Abstract
The occurrence/non-occurrence of an event is being observed at equidistant points of time. This yields a sequence of binary variables which are assumed to form a stationary time series. A second stationary binary sequence is observed independently of the first one. Four exact tests are proposed for the comparison of the two sequences. The four tests differ with respect to the parameters which are compared and the assumed dependence structure. Similar problems were considered by (1998) for dichotomous spatial data. However, due to the complexity of the spatial models only Markov chain Monte Carlo approximations were considered by these authors. We illustrate our exact tests by comparing the structure of two epidemiological data sets.
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References
Besag, J. E. (1972): Nearest-neighbour Systems and the Auto-logistic Model for Binary Data. Journal of the Royal Statistical Society, Series B, 34, 75–83.
Besag, J. (1974): Spatial Interaction and the Statistical Analysis of Lattice Systems (with Discussion). Journal of the Royal Statistical Society, Series B, 36, 192–236.
Knox, G. (1959): Secular Patterns of Congenital Oesophageal Atresia. British Journal of Preventive Social Medicine, 13, 222–226.
Krauth, J. (1998): Upper Bounds for the P-values of a Scan Statistic with a Variable Window. In: I. Balderjahn, R. Mathar, and M. Schader (eds.): Classification, Data Analysis, and Data Highways. Springer, Berlin, Heidelberg, New York, 155–163.
Krauth, J. (1999): Discrete Scan Statistics for Detecting Changepoints in Binomial Sequences. In: W. Gaul, and H. Locarek-Junge (eds.): Classification in the Information Age. Springer, Berlin, Heidelberg, New York, 196–204.
Lehmann, E. L. (1986): Testing Statistical Hypotheses. Second Edition. John Wiley & Sons, New York, Chichester, Brisbane, Toronto, Singapore.
Nagarwalla, N. (1996): A Scan Statistic with a Variable Window. Statistics in Medicine, 15, 845–850.
Sim, S. and Johnson, R. A. (1998): Comparisons of Spatially Correlated Binary Data. Statistics & Probability Letters, 39, 81–87.
Weinstock, M. A. (1981): A Generalized Scan Statistic Test for the Detection of Clusters. International Journal of Epidemiology, 10, 289–293.
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© 2002 Springer-Verlag Berlin Heidelberg
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Krauth, J. (2002). Exact Tests for the Comparison of Binary Data Structures in Time. In: Gaul, W., Ritter, G. (eds) Classification, Automation, and New Media. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55991-4_10
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DOI: https://doi.org/10.1007/978-3-642-55991-4_10
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