A critical issue for many watermarking applications is the probability that the watermark detector incorrectly identifies an unwatermarked work as watermarked. This false positive probability is well understood for detectors that use a normalized correlation detection measure. However, in an effort to increase watermark robustness, a number of researchers have proposed detection measures that combine multiple normalized correlations. One such measure is the ratio of the largest normalized correlation to the second largest when an extracted vector is compared to multiple reference vectors. In this paper we analyze the false positive probability of the correlation ratio detection measure under a reasonable assumption about the distribution of unwatermarked works. We derive an analytic formula for the false positive probability and validate this with empirical data.