12.9 A manufacturer of ice cream carried out a taste preference test on seven varieties of ice cream, denoted by A, B, C, D, E, F, G. The subjects were a random sample of 21 tasters and each taster had to compare only three varieties. Each pair of varieties is presented together three times, to a subset of seven of the tasters, with the design shown below repeated each of the three times.

Taster Varieties Presented 1 A B D 2 B C E 3 C D F 4 D E G 5 E F A 6 F G B 7 G A C The ranks resulting from the three repetitions are shown below with each rank corresponding to the variety indicated above. For example,

the rank 3 by taster 12 is for variety E. Determine whether there is a positive association between the rankings.
Taster Ranks Taster Ranks Taster Ranks 1 2 1 3 8 2 1 3 15 2 1 3 2 1 2 3 9 2 1 3 16 1 2 3 3 2 3 1 10 1 3 2 17 3 2 1 4 3 2 1 11 3 2 1 18 2 1 3 5 3 1 2 13 2 3 1 20 2 1 3 7 1 3 2 14 1 3 2 21 2 1 3