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I am new to Psychology, particularly the signal detection theory (SDT). Before understanding SDT, I performed an experiment to measure what speed difference between a subject's car and the front vehicle could a subject correctly percieve. But I ignorantly only tested subjects on 'signal + noise' trials, i.e. there always was a speed difference in each trial. There never was a catch trial (no speed difference). Thus, I can't estimate the false alarm rate. I only have the Hit and Miss rates for a given speed difference stimulus.

Can I still use SDT by any chance? Or the estimation of the 'threshold' of detectable speed difference my only option?

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  • $\begingroup$ I actually do have trials with a very small speed difference of +/- 0.5 m/s which most subjects could not correctly identify. I am not sure how can I extrapolate to a zero speed difference. $\endgroup$
    – umair durrani
    Commented Jun 7, 2019 at 2:09

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In order to estimate d' for a particular signal level, we need an estimate of the hit rate at that signal level and an estimate of the false alarm (FA) rate. Typically, the FA rate is estimated from the no-signal catch trials.

With a paradigm like the method of constant stimuli, the assumption is that the false alarm rate is constant and doesn't depend on the past trials. Therefore, if you had 500 trials spread across 4 different signal levels and catch trials, you can either use all the catch trials to calculate a single common FA rate or you can randomly group the catch trials to get 4 estimates of the FA rate (this has some statistical advantages). The key is the catch trials are all assumed to be independent.

If instead of 500 trials with 4 signal levels and catch trials, you have 500 trials and 5 signal levels and no catch trials, it might seem that you have no way to estimate the FA rate. That is wrong. If you fit a psychometric function to the hit rate data, the lower asymptote is the FA rate. If all you signal levels lead to high hit rates and you don't know the underlying psychometric function, your estimate of the FA rate is going to be crappy. If they are all at high hit rates and the underlying psychometric function is know and well behaved at the tails, then you can get a good estimate of the FA rate. Even better is if some of the signal levels had low hit rates and that you have a reasonable estimate of the tail.

For data like yours where there are multiple signal levels:

  • chose a psychometric function
  • fit the the curve
  • if the fit is good, estimate the lower asymptote
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