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I am using a two-interval force choice (2IFC) task to estimate detection threshold and choose an appropriate signal level for my following experiment, by estimating sensitivity ($d'$) for each signal level.

Since it is a 2IFC task with signal equally distributed on two intervals, I expect close-to-zero response bias and plan to estimate $d'$ directly from proportion correct. After running experiment on 3 subjects (one complete 2500 trials, two complete 1250 trials), two of them show slight response bias (ratio of response to interval 1 vs. 2 is 0.91 and 1.12), but one subject shows large response bias (ratio of response to interval 1 vs. 2 is 0.53).

Here is my question:

  1. For the subject with large response bias, is it still valid to estimate $d'$ from proportion correct anymore? And is it still valid to estimate $d'$ directly from hit rate and false-alarm rate?

  2. If I hope to let this subject to continue participating in this experiment, how should I let him/her to lower response bias? Directly telling him/her "You have pressed key #1 too often, press key #2 more when you are not sure"? Is it going to interfere the experiment?

  3. For future naïve participants, should I let them know do not bias toward one response too much before the start of experiment, or should I tell them only when they have made too much bias? If the latter case, how much bias is considered to be "too much"?

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  • $\begingroup$ How do you determine the false alarm rate from a 2AFC task? $\endgroup$ – AliceD Nov 12 '18 at 8:54
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    $\begingroup$ Signal: Interval 1; Response: Interval 1 - Hit. Signal: Interval 2; Response: Interval 1 - False alarm. Interval 1 and 2 can be exchanged, but the calculated $d'$ remains the same. Reference: p162, Psychophysics - A Practical Introduction, 2nd edition. $\endgroup$ – Cloudy Nov 12 '18 at 9:46
  • $\begingroup$ You can show the participants c after each N trials and ask them to adjust be more liberal/conservative. d' should remain the same regardless of c, but d' will be estimated with the greatest power (fewest trials) for c=0. $\endgroup$ – Jonas Lindeløv Nov 12 '18 at 9:57
  • $\begingroup$ @JonasLindeløv while I don't doubt it, do you have a reference that proves that c=0 gives the greatest power? $\endgroup$ – StrongBad Nov 13 '18 at 19:05
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For the subject with large response bias, is it still valid to estimate d′ from proportion correct anymore?

No. Within the signal detection theory framework, a 2I-2AFC paradigm is identical to a 1I-2AFC paradigm except that the decision variable Y in the 2I-2AFC paradigm is X2-X1 (difference between the observations on the first and second intervals). The effects of bias are the same and d' needs to account for any bias.

And is it still valid to estimate d′ directly from hit rate and false-alarm rate?

Maybe. If all of the assumptions from the 1I-2AFC paradigm still hold, then with appropriately defined hits and false alarms (e.g., a hit is when the subject responds "1" when the signal in the first interval) and you account for the $\sqrt(2)/2$ improvement from having two intervals, then yes you can still calculate d'. That said, with typical assumptions, the 2I-2AFC paradigm results in distributions that are symmetric about zero and therefore we don't expect a response bias. I would be worried that with a non-zero bias that the subject is not behaving as assumed. If that is the case, d' does not really mean anything.

If I hope to let this subject to continue participating in this experiment, how should I let him/her to lower response bias? Directly telling him/her "You have pressed key #1 too often, press key #2 more when you are not sure"? Is it going to interfere the experiment?

Correct answer feedback sometimes works, but not always. The effect of influencing the preferred response bias of a subject depends on the subject and experiment.

For future naïve participants, should I let them know do not bias toward one response too much before the start of experiment, or should I tell them only when they have made too much bias? If the latter case, how much bias is considered to be "too much"?

This comes down to the experimental design. If possible, I would exclude the subject from the analysis. If you are looking at population statistics, you need to include everyone. If instead, you are interested in the best subjects, a subject with an odd bias is probably not worth your time of dealing with.

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