On selection procedures based on ranks - Counterexamples concerning least favorable configurations

IN RECENT YEARS CONSIDERABLE ATTENTION HAS BEEN GIVEN TO CERTAIN MULTIPLE-DECISION PROCEDURES BASED ON RANK SUMS FOR THE ONE-WAY LAYOUT. A THEORETICAL MODEL IS PRESENTED. IN PROBLEM I THE EXPERIMENTER SETS A PREASSIGNED PROBABILTY THRESHOLD AND REQUIRES THAT THE PROCEDURE HE USES HAVE THE PROPERTY THAT THE PROBABILITY OF CORRECT SELECTION IS GREATER THAN OR EQUAL TO THE PROBABILITY THRESHOLD WHENEVER THE LARGEST THETA VALUES ARE AT LEAST LARGER THAN THE REST OF THE THETA VALUES. IN PROBLEM II THE EXPERIMENTER SETS ONLY THE PROBABILITY THRESHOLD VALUE AND REQUIRES THAT WITH PROBABILITY GREATER THAN OR EQUAL TO PROBABILITY THRESHOLD, THE SELECTED SUBSET CONTAINS THE INDEX OF THE LARGEST THETA VALUE. THIS SITUATION MIGHT ARISE IN THE FIRST STAGE OF SCREENING CERTAIN TYPES OF ROADS. ONE WOULD WANT TO REDUCE THE NUMBER OF TYPES OF ROADS WHICH ARE TO BE SUBMITTED TO FURTHER TESTS BUT AT THE SAME TIME BE REASONABLY SURE OF NOT ELIMINATING ANY TYPE WHICH HAS GREAT POTENTIALITY AS TO ITS USE. THIS PAPER EXAMINES CERTAIN PROCEDURES WHICH HAVE BEEN CLAIMED TO BE SOLUTIONS TO THE ABOVE PROBLEMS. SPECIFIC EXAMPLES ARE CITED WHICH SHOW THAT SOME OF THE ASSERTIONS IN THE LITERATURE ARE NOT TRUE. NO SOLUTION TO THE PROBLEM IS OFFERED. /AUTHOR/