Confidence
If only one ABX trial were performed, random guessing would incur a 50% chance of choosing the correct answer, the same as flipping a coin. In order to make a statement having some degree of confidence, many trials must be performed. By increasing the number of trials, the likelihood of statistically asserting a person's ability to distinguish A and B is enhanced for a given confidence level. A 95% confidence level is commonly considered statistically significant. The company QSC, in the ABX Comparator user manual, recommended a minimum of ten listening trials in each round of tests.
Results required for a 95% confidence level:
| Number of trials | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Minimum number correct | 9 | 9 | 10 | 10 | 11 | 12 | 12 | 13 | 13 | 14 | 15 | 15 | 16 | 16 | 17 | 18 |
QSC recommended that no more than 25 trials be performed, as listener fatigue can set in, making the test less sensitive (less likely to reveal one's actual ability to discern the difference between A and B). However a more sensitive test can be obtained by pooling the results from a number of such tests using separate individuals or tests from the same listener conducted in between rest breaks. For a large number of total trials N, a significant result (one with 95% confidence) can be claimed if the number of correct responses exceeds . Important decisions are normally based on a higher level of confidence, since an erroneous "significant result" would be claimed in one of 20 such tests simply by chance.
Read more about this topic: ABX Test
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—Andrew Jackson (1767–1845)
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—Plato (c. 427–347 B.C.)