Single Subject Designs in Biomedicine by Janine E. Janosky Terry M. Libkuman Shelley L. Leininger & Michael P. Hoerger

Author:Janine E. Janosky, Terry M. Libkuman, Shelley L. Leininger & Michael P. Hoerger
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht

4.7.9 The C Statistic

According to Krishef [20], the C statistic can be used in determining whether there are abrupt changes in level, but only when there are minimal changes in slope or direction. The C statistic can be used to test the stability of the baseline, as well as comparing the baseline with the treatment phases. The latter is accomplished by determining whether the slopes are different for the baseline and treatment phases. This statistic requires a minimum of 8 observations. The advantages of this statistic are that it can be used to determine the effectiveness of the treatment with 8 or more observations, even though the data may be serially dependent. Furthermore, the statistic is simple to calculate especially relative to the more complicated and consuming analyses dealing with time series data {e.g., ARIMA (auto-regressive integrated moving averages; Houle [21])}. One disadvantage includes the failure of the statistic to detect abrupt changes in direction of the function. A second disadvantage is the effect on statistical power. Simply having more data points when the baseline and treatment are combined for analysis may lead to statistical significance , whereas only analyzing the baseline may not. See Jones [44] and Krishef [20] for additional discussion.

What should the role of inferential statistics be in single subject design research? There is considerable diversity of opinion regarding the utility of inferential statistics in single subject research. Some have relied largely on visual analysis [15], arguing that clinical significance requires large effects that can be easily interpreted using visual analysis, and statistical analysis may be misleading if small effects are found to be significant [2, 4]. Barlow et al. [4] further state that one may find statistical significance with considerable error, which may indicate the treatment is effective for some individuals and not others. Essentially, trends and intra-subject averaging may mask the variability in the data. Finally, Kazdin [2] has argued that because of the pervasiveness of statistical inferential testing in the sciences, researchers may fail to conduct single subject research on a promising topic or change the design because there is no statistical analysis available to evaluate the data. Furthermore, Kazdin [2] has discussed the debate regarding whether inferential statistics should be used and whether the data from single subject designs meet the assumptions of parametric statistics. Kazdin [2] states that statistics can be used when baselines are unstable, whether the intervention is reliably different from the baseline, when there is considerable intra-subject variability, and during the investigation of new areas where weak effects may be detected, but show some promise for future research. Kazdin [2, 14] has recommended the use of parametric statistics under these conditions, if the assumptions of parametric statistics can be satisfied. Unfortunately, it is rare that these assumptions can be met because of the inherent characteristics of single subject research. A more conservative approach is to use statistics as a supplement to visual analysis [16, 20, 21] and possibly to restrict their use to descriptive statistics, as the requirements for descriptive statistics are more readily met for single subject designs [45].

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