TESTING AND VIEWING SYMMETRY IN CONTINGENCY-TABLES, WITH APPLICATION TO READERS OF FISH AGES

If there are several methods for assigning an integer score to somethi ng and the true value is unknown (or even nonexistent), then one can c ompare the methods only with each other. We develop a new approach to detecting nonrandom differences among methods based on subtracting the smallest reading from all the readings on a specimen before combining counts into a contingency table. Then there are three methods, the ap proach projects the cube of possible triples of scores into a regular hexagon. It conceals some information: but patterns that survive proje ction can become easier to detect both formally and visually. Summariz ing data by projection may be necessary for achieving sufficient power to detect that methods are not equivalent. We illustrate with data on age determination of scallops from shell markings.