The venerable auction house of Snootly & Snobs will soon be putting three fine 17th-and 18th-century violins, A, B, and C, up for bidding. A certain musical arts foundation. wishing to determine which of these instruments to add to its collection, arranges to have them played by each of 10 concert violinists. The players are blindfolded, so that they cannot tell which violin is which; and each plays the violins in a randomly determined sequence (BCA, ACB, etc.)
The violinists are not informed that the instruments are classic masterworks; all they know is that they are playing three different violins. After each violin is played, the player rates the instrument on a 10-point scale of overall excellence (1 = lowest, 10 = highest). The players are told that they can also give fractional ratings, such as 6.2 or 4.5, if they wish. The results are shown in the table below. For the sake of consistency, the n = 10 players are listed as "subjects."
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