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Subjects presented with sets of three samples, two of distilled water and one of tap water, were significantly more consistent in choosing the tap water as preferable than they were in identifying it as the odd sample in the set. The result is opposite to the prediction of high-threshold models of sensory discrimination, which say that if a difference is not noticed, preferences will be random, whereas if a difference is noticed, preferences may still be in either direction. The result can be quantitatively explained by a model advanced by Frijters to explain an analogous anomaly found with the triangle test used in the food industry. Applying his model to the observed proportions yields essentially equivalent estimates of sensory difference (d' = 1.5, approximately) from the two tasks, and a direction of preference almost unanimously in favor of the tap water that was used. Since the model predicts that the proportion of subjects choosing the odd item will depart further from chance in the preference task than in the oddity task, the former has greater power to reject the null hypothesis of no sensory difference if one exists and if preference is overwhelmingly in one direction.

Preference can be more powerful than detection of oddity as a test of discriminability