Gene duplications are a major source of raw material for evolution and a likely contributor to the diversity of life on earth. Duplicate genes (i.e., homeologs, in the case of a whole genome duplication) may retain their ancestral function, sub- or neofunctionalize, or be lost entirely. A primary way that duplicate genes may evolve new functions is by altering their expression patterns. Comparing the expression patterns of duplicate genes may give clues as to whether any of these evolutionary processes have occurred. Here we develop a likelihood ratio test for the analysis of the expression ratios of duplicate genes across two conditions. We demonstrate an application of this test by comparing homeolog expression patterns of 1,448 homeologous gene pairs using RNA-seq data generated from the leaves and petals of a tetraploid monkeyflower (Mimulus luteus). Using simulated data, we show the sensitivity of this test to different levels of homeolog expression bias. While we have developed this method for the analysis of duplicate genes, it can be used for comparing expression patterns of any two genes (or alleles) across any two conditions.