Asymptotic approximation to the expected size of a selected subset

Abstract

An asymptotic approximation is given to the expectation of the size of a selected subset from a set of t objects, where the design is a balanced paired comparison experiment of n replicates. The paper also contains an excerpt (Table 4) of a table of expected sizes of the selected subset, expressed as proportions of t . The complete set of tables, which may be obtained by writing to the author, includes entries for combinations of t = 3(1) 20, n = 1(1)20(5)50(10)100 and preference probabilities p = 0.60(0.10)1.00 at each level of selection P * 0.75, 0.90, 0.95, 0.975, 0.99. Examples of applications are directed towards an optimization of designs for selection.