The object of the present investigation is to study some properties of a class of Spearman rank statistics and to apply these results in studying the properties of a sequential procedure proposed in Section 3. The problem is one of bounded length confidence intervals for simple regression coefficients in linear models where both variables are subject to error. It is shown that the proposed procedure is asymptotically ‘consistent’ and ‘efficient’ in the sense of Chow and Robbins [3].