Click here to purchase the entire book in PDF format. Two-alternative forced choice (TAFC or 2AFC) Let's say that you want to do a test to determine what the smallest perceptible difference in loudness is. This would be better known as a Just Noticeable Difference or JND. You can test for this by playing two stimuli (the same sound, but with two different loudness levels) and asking ``Which sound was louder?'' This is called a two-alternative forced choice (TAFC or 2AFC test because the subject is forced to make a choice between two stimuli, even if he or she cannot detect a difference. This probably sounds a little like a paired-comparison test, and as far as the subject is concerned, these two tests are the same. The difference is is how the questions change throughout the test. For example, let's think of the loudness test that I just described. You make stimulus A 6 dB louder than stimulus B, and ask which is louder? The subject answers correctly (A is louder), so you repeat the test, this time with B only 3 dB louder than A. Ask again.... Each time the subject gets the correct answer, you make the difference in level smaller. Each time the subject gets the wrong answer, you make the difference in level bigger. So, in a TAFC test, the difference is adapting to the response the subject gives. As the subject gets closer and closer to the JND, they'll start alternating between correct and incorrect answers. If the difference is greater than the JND, then they will probably get the correct answer, the difference is reduced to less than the JND, and they have a 50% chance of getting the wrong answer, so the difference is increased to greater than the JND and so on and so on. This can go on forever, so, we stop asking questions after a given number of reversals. This means that you constantly keep track of correct and incorrect answers, therefore decreases and increases in the difference that you're testing. After a number of reversals (from decreases to increases or vice versa) you stop the test and move on to the next one. This is illustrated in Figure 5.19. Figure 5.19: An example of the results of a TAFC test looking for the perceptible difference in loudness between two stimuli. The ``reversals'' cause by a change from an incorrect to a correct answer (or the opposite) are indicated in red. In this case, the test was stopped after five reversals. Take a look at the example results shown in Figure 5.19. This shows a test where the level difference between two stimuli was changed, and the subject was asked which of the two stimuli was loudest. If the subject answered correctly, then the difference in level was reduced by 1 dB. If the subject got the wrong answer, then the level was increased by 1 dB. The test was stopped after 5 reversals. So, to get the ``answer'' to the question (what is the just noticeable difference in level for this subject and this program material?) we take the level differences at the 5 reversals (0 dB, 1 dB, 0 dB, 2 dB and 0 dB) and find the mean (0.6 dB) and that's the answer. There are a couple of other issues to mention here... If you look at the first 6 responses, you can see that the subject got these all correct, therefore the level difference was reduced each time. This is called a run - a consecutive string of correct (or incorrect) answers. Also, you can modify the way the test changes the level. For example, maybe you want to say that if the subject gets the answer correct, you drop the level difference by 1 dB, but if they get it incorrect, you increase by 3 dB. This is not only legal, but standard practice. You can choose how your results reflect the real word in this way. This is described in a paper that is cited everywhere by Levitt [Levitt, 1971] and we'll talk about later. If you're doing any number of serious listening tests, you should get your hands on a copy of this paper. One important thing to remember about a TAFC test is that the subject must choose one or the other stimuli. They can never answer ``I don't know'' or ``I can't hear a difference.'' Interestingly, it turns out that, if you don't allow people to say ``I don't know'' then they still might give you the correct answer, even through they aren't able to tell that they're giving the right answer. This is why you force them to choose - you decide when they don't know instead of them deciding for you.