We are interested in methods of analysis of unreplicated factorial experiments which provide strong control of error rates. Small fractions of 2^k factorial experiments are useful for screening many factors when few non-negligible effects are anticipated. Such screening experiments often utilize designs which are nearly saturated, saturated, or super-saturated, providing few or no error degrees of freedom. Lacking an independent variance estimator, a saturated design can be analyzed by comparing the relative magnitudes of either the normalized parameter estimates or the corresponding sums of squares. Many methods have been proposed for the analysis of saturated designs (see Hamada and Balakrishnan, 1998). Proposed methods are increasingly reflecting methods and ideas from multiple comparisons, but few of the methods are known to control error rates over all parameter configurations. Kinateder, Voss and Wang (2000) reviewed methods known to control error rates and discussed related open problems. In this talk, we will provide a current review of open problems and known results concerning the control of error rates in the analysis of saturated, nearly saturated, and super-saturated designs.

References:

1. Hamada, M. and Balakrishnan, N. (1998). Analyzing unreplicated factorial experiments: A review with some new proposals. Statistica Sinica, 8, 1--41.
2. Kinateder, K. K. J., Voss, D. T., and Wang, W. (2000). Analysis of saturated and super-saturated factorial designs: A review. In N. Balakrishnan (Ed.), Proceedings of the Indian International Statistical Association 1998 International Conference. Newark, New Jersey: Gordon and Breach. In press.