Journal of Psychopathology and Behavioral Assessment

, Volume 7, Issue 3, pp 191–205

The linear regression line as a judgmental aid in visual analysis of serially dependent A-B time-series data

  • Johannes Rojahn
  • Hans -Henning Schulze


The purpose of this study was to investigate the effects of different types and magnitudes of serial dependence (first-order moving average and autoregression) and of linear regression lines within experimental phases on the agreement between results of visual and results of statistical data analyses. The stimulus material consisted of computer-simulated A-B-design data graphs. The time series were generated with a constant variance, varying degrees of treatment effects (changes in level), five conditions of serial dependency, and with or without linear regression lines. The material was presented to three groups of student raters (n1=52, n2=14, n3=17) who rated the treatment effect in the graphs on a five-point scale. These ratings were compared with statistical results (time-series analyses). Each group had to interpret 70 graphs, 35 of which had regression lines. Data were analyzed by means of two three-factor and one four-factor ANOVA and by graphic display. The linear regression lines generally enhanced the agreement between the raters' estimations and the statistical results. Serial dependency also increased the agreement between the two analysis methods. However, with strong autoregression processes in the data, the raters tended to overestimate treatment effects relative to time-series analysis.

Key words

visual analysis time-series analysis regression line serial dependency 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baer, D. M., & Parsonson, R. S. (1981). Applied changes from steady state: Still a problem in the visual analysis of data. In C. M. Bradshaw, E. Szabadi, & E. Lowe (Eds.),Quantification of steady state operant behavior (pp. 273–285). Elsevier: North-Holland Biomedical Press.Google Scholar
  2. Box, G. E. P., & Jenkins, G. M. (1970).Time series analysis: Forecasting and control. San Francisco: Holden Day.Google Scholar
  3. DeProspero, A., & Cohen, S. (1979). Inconsistent visual analysis of intra-subject data.Journal of Applied Behavior Analysis, 12, 573–579.Google Scholar
  4. Furlong, M. J., & Wampold, B. E. (1982). Intervention effects and relative variation as dimensions in experts' use of visual inference.Journal of Applied Behavior Analysis, 15, 415–421.Google Scholar
  5. Gentile, J. R., Roden, A. H., & Klein, R. D. (1972). An analysis of variance model for the intrasubject replication design.Journal of Applied Behavior Analysis, 5, 193–198.Google Scholar
  6. Glass, G. V., Willson, V., & Gottman, J. M. (1975).Design and analysis of time-series experiments. Boulder: Colorado Associated University Press.Google Scholar
  7. Gottman, J. M., & Glass, G. V. (1978). Analysis of interrupted time-series experiments. In T. R. Kratochwill (Ed.),Single subject research. Strategies for evaluating change (pp. 197–235). New York: Academic Press.Google Scholar
  8. Jones, R. R., Weinrott, M., & Vaught, R. S. (1975). Visual vs. statistical inferences in operant research. Paper presented at the American Psychological Association Convention, Chicago.Google Scholar
  9. Jones, R. R., Weinrott, M. R., & Vaught, R. S. (1978). Effects of serial dependency on the agreement between visual and statistical inference.Journal of Applied Behavior Analysis, 11, 277–283.Google Scholar
  10. Knapp, T. J. (1983). Behavior analysts' visual appraisal of behavior change in graphic display.Behavioral Assessment, 5, 155–164.Google Scholar
  11. McCleary, R., & Hay, R. A. (1980).Applied time series analysis for the social sciences, London: Sage.Google Scholar
  12. Parsonson, B. S., & Baer, D. M. (1978). The analysis and interpretation of graphic data. In T. R. Kratochwill (Ed.),Single subject research: Strategies for evaluating change (pp. 101–165). New York: Academic Press.Google Scholar
  13. Revenstorf, D., & Keeser, W. (1979). Zeitreihenanalyse von Therapieverläufen — ein Überblick (Time series analysis of therapy development). In F. Petermann & F. J. Hehl (Eds.),Einzelfallanalyse (Single case analysis) (pp. 183–229). Munich: Urban & Schwarzenberg.Google Scholar
  14. Wampold, B. E., & Furlong, M. J. (1981). The heuristics of visual inference.Behavioral Assessment 3 79–92.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Johannes Rojahn
    • 1
  • Hans -Henning Schulze
    • 3
  1. 1.Western Psychiatric Institute and ClinicUniversity of Pittsburgh School of MedicinePittsburgh
  2. 2.Western Psychiatric Institute and ClinicPittsburgh
  3. 3.Phillips-University MarburgMarburgFRG

Personalised recommendations