# Yes-No question in 2AFC staircase test

I understand the task of a 2AFC test is to select one of the two stimuli presented (e.g. the stronger one), whereas in Yes-No test there is only one stimulus presented. But is it ok to ask a Yes-No question (e.g. was there a difference between A and B?) in a test with 2 stimuli? and can it still be called a 2AFC test? (Or is it valid to do Yes-No test with two stimuli?)

I am asking this with regard to a threshold test using a 2AFC transformed staircase (2 down 1 up procedure). It'd be a lot easier for subject to respond whether there was a perceivable difference between two stimuli rather than having to choose the stronger one. As my main interest is to see just noticeable difference, which is stronger is not of a concern. However, I guess there must be a specific reason why one stimulus has to be chosen over the other in a 2AFC test (re bias and sensitivity?). And I wonder what would be the implication of using a Yes-No question instead.

Many thanks in advance for your answers.

• Are you asking about a same-different paradigm: ncbi.nlm.nih.gov/pubmed/18613624 Dec 8, 2018 at 0:01
• Thanks, but no it's not the test I'm asking about. Same-different paradigm uses a same stimuli pair and different stimuli pair for each trial, but what I am wondering about is whether I can do 1-up 2-down "2AFC" staircase asking "did you perceive a difference between A and B?" instead of "which one of A and B is the stronger one?".
– Lee
Dec 8, 2018 at 20:33
• So every trial you will present A and B? If they say there is no difference you will increase the difference between them and if they say there is a difference twice you will decrease the difference? Dec 8, 2018 at 20:36
• Yes precisely. 2AFC is about whether the answer is correct for each trial, but in my case it's about whether to perceive a difference or not. Actually, the paper you referenced is 4IAX test where two pairs of stimuli are presented, but I found simple AX same-different paradigm where only one pair of stimuli is presented. But still my question is whether this can be applied to staircase 1 up 2 down procedure.
– Lee
Dec 9, 2018 at 13:19
• You can use either technique. However from experience I can tell you that observers will prefer a 2AFC task than a same/different task. In a 2AFC task there is an objective correct answer. In a same/different task observers are free to place their criterion. They must decide "is this difference large enough that I would describe it as different?". Because they usually want to perform as well as possible it is actually more frustrating for them not to have a clearly objective task.
– user17122
May 4, 2020 at 16:21

## 1 Answer

Lets introduce some notation. Lets $$S_i$$, with $$i = 1 ,2$$, represents the different stimulus classes and $$R_j$$, with $$j = 1, 2$$, represents the different responses. In a one-interval task$$^1$$, $$S_1$$ is presented half the time and $$S_2$$ is presented half the time. In a typical two-interval task, stimulus $$U_1 = $$ is presented half the time and and $$U_2 = $$ is presented the other half.

The responses $$R_1$$/$$R_2$$ can be yes/no, a/b, up/down, or anything you want and it does not matter in either the one or two interval cases. In the two interval case, it is just as valid to ask did the first interval contain the signal: YES -- NO? as which interval contained the signal: 1 -- 2?

With a transformed staircase, you might run into problems. It is not clear exactly what you are proposing to do. If you always present $$U_1$$, or present $$U_1$$ half the time and $$U_2$$ the other half, then the response that causes you to increase the difference between $$S_1$$ and $$S_2$$ would always be $$R_j$$ (with whatever $$j$$ you arbitrarily choose based on your labeling of the responses). To get around this you could present some catch trials with $$$$ and maybe even some $$$$, but what happens if you get unlucky and get a bunch of $$$$ trials in a row. You will likely keep reducing the difference between $$S_1$$ and $$S_2$$, but that is strange since the signal level is not relevant in the catch trials.

While you can probably get away with it, there are likely better procedures/methods (e.g., dual pair comparison)

$$^1$$ I study audition so am used to talking about temporal intervals while sometimes in vision multiple stimuli are presented across different regions of the visual field. From a signal detection vantage, it doesn't matter.

• Thanks for your detailed answer. It's very helpful. The Yes-No question you refer implies hit/false alarm, which allows you to look at the data from signal detection theory point of view, right? According to my understanding, bias is cancelled out or at least reduced in 2AFC because there is equal chance of internal bias for choosing either S1 or S2. However, my Yes-No question simply asks "Did you hear any difference in loudness?" rather than "Was the first one louder" or "which one was louder"?
– Lee
Dec 11, 2018 at 18:07
• In this case, my concern is that there may be no way to make sure the bias is reduced because I am simply asking whether there was a difference, not which was louder, so there is no way to see hit/false alarm. I guess the traditional Yes/No test with a single stimulus has a similar issue?
– Lee
Dec 11, 2018 at 18:07
• I think asking "did you hear a difference" question is much easier for the subject to respond to, and more straightforward if you aim to find a threshold, but I haven't seen anyone using this approach. The AX paradigm is the closest one I found. Do you think this approach is justifiable other than the fact that it is potentially more prone to bias? Thanks!
– Lee
Dec 11, 2018 at 18:07
• @Lee yes bias is going to be a potential problem with your procedure. Why not use an oddball paradigm or a dual pair comparison? Dec 11, 2018 at 18:34
• Yes I think the 4IAX procedure might be most suitable for my purpose. Thanks for your comments!
– Lee
Dec 12, 2018 at 16:01