How to determine an unbiased estimate of threshold in a single-stimulus forced choice experiment?

Question

Objective

I need to estimate the unbiased threshold of detectable speed difference in a car-following task. The details are as follows:

Experiment Design

This experiment was performed in a driving simulator. In each trial, the participant drives a car in a single lane.

Procedure

1. Initially, the participant's car and the lead vehicle (car or truck) moved at 100 km/h (27.78 m/s). The lead vehicle was at one of the two distances from the participant's car in a given trial: 50 m or 100 m.
2. After few seconds, the 'Observe' message appeared on participant's windscreen. At the onset of this message, the lead vehicle began to change its speed (increase or decrease) by 1 m/s or 3 m/s at the rate of 0.5 m/s (e.g. it would take 6 seconds to decrease speed by 3 m/s).
3. Once the speed difference was complete (e.g. lead vehicle reached 27.78 - 3 = 24.78 m/s speed), the participant was given 4 seconds to observe this change in speed. Then the 'Change Speed' message appeared. At this point, participants were forced to push either the gas pedal or the brake pedal to indicate that they noticed a positive speed difference (e.g. +3 m/s) or a negative speed difference (e.g. -3m/s). They had to provide their reaction even if they did not see any speed difference. Please note that the instructions were given before the experiment began.

Details/Limitations

1. There were no catch trials, i.e. there was no trial in which a speed difference was not created.
2. The trials were done with random combinations of spacing and speed difference. Sometimes negative speed difference trials were done consecutively; in other cases the trials were positive speed difference followed by a negative one. For example: 50 m and +1 m/s -> 50 m and +3 m/s -> 100 m and -3m/s -> 100 m and -1 m/s. These could be in any order.

Possible sources of bias

A smaller distance of 50 m is relatively unsafe compared to 100 m, especially when the lead vehicle is a truck. So, with small distance, small speed difference and/or a truck, participants might be biased to apply brakes even if the lead vehicle accelerates.

Results

I now have proportions of correctly detected responses for each combination of distance and speed difference.

Question

How do I determine an unbiased measure of the threshold of speed difference in each case? Does a speed difference that is correctly detected in at least 75% of the trials an appropriate threshold?

Kindly share any beginner-friendly resources for estimating threshold in a single stimulus forced choice task. Thank you in advance.

Answer 1

Any estimate you make is going to be pretty bad. To answer this question requires so many assumptions about the data, experiment, and intended usage, it is just not possible. You would be better off running the experiment again after consulting someone who knows more about experimental design. Beyond that, you could hire a stats consultant.

Apart from the lack of catch trials, you only have 2 speeds. Even if you get lucky and they bracket threshold (e.g., d' of 1 or 75% correct), without more theory (or data), you cannot interpolate between the points.