Robust testing of level changes in interrupted time-series analysis

Abstract

Ramsey and Ramsey [Ramsey, P.P. and Ramsey, P.H., 2003, Comparing lease-squares lines for testing level changes in interrupted time-series analysis. Journal of Statistical Computation and Simulation, 73, 31–44.] have shown that a composite procedure (CP) can provide accurate tests of level changes in interrupted time-series analysis. A CP combines the Mann–Wald procedure [Gottman, J.M., 1981, Time-Series Analysis (New York: Cambridge University Press): Mann, H.B. and Wald, A., 1943, On the statistical treatment of linear stochastic difference equations. Econometrica, 11, 173–220.] with the Kromrey and Foster-Johnson [Kromrey, J.D. and Foster-Johnson, L., 1996, Determining the efficacy of intervention: the use of effect sizes for data analysis in single-subject research. The Journal of Experimental Education, 65, 73–93.] regression procedure allowing for testing changes in level, as well as changes in both trend and level in the presence of trend effects in time-series data. Monte Carlo simulation was used to demonstrate Type I error rates for sample sizes from 5 to 20. A variety of composite procedures were found to provide such control.