On 25/03/2021 10:25 p.m., Rolf Turner wrote:
On Fri, 26 Mar 2021 13:41:00 +1300
Abby Spurdle <spurdl...@gmail.com> wrote:
I haven't checked this, but I guess that the number of students that
*pass* a particular exam/subject, per semester would be like that.
e.g.
Let's say you have a course in maximum likelihood, that's taught once
per year to 3rd year students, and a few postgrads.
You could count the number of passes, each year.
If you assume a near-constant probability of passing in each
exam/semester: Then I would assume it would follow the distribution
that you're requesting.
<SNIP>
Thanks Abby. I've experimented (simulated) a wee bit and found
that if I keep the numbers of students (undergrad and grad) exactly
constant, then the results are underdispersed. However if the
numbers are allowed to vary then the results are overdispersed.
It seems that the universe is very reluctant to produce underdispersed
pseudo-binomial data!
I'd expect underdispersion to happen in competitive situations: if
subject A succeeds, that makes it less likely that other subjects will
also succeed.
An extreme case is a contest winner. With some contests there will
always be one winner (a little too-underdispersed for you, probably),
but others allow a small amount of variation.
For example, sports events that allow ties. This page
https://en.wikipedia.org/wiki/List_of_ties_for_medals_at_the_Olympics
seems to indicate that speed skating had a lot of ties up until 1980.
Duncan Murdoch
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