A combination of configural frequency analysis (CFA) and time-series analysis is proposed for studying the effects of psychotherapy. By means of Two-sample CFA the multivariate behavior patterns observed in clients for each session are reduced to a zero-one criterion. For the resulting binary sequences a first-order Markov dependence is assumed. Using results on intercalary independence and the truncation property of Markov processes we can test nonparametrically for therapy effects in single-case studies. Procedures for combining and comparing the effects of independent single-case studies are described. The performance of a single-case analysis is demonstrated for an empirical data set from therapy research.
Key words: Psychotherapy research, Two-sample CFA, single-case studies, time-series analysis
For several reasons it is difficult to show that psychotherapies have positive effects. One problem is that it is quite often not clear which kind of effect the researcher is looking for. In Krauth (1983a) we made a difference between the measurement of effect, of success and of change. In most cases, the therapist, either in cooperation with the client or alone, formulates the target of the therapy, and if both therapist and client agree at the end of the therapy that this object has been achieved it is claimed that the therapy was successful. It is obvious that this kind of measuring the success of a therapy is very subjective. Often a multivariate criterion of success is used and the therapy is claimed to be successful if at least some of the components of the criterion seem to be improved. In most cases it is neither asked whether the criterion is realistic, e.g. whether it could be achieved by a normal subject, nor whether it reflects the behavior of a normal subject. For these reasons it is often only claimed at the end of a therapy that the therapy has had a positive effect, i.e. the state of the client seems to be improved in comparison with the beginning of the therapy even if this observed effect may be in no relation to a criterion of success which had been formulated before the therapy started. In practice, even this very weak criterion of a positive outcome is often not applicable and at least the therapist may be often inclined to formulate that the therapy has been useful for the client because it has caused a certain change of behavior and this is considered as a kind of success by itself.
In my opinion, neither an observed success nor an observed effect nor an observed change of behavior can justify post hoc the performance of a therapy. Even if we could perform a controlled randomized double-blind study - which is not really possible in psychotherapy - in order to measure the effectiveness of a therapy on the basis of a criterion of success, effect or change as described above, it cannot be ruled out that a given therapy had no effect at all or even a harmful effect. The reason for this is obvious: Anything may happen if subjective or arbitrary measures of success (or effect or change) are used.
In the following we propose a procedure by which at least some difficulties connected with the considered problem are addressed, e.g. the selection of an objective multivariate criterion and the dependence of observations in longitudinal studies.
2. Selection of a criterion
The first step is the selection of an appropriate measuring device or test by which the behavior of a client can be measured at given points of time. The result of a measurement can be a multivariate vector of measurements where we assume that the dimension of the vector (related to one point of time) is not too high (a maximum of 6 components might be appropriate). For example, we might consider the items or subtests of a global rating scale describing the behavior or state of health of the client. Here, it is important that this scale is sensitive to change (Krauth, 1983b; Krauth, 1995, pp. …