Improved statistical inference from DNA microarray data using analysis of variance and a Bayesian statistical...

We describe statistical methods based on the t test that can be conveniently used on high density array data to test for statistically significant differences between treatments. These t tests employ either the observed variance among replicates within treatments or a Bayesian estimate of the variance among replicates within treatments based on a prior estimate obtained from a local estimate of the standard deviation. The Bayesian prior allows statistical inference to be made from microarray data even when experiments are only replicated at nominal levels. We apply these new statistical tests to a data set that examined differential gene expression patterns in IHF(+) and IHF(-) Escherichia coli cells (Arfin, S. M., Long, A. D., Ito, E. T., Tolleri, L., Riehle, M. M., Paegle, E. S., and Hatfield, G. W. (2000) J. Biol. Chem. 275, 29672-29684). These analyses identify a more biologically reasonable set of candidate genes than those identified using statistical tests not incorporating a Bayesian prior. We also show that statistical tests based on analysis of variance and a Bayesian prior identify genes that are up- or down-regulated following an experimental manipulation more reliably than approaches based only on a t test or fold change. All the described tests are implemented in a simple-to-use web interface called Cyber-T that is located on the University of California at Irvine genomics web site.