Array-based comparative genomic hybridization (ABCGH) is an emerging high-resolution and high-throughput molecular genetic technique that allows genome-wide screening for chromosome alterations associated with tumorigenesis. Like the cDNA microarrays, ABCGH uses two differentially labeled test and reference DNAs which are cohybridized to cloned genomic fragments immobilized on glass slides. The hybridized DNAs are then detected in two different fluorochromes, and the significant deviation from unity in the ratios of the digitized intensity values is indicative of copy-number differences between the test and reference genomes. Proper statistical analyses need to account for many sources of variation besides genuine differences between the two genomes. In particular, spatial correlations, the variable nature of the ratio variance and non-Normal distribution call for careful statistical modeling. We propose two new statistics, the standard t-statistic and its modification with variances smoothed along the genome, and two tests for each statistic, the standard t-test and a test based on the hybrid adaptive spline (HAS). Simulations indicate that the smoothed t-statistic always improves the performance over the standard t-statistic. The t-tests are more powerful in detecting isolated alterations while those based on HAS are more powerful in detecting a cluster of alterations. We apply the proposed methods to the identification of genomic alterations in endometrium in women with endometriosis.