Gene expression arrays present unique challenges for statistical inference. They typically small number of replicated expression values in array studies make the use of standard parametric statistical tests problematic. Such test have low sensitivity and return potentially inaccurate probability values. This paper describes novel alternative statistical modeling procedures which circumvent these difficulties by pooling random error estimates obtained from replicate expression values. The procedures, which can be used with both micro- and macro-arrays, include outlier detection, confidence intervals, statistical test of differences between conditions, and statistical power analysis for determining number of replicates needed to detect between-condition differences of specified magnitude. The methods are illustrated with experimental data.