Regression models used in the analysis of interrupted time-series designs assume statistically independent errors. Four methods of evaluating this assumption are the Durbin-Watson (D-W), Huitema-McKean (H-M), Box-Pierce (B-P), and Ljung-Box (L-B) tests. These tests were compared with respect to Type I error and power under a wide variety of error models and sample sizes. Although the B-P and L-B tests are portmanteau methods that incorporate information from a large portion of the autocorrelation function, the more focused D-W and H-M first-order autoregressive tests are shown to be considerably more powerful. The popular L-B test has unacceptable Type I error and should not be used in the context of the intervention model applied in this study.
Andrews, D.W.K., & Ploberger, W. (1996). Testing for serial correlation against an ARMA (1, 1) process. Journal of the American Statistical Association,91, 1331-1342.
2.
Berry, W.D., & Lewis-Beck, M.S. (1986). Interrupted time series . In W. D. Berry & M. S. Lewis-Beck (Eds.), New tools for social scientists: Advances and applications in research methods (pp. 209-240). Newbury Park, CA: Sage.
3.
Box, G.E.P., Jenkins, G.M., & Reinsel, G.C. (1994). Time series analysis: Forecasting and control (3rd ed.). Englewood Cliffs, NJ: Prentice Hall.
4.
Box, G.E.P., & Pierce, D.A. (1970). Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association,65, 1509-1526.
5.
Box, G.E.P., & Tiao, G.C. (1965). A change in level of non stationary time series . Biometrika, 52, 181-192.
6.
Box, G.E.P., & Tiao, G.C. (1975). Intervention analysis with application to economic and environmental problems. Journal of the American Statistical Association,70, 70-92.
7.
Cohen, J., Cohen, P., West, S.G., & Aiken, L.S. (2003). Applied multiple regression/correlation for the behavioral sciences (3rd ed.). Mahwah, NJ: Lawrence Erlbaum.
8.
Durbin, J., & Watson, G.S. (1950). Testing for serial correlation in least squares regression. Biometrika, 37, 409-428.
9.
Durbin, J., & Watson, G.S. (1951). Testing for serial correlation in least squares regression—II. Biometrika, 38, 159-178.
10.
Enders, W., Sandler, T., & Cauley, J. (1990). Assessing the impact of terrorist-thwarting policies: An intervention time series approach. DefenseEconomics, 2, 1-18.
11.
Glass, G.V., Willson, V.L., & Gottman, J.M. (1975). Design and analysis of time series experiments . Boulder: Colorado Associated University Press.
Huitema, B.E., & McKean, J.W. (2000a). Design specification issues in time-series intervention models. Educational and Psychological Measurement, 60, 38-58.
16.
Huitema, B.E., & McKean, J.W. (2000b). A simple and powerful test for autocorrelated errors in OLS intervention models. Psychological Reports, 87, 3-20.
17.
Johnston, J. (1984). Econometric methods (3rd ed.). New York: McGraw-Hill.
18.
Kahaner, D., Moler, C., & Nash, S. (1989). Numerical methods and software. Englewood Cliffs, NJ: Prentice Hall.
19.
Koopmans, L.H. (1995). The spectral analysis of time series. San Diego, CA: Academic Press.
20.
Kutner, M.H., Nachtsheim, C.J., & Neter, J. (2004). Applied linear regression models (4th ed.). New York: McGraw-Hill.
21.
Ljung, G.M., & Box, G.E.P. (1978). On a measure of lack of fit in time series models . Biometrika, 65, 297-303.
22.
Marsaglia, G., & Bray, T.A. (1964). A convenient method for generating normal variables . SIAM Review, 6, 260-264.
23.
McCleary, R., & Hay, R.A., Jr. (1980). Applied time series analysis for the social sciences. Beverly Hills, CA: Sage .
24.
McKnight, S., McKean, J.W., & Huitema, B.E. (2000). A double bootstrap method to analyze linear models with autoregressive error terms. Psychological Methods, 5, 87-101.
25.
Minitab, Inc. (2004). Minitab 14.0 [Computer software]. State College, PA: Author.
26.
Reichardt, C.S., & Mark, M. (1998). Quasi-experimentation. In L. Bickman & D. J. Rog (Eds.), Handbook of applied social research methods (pp. 193-228). Thousand Oaks, CA: Sage.
27.
Shadish, W.R., Cook, T.D., & Campbell, D.T. (2002). Experimental and quasi-experimental designs for generalized causal inference. New York: Houghton Mifflin.
28.
Shumway, R.H. (1988). Applied statistical time series analysis. Englewood Cliffs, NJ: Prentice Hall.
29.
SPSS, Inc. (2004). SPSS 13.0 [Computer software]. Chicago: Author .
30.
Velicer, W.F., & Fava, J.L. (2003). Time series analysis. In J. A. Schinka, & W. F. Velicer (Eds.), Research methods in psychology (pp. 581-606). New York: John Wiley.
31.
West, M., Harrison, P.J., & Migon, H.S. (1985). Dynamic generalised linear models and Bayesian forecasting (with discussion). Journal of the American Statistical Association,80, 73-97.
