Automatic selection of the proper family for simultaneous confidence intervals
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Statisticians often employ simultaneous confidence intervals to reduce the likelihood of their drawing false conclusions when they must make a number of comparisons. To do this properly, it is necessary to consider the family of comparisons over which simultaneous confidence must be assured. Sometimes it is not clear what family of comparisons is appropriate. We describe how computer software can monitor the types of contrasts a user examines, and select the smallest family of contrasts that is likely to be of interest. We also describe how to calculate simultaneous confidence intervals for these families using a hybrid of the Bonferroni and Scheffé methods. Our method is especially suitable for problems with discrete and continuous predictors.
Keywordscontrasts Bonferroni inequality Scheffe method
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- DuMouchel, W. H. and Lane, T. P. (1989) Simultaneous confidence intervals in multiple regression. Computer Science and Statistics: 21st Symposium on the Interface, ed. K. Berk and L. Malone, pp. 370–375. American Statistical Association, Alexandria, VA.Google Scholar
- Hayter, A. J. (1989) Pairwise comparisons of generally correlated means. Journal of the American Statistical Association, 84, 208–213.Google Scholar
- Hochberg, Y. and Tamhane, A. C. (1987) Multiple Comparison Procedures. Wiley, New York.Google Scholar
- Hunter, D. (1976) An upper bound for the probability of a union. Journal of Applied Probability, 13, 597–603.Google Scholar
- Lane, T. P. and DuMouchel, W. H. (1993) Simultaneous confidence intervals in multiple regression. American Statistician, 48.Google Scholar
- Lebow, W. (1989) Enforcing a hierarchy of terms in a multiple regression model. Computer Science and Statistics: 21st Symposium on the Interface, pp. 364–369. American Statistical Association, Alexandria, VA.Google Scholar
- Miller, R. G. (1981) Simultaneous Statistical Inference. Springer-Verlag, New York.Google Scholar
- RS/Explore Statistical Appendices (1992) BBN Software Products Corporation, Cambridge, MA.Google Scholar
- Seber, G. A. F. (1977) Linear Regression Analysis. Wiley, New York.Google Scholar
- Worsley, K. J. (1982) An improved Bonferroni inequality and applications. Biometrika, 69, 297–302.Google Scholar