Abstract
The current review and analysis investigated the presence of serial dependency (or autocorrelation) in single-subject applied behavior-analytic research. While well researched, few studies have controlled for the number of data points that appeared in the time-series and, thus, the negative bias of the r coefficient, and the power to detect true serial dependency effects. Therefore, all baseline graphs that appeared in the Journal of Applied Behavior Analysis (JABA) between 1968 and 1993 that provided more than 30 data points were examined for the presence of serial dependency (N = 103). Results indicated that 12% of the baseline graphs provided a significant lag-1 autocorrelation, and over 83% of them had coefficient values less than or equal to (±.25). The distribution of the lag-1 autocorrelation coefficients had a mean of .10. Subsequent distributions of partial autocorrelations at lags two through seven had smaller means indicating that as the distance between observations increases (i.e., the lag), serial dependency decreased. Although serial dependency did not appear to be a common property of the single-subject behavioral experiments, it is recommended that, whenever statistical analyses are contemplated, its presence should always be examined. Alternatives for coping with the presence of significant levels of serial dependency were discussed in terms of: (a) using alternative statistical procedures (e.g., ARIMA models, randomization tests, the Shewhart quality-control charts); (b) correcting statistics of traditional parametric procedures (e.g., t, F); or (c) using the autocorrelation coefficient as an indicator and estimate of reliable intervention effects.
Similar content being viewed by others
REFERENCES
Baer, D. M. (1977). Perhaps it would be better not to know everything. Journal of Applied Behavior Analysis, 10, 167–172.
Busk, P. L., & Marascuilo, L. A. (1988). Autocorrelation in single-subject research: A counterargument to the myth of no autocorrelation. Behavioral Assessment, 10, 229–242.
DeProspero, A., & Cohen, S. (1979). Inconsistent visual analyses of intrasubject data. Journal of Applied Behavior Analysis, 12, 573–579.
Edgington, E. S. (1980a). Random assignment and statistical tests for one-subject experiments. Behavioral Assessment, 2, 19–28.
Edgington, E. S. (1992). Nonparametric tests for single-case experiments. In T. R. Kratochwill, & J. R. Levin (Eds.), Single-case research design and analysis: New directions for psychology and education (pp. 41–64). Hillsdale, NJ: Erlbaum.
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.
Gottman, J. M. (1981). Time-series analysis: A comprehensive introduction for social scientists. New York: Cambridge University Press.
Hartmann, D. P., Gottman, J. M., Jones, R. R., Gardner, W., Kazdin, A. E., & Vaught, R. S. (1980). Interrupted time-series analysis and its application to behavioral data. Journal of Applied Behavior Analysis, 13, 543–559.
Hibbs, D. A. (1974). Problems of statistical estimation and causal inference in time-series regression models. In H. L. Costner (Ed.), Sociological methodology (pp. 252–308). San Francisco: Jossey-Bass.
Huitema, B. E. (1985). Autocorrelation in applied behavior analysis: A myth. Behavioral Assessment, 7, 107–118.
Huitema, B. E. (1986). Autocorrelation in behavioral research: Wherefore art thou? In A. Poling, & R. W. Fuqua, (Eds.), Research methods in applied behavior analysis (pp.187–208). New York: Plenum Press.
Huitema, B. E. (1988). Autocorrelation: 10 years of confusion. Behavioral Assessment, 10, 253–294.
Huitema, B. E., & McKean, J. W. (1994). Reduced bias autocorrelation estimation: Three jackknife methods. Educational and Psychological Measurement, 54, 654–665.
Jones, R. R., Vaught, R. S., & Weinrott, M. (1977). Time-series analysis in operant research. Journal of Applied Behavior Analysis, 10, 151–166.
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.
Judd, C. M., & Kenny, D. A. (1981). Estimating the effects of social interventions. New York: Cambridge University Press.
Kazdin, A. E. (1980). Obstacles in using randomization tests in single-case experimentation. Journal of Educational Statistics, 5, 253–260.
Kazdin, A. E. (1982). Single-case research designs. New York: Oxford University Press.
