Re: Question about the usage of Binomial dist


David Winsemius wrote:
"Kevin E. Thorpe" <kevin.thorpe@xxxxxxxxxxx> wrote in
news:1155870783.223875.287420@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:

If you still have the sequences of success and failure, you can
form the partial proportions p_i = #successes/i for i=1 to n.
You could do this for each person. Then fit something like
an AR(1) model p_i = a*p_(i-1) and compare the estimated
parameter between the people. You would probably have
to start the series at the first success.

This approach may be totally fruitless too, so hopefully
some others will offer opinions.


After seeing your idea, Kevin, which did look as though it might capture
some of the dynamic character, I wondered if approaches such as are used in
survival analysis might work. They allow a summary measure of a cumulative
proportion and also allow statistical comparisons at least over the period
when the two subjects were at the same point in the learning curve. I don't
think any inference could be made on the relative perfomance after each had
made 32 trials (the smaller number of trials in the hypothesized results).
You would be looking at (perhaps) a Cox model and estimating relative
"hazard" of a failure in each sequenced trial in subjects A vs. B.

Thank you for the comment. A survival analysis approach did also
occur to me. It certainly could allow a more flexible time-dependent
hazard. With two people, you would essentially have an n of 2 to
compare these changing hazards. While you potentially have the
same problem with the AR(1) approach, at least the parameter
is simpler.

By my reply I am in no way inferring "I'm right and you're wrong,"
just elaborating on the reasoning that led to my AR(1) suggestion.

--
Kevin E. Thorpe
Assistant Professor, Department of Public Health Sciences
Faculty of Medicine, University of Toronto

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