Simultaneous confidence intervals for the population cell means, for two-by-two factorial data, that utilize uncertain prior information
Abstract
Consider a two-by-two factorial experiment with more than 1 replicate. Suppose that we have uncertain prior information that the two-factor interaction is zero. We describe new simultaneous frequentist confidence intervals for the 4 population cell means, with simultaneous confidence coefficient 1-alpha, that utilize this prior information in the following sense. These simultaneous confidence intervals define a cube with expected volume that (a) is relatively small when the two-factor interaction is zero and (b) has maximum value that is not too large. Also, these intervals coincide with the standard simultaneous confidence intervals obtained by Tukey's method, with simultaneous confidence coefficient 1-alpha, when the data strongly contradict the prior information that the two-factor interaction is zero. We illustrate the application of these new simultaneous confidence intervals to a real data set.
Keywords
Cite
@article{arxiv.0812.1625,
title = {Simultaneous confidence intervals for the population cell means, for two-by-two factorial data, that utilize uncertain prior information},
author = {Paul Kabaila and Khageswor Giri},
journal= {arXiv preprint arXiv:0812.1625},
year = {2015}
}
Comments
The exposition has been improved. In particular, the introduction has been improved and some new references have been added