A-efficient block designs for symmetric parallel line assays.

Abstract

A-efficient block designs are obtained for symmetric parallel line assays. These designs ensure estimability of all the three important contrasts, namely preparation, combined regression and parallelism. Two general methods of construction are given. The first follows on the lines of Chai, Das and Dey (2001) and the second utilizes disconnected block designs. The designs obtained from the first method may not always be A-optimal even for the estimation of preparation and combined regression contrasts, but are more efficient for estimation of all the three important contrasts than the designs given by Chai, Das and Dey (2001). A catalogue of 41 A-efficient block design 3<=m<= 6, 4 <= k<=10, bk <= 50 is given, where m denotes the number of doses for standard and test preparations, k is the block size and b the number of blocks. The disconnected block designs obtained in this investigation are A-optimal for estimation of all three contrasts of interest. A catalogue of 28 such designs 3<=m<= 6, k = 4, bk<=50 is also included.