<p>Lets introduce some notation. Lets <span class="math-container">$S_i$</span>, with <span class="math-container">$i = 1 ,2$</span>, represents the different stimulus classes and <span class="math-container">$R_j$</span>, with <span class="math-container">$j = 1, 2$</span>, represents the different responses. In a <em>one-interval</em> task<span class="math-container">$^1$</span>, <span class="math-container">$S_1$</span> is presented half the time and <span class="math-container">$S_2$</span> is presented half the time. In a typical two-interval task, stimulus <span class="math-container">$U_1 = &lt;S_1,S_2&gt;$</span> is presented half the time and and  <span class="math-container">$U_2 = &lt;S_2,S_1&gt;$</span> is presented the other half.</p>

<p>The responses <span class="math-container">$R_1$</span>/<span class="math-container">$R_2$</span> 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 <em>did the first interval contain the signal: YES -- NO?</em> as <em>which interval  contained the signal: 1 -- 2?</em></p>

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

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

<p><span class="math-container">$^1$</span> 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. </p>

CC BY-SA 4.0
2018-12-11T18:07:03.777Z
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
CC BY-SA 4.0
2018-12-11T18:07:26.330Z
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
CC BY-SA 4.0
2018-12-11T18:07:29.367Z
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
CC BY-SA 4.0
2018-12-11T18:34:11.037Z
@Lee yes bias is going to be a potential problem with your procedure. Why not use an oddball paradigm or a dual pair comparison?
StrongBad
CC BY-SA 4.0
2018-12-12T16:01:40.337Z
Yes I think the 4IAX procedure might be most suitable for my purpose. Thanks for your comments!
Lee
CC BY-SA 4.0
2018-12-10T16:16:36.173Z
2018-12-10T16:16:36.173Z
StrongBad
<p>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?)</p>

<p>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.</p>

<p>Many thanks in advance for your answers.</p>

CC BY-SA 4.0
2018-12-08T00:01:33.503Z
Are you asking about a same-different paradigm: https://www.ncbi.nlm.nih.gov/pubmed/18613624
StrongBad
CC BY-SA 4.0
2018-12-08T20:33:28.890Z
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
CC BY-SA 4.0
2018-12-08T20:36:34.500Z
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?
StrongBad
CC BY-SA 4.0
2018-12-09T13:19:14.060Z
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
<cognitive-psychology><cognitive-neuroscience><psychophysics>
Yes-No question in 2AFC staircase test
Lee
# Yes-No question in 2AFC staircase test

(Asked by: username_0 on 2018-12-07)

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.

**Tags:** cognitive-psychology, cognitive-neuroscience, psychophysics

> **Comments:**
> **username_1**: Are you asking about a same-different paradigm: https://www.ncbi.nlm.nih.gov/pubmed/18613624  
> **username_0**: 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?".  
> **username_1**: 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?  
> **username_0**: 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.  

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## 1 answers

### Answer by username_1 on 2018-12-10. Score: 1

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.

> **Comments:**
> **username_0**: 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"?  
> **username_0**: 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?  
> **username_0**: 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!  
> **username_1**: @username_0 yes bias is going to be a potential problem with your procedure. Why not use an oddball paradigm or a dual pair comparison?  
> **username_0**: Yes I think the 4IAX procedure might be most suitable for my purpose. Thanks for your comments!  

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