Kazdin, A. E. (1984). Statistical analyses for single-case experimental designs. In D. H. Barlow & M. Hersen, Single case experimental designs: Strategies for studying behavior change (pp. 285–324). New York: Pergamon Press.
Kenny, D. A., & Judd, C. M. (1986). Consequences of violating the independence assumption in analysis of variance. Psychological Bulletin, 99, 422–431.
Kratochwill, T. R., & Brody, G. H. (1978). A perspective on the controversy over employing statistical inference and implications for research and training in behavior modification. Behavior Modification, 2, 291–307.
Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65, 297–303.
Matyas, T. A., & Greenwood, K. M. (1991). Problems in the estimation of autocorrelation in brief time series and some implications for behavioral data. Behavioral Assessment, 13, 137–157.
Michael, J. (1974). Statistical inference for individual organism research: Mixed blessing or curse? Journal of Applied Behavior Analysis, 7, 647–653.
Minium, E. W. (1978). Statistical reasoning in psychology and education. New York: John Wiley.
Ottenbacher, K. J. (1990). When is a picture worth a thousand p values? A comparison of visual and quantitative methods to analyze single-subject data. Journal of Special Education, 23, 436–449.
Parsonson, B. S., & Baer, D. M. (1986). The graphic analysis of data. In A. Poling & R. W. Fuqua (Eds.), Research methods in applied behavior analysis: Issues and advances (pp. 157–186). New York: Plenum Press.
Pavur, R., & Nath, R. (1984). Exact F tests in an ANOVA procedure for dependent observations. Multivariate Behavioral Research, 19, 408–420.
Pfadt, A., Cohen, I. L., Sudhalter, V., Romanczyk, R. G., & Wheeler, D. J. (1992). Applying statistical process control to clinical data: An illustration. Journal of Applied Behavior Analysis, 25, 551–560.
Phillips, J. P. N. (1983). Serially correlated errors in some single-subject designs. British Journal of Mathematical and Statistical Psychology, 36, 269–280.
Rowley, G. L. (1989). Assessing error in behavioral data: Problems of sequencing. Journal of Educational Statistics, 26, 273–284.
Rushe, R. H., & Gottman, J. M. (1993). Essentials in the design and analysis of time-series experiments. In G. Keren, & C. Lewis (Eds.), A handbook for data analysis in the behavioral sciences: Statistical issues (pp. 493–528). Hillsdale, NJ: Erlbaum.
Scheffe, H. (1959). The analysis of variance. New York: John Wiley.
Sharpley, C. (1986). Fallibility in the visual assessment of behavioural interventions: Time-series statistics to analyse time-series data. Behaviour Change, 3, 26–33.
Sharpley, C. F., & Alavosius, M. P. (1988). Autocorrelation in behavioral data: An alternative perspective. Behavioral Assessment, 10, 243–251.
Sideridis, G. D., & Greenwood, C. R., (1996). Evaluating treatment effects in single-subject behavioral experiments using quality control charts. Journal of Behavioral Education, 6, 203–211.
Suen, H. K., & Ary, D. (1989). Analyzing quantitative behavioral observation data. Hillsdale, NJ: Erlbaum.
Suen, H. K., & Ary, D. (1987). Autocorrelation in applied behavior analysis: Myth or reality? Behavioral Assessment, 9, 125–130.
Wampold, B. E., & Furlong, M. J. (1981). The heuristics of visual inference. Behavioral Assessment, 3, 79–82.
Wampold, B. E., & Worsham, N. L. (1986). Randomization tests for multiple-baseline designs. Behavioral Assessment, 8, 135–143.
Wheeler, D. J., & Chambers, D. S. (1992). Understanding statistical process control. Knoxville, TN: SPC Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sideridis, G.D., Greenwood, C.R. Is Human Behavior Autocorrelated? An Empirical Analysis. Journal of Behavioral Education 7, 273–293 (1997). https://doi.org/10.1023/A:1022895805201
Issue Date:
DOI: https://doi.org/10.1023/A:1022895805201