Statistics of response slopes.

Daubenspeck and Ogden in a recent paper recommended the use of directional statistics in the analysis of response slopes, and their advice has been followed by other workers. Their method is not valid, since it does not follow directly from their model. An efficient estimator of the slope (i.e., an estimator with minimum variance) is well known and is given here with a confidence interval for the true slope. They were also concerned with the two-sample problem to compare the slopes from two different samples. The method for this is more complicated but is summarized here. The likelihood ratio test and point and interval estimates are given. We discuss Daubenspeck and Ogden's example and the reason why, despite its invalidity, their method gave good results using their own data. Their data are also used to illustrate the methods described in this paper, and examples are given to highlight the practical differences between the two methods. Step-by-step procedures are included in the appendixes to enable readers to use these methods.