It is emphasized that two types of errors are made in the testing of a hypothesis, false positive (type I) and false negative (type II). Genome-wide scans involving many markers give rise to the problem of multiple testing, which results in an increased number of false positives, thus necessitating a correction in the nominal significance level. While the literature has concentrated reasonably heavily on controlling false positives in genomic scans, the need to control false negatives has been largely neglected. This chapter highlights this need and attempts to strike a balance between the two error types. The need to develop alternative methods for discriminating between false positives and true positives is also stressed.