Re: Questions about a distribution

"filia&sofia" <in_tyrannos@xxxxxxxxxxx> wrote in news:d3b77c0b-178b-4222-
b314-2a378c39e0d4@xxxxxxxxxxxxxxxxxxxxxxxxxxx:

I have a simple human reaction time test. The variable I'm measuring
is reaction time in milliseconds. Let's say the PDF has the mean = 250
ms. Now, mean gives the location of the "peak". The variance tells how
"wide" the distribution is and the deviation is squared root of the
variance.

Not the precise formulation I would have chosen. The SD is in the same
units as the reaction time measurements, so I would have said that the SD
lets you know how "wide" the distribution is. The variance is on a
different set of units, seconds-squared. Variances have useful
mathematical properties but ease of saying what they characterize is not
among them.

Now, I have few questions. Is there any way to tell how the reaction
times of an individual are (or could be) distributed?

After you do replicate tests on the same individual, you could. If you
don't, then you can't determine how much the intra-individual variability
contributes to the observed population variance (or SD).

In other words,
could we think that the distribution can be constructed from smaller
distributions? Another ways to ask this: "Given reaction times of a
single person, what is the probability that this person's results
belong to the distribution above?"

or "Is it possible to simulate a
group of people whose individual results generate the distribution
above?"

Of course it's possible to simulate it. The question will remain: does
the simulation accurately capture the sources of variability in the
population. The best case would be to get some intra-individual data
before trying to do simulation work.

Basically, I would like to simulate an individual taking the test.
This person could be parametrized to be "fast", "average" or "slow".
And then, if I simulate N individuals, their results form a gaussian
PDF. For example a fast person could have most of the reaction times
less than, let's say, 220 ms and later N = 10000. Hope you get the
idea...

Go ahead. Do it. If you want to do some searching you might try the term
"mixture distributions" or "mixture of Gaussians". You will find that
when the SD of the intra-individual distributions are significantly
smaller than the population SD that you will see a peaked distribution
(assuming your simulated sample sizes are large enough.)

--
David Winsemius
.

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