> When using the method of constant stimuli,
> I often wonder whether it is possible to know a priori
In general, no.
I have a few "rules of thumb" that I follow, which usually
work well, but you always need to run a couple of pilot runs
to make sure things are reasonable...
> what is the best compromise between number of trials,
I like 30 per condition (but I always use a staircase with
adaptive step size).
> of levels of the variable
A general rule is that for things like contrast threshold,
steps of 0.1 log unit will place 4 or 5 samples on the interesting
part of the psychometric function. For other types of measures
(e.g. orientation discrimination), you need to do a little
trial and error.
> and number of observers.
3 or 4 with consistent data is usually enough to satisfy reviewers.
If you are interested in individual differences you will want more.
> I'm looking for theoretical reference(s)
> related to this issue.
Can't give you too much help here... there was a paper
in the last few years by Kontsevich on adaptive trial placement
(an improvement on the QUEST procedure...). This might be of
interest, or contain some interesting references.
I see that Tim Meese has already referred you to the work of my
colleague Andrew Watson... He concluded that a procedure such
as QUEST is better than a simple staircase, but that is mainly because
a staircase that starts with the minimum step size can take a while
to get the the region of interest. I use an adaptive step size that
is halved on each reversal until the minimum increment is reached.
My former graduate advisor Donald MacLeod made the observation that
a staircase with a short memory (e.g. a staircase) is superior
to one with a long memory (e.g. QUEST) when the threshold
is unstable during the course of the experiment, because the simple
staircase will be able to track the fluctuations better.
My main gripe is that it is still a fairly widespread practice to average
some number of staircase reversal points to estimate the threshold...
It is much better to estimate the psychometric function from all the data.
Reversal points can be moved with a single finger error.
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