Poisson distributions?

[Clive Downs]

Hi Everyone,

If you have a dataset that looks like it may be a Poisson distribution (eg
it relates to the observed no of events over a specified period of time,
for a defined set of individuals - in fact the data relates to no of days
absence from school for a set of students), how would you establish that it
is in fact a Poisson?

Also, how would you go about exploratory data analysis, parallel to the
procedure for normally distributed data? OK, so you can calculate variance,
SD and produce a frequency distribution (and calculate this on a reciprocal
or square root transformation), but what can you do further than that?

Any help appreciated!

Thanks

Clive.

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[Swank, Paul R]

When I look at such models with other software, I typically consider the deviance or Pearson Chi-square divided by df. The value should be around 1. If not, then an alternative formulation, such as a negative binomial can be used which has an additional parameter for dispersion. I'm sorry but I don't know if SPSS has this option. I know it does the Poisson regression.

Dr. Paul R. Swank,
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center-Houston


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Clive Downs
Sent: Monday, March 09, 2009 10:31 AM
To: [hidden email]
Subject: Poisson distributions?

Hi Everyone,

If you have a dataset that looks like it may be a Poisson distribution (eg
it relates to the observed no of events over a specified period of time,
for a defined set of individuals - in fact the data relates to no of days
absence from school for a set of students), how would you establish that it
is in fact a Poisson?

Also, how would you go about exploratory data analysis, parallel to the
procedure for normally distributed data? OK, so you can calculate variance,
SD and produce a frequency distribution (and calculate this on a reciprocal
or square root transformation), but what can you do further than that?

Any help appreciated!

Thanks

Clive.

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
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[Clive Downs]

Hi,

Thank you for the responses to this.

After posting this, I wondered if the data I have meet the conditions for a
Poisson distribution.The data consists of SPSS cases where each case gives
the student ID, the school ID, the number of possible sessions (ie half-day
attendance) and the number of sessions where they were absent.

According to Rumsey (Probability for Dummies), the conditions for a Poisson
are:

1. the random variable refers to events such that only one event can occur
at the same time
2. events are independent
3. events are those that occur over a specified time span

However, with school absence, it can be argued that:

(1) more than one event can occur at the same time (ie more than one
student may be absent at one time)
(2) events are not independent (a student' absence on one day may influence
their absence on another day, or indeed, other students' absence.

On the other hand, the examples often quoted as Poissons include situations
like the number of customers entering a shop over some period. It is quite
possible that more than one customer can enter a shop at the same time.
Equally, you could recast student absence as their absence being notified
to the school, and such notifications arriving sequentially (eg by phone
calls). As for independence of events, I'm not so sure you can get round
that!

Also I forgot to check the SPSSX-L archives, and there were several items
about Poisson distributions.

Regards

Clive.

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