials under treatment A is followed by a series of trials under treatment B.
Analysis of serial observation data faces two difficult problems: reliability and validity. In the given A–B design, the first question is whether the A–B difference is reliable. The answer obviously involves comparison of the mean difference between treatments to the variability within treatments.
This reliability question is troubled by possible nonindependence of observations in the form of serial correlation between successive responses. Non-independence typically makes the data look more reliable than they really are. This is even more a problem for visual inspection than for formal statistics.
The second question is validity: Can the A–B difference be attributed to the treatment conditions themselves, or are there likely confounds? The A–B design has two obvious major confounds: confounds with shifts in the external environment; and confounds with order effects in the subject, such as learning, adaptation, treatment-specific transfer, and illness. Various methods have been developed to deal with these confounds, especially repeated A–B series and baseline treatment interpolated between successive experimental treatments.
Although single subject design is widely used and essential in diverse areas, it has been completely neglected in graduate statistics texts. With this neglect has gone corresponding neglect of the foregoing methodological problems. Not much is known about serial correlation, in particular, despite its importance. This chapter aims for better integration of empirics and statistics in this vital area of experimental analysis.