Uses of the coefficient of detection and sample size determination

The coefficient of detection (CD) is said to represent the minimal difference statistically detectable with a t-test at some preselected alpha. Although the CD does not explicitly take statistical power into consideration, it is mathematically and empirically demonstrable that the CD operates at approximately 50% power. The CD, as reported in the Collaborative Behavioral Teratology Study (CBTS), also applies only to hypotheses about the difference between one sample mean and a selected standard value, and, consequently, does not apply to a situation where a difference between two sample means is considered. Therefore, the low one-sample CDs reported in the CBTS cannot be used to approximate sample sizes for purposes of meeting the requirement by the Environmental Protection Agency that a 20% difference between two sample means (e.g., control vs. experimental groups) should be detected with a power of 80% (or 90%) at a 5% certainty level.