# PMT statistics issue

Discussion in 'Electronic Design' started by mook Johnson, Oct 21, 2006.

1. ### mook JohnsonGuest

I'm working with a PMT in pule counting mode. NAI scintillator is connected
to the PMT.

I set the discriminator level to 60kEV with plenty of dynamic range above
that.

I'm measuring background counts at around 90 CPS long term average. We are
applying a Cs source that raises teh count rate to about 700CPS long term
average.

What the user wants to do is measure the background at 1sample/sec for 45
seconds then measure a 1 sample/second with the source for 45 seconds.
Subtract the mean of those two for use elseware.

the problem is that when the measurement is repeated there is a fairly wide
spread in the two averages taken.

What I would like to know is how to calculate the spread in the two
averages. given the same source is used and the background levels are the
same(no sources running around).

2. ### John LarkinGuest

Poisson statistics, right?

John

yup

4. ### Guest

http://hyperphysics.phy-astr.gsu.edu/hbase/math/poifcn.html

If you are counting random events, the standard deviation on your count
is just the square root of the accumulated count. Successive counts are
likely to differ by around a standard devaition. A range of +/-2
standard deviations includes about 95% of a long series of counts,
+/-2.5 standard deviations gets this up to about 99%.

5. ### GenomeGuest

If I sampled the erect status of my cock at one sample per day for
forty-five days what is the probability that it is permanently floopy?

DNA

6. ### Jim ThompsonGuest

100% ? ...Jim Thompson

Bugger!

DNA

8. ### mook JohnsonGuest

What about conecutive 45 sample means?

9. ### Michael A. TerrellGuest

So that's why its floopy? You need to find new friends, or lay off
the female hormones.

--
Service to my country? Been there, Done that, and I've got my DD214 to
prove it.
Member of DAV #85.

Michael A. Terrell
Central Florida

10. ### mook JohnsonGuest

I would hope 100% if your talkin to me. LOL

11. ### Guest

Try bottom posting.

If each sample covers the same amount of time on the same source, the
standard deviation of the mean over the 45 samples has a standard
deviation that is root 45, or 6.71 smaller than the standard deviation
on any single mean.

There are a couple of ways of screwing this up, but you will have to
read up on elementary statistics before you start needing to worry

12. ### Mook JohnsonGuest

I'm not sure I understand what you're saying.

Heres the question in a simplified manner.

If I measure the counts acquired in 1 second, 45 consecutive times, and
calculated an average of those 45 samples and came out with say a mean of
700 counts / sec.

Standard Dev. would be sqrt(700) = ~26 assuming a poisson distribution

If I ran this test say 10 times. How much scatter in the MEAN would I expect
for the consecutive runs of the 45 sample test?

I realize that the next 1 second sample would fall with in 3 sigma of the
mean but I'm curious about how to calculate standard deviation of the means
of several 45 sample tests.

13. ### Guest

If your mean count rate is 700counts/sec, the standard deviation on a
single 1 second observation is 26.5 counts.

If you accumulate 45 seconds worth of 700count/sec data, you've got
45x700 counts -31,500 counts, and the standard deviation on that is
going to be 177.5.

This implies that you then know that your count rate is 700+/-10 counts
per second with 99% confidence.

If you process is stable at 700 counts per second., the standard
deviation on any one second sample will stay at 26.5 counts, and any 45
second sample will have a standard deviation of 177.5 counts.

Note that if you got a count of 700 after one second of observation,
all you can say about the "true"count rate is that is has an even
chance of lying between 673.5 and 726.5, and that 99 times out of a
hundred it will lie between 633.75 and 766.25.

As you average over long time periods, the confidence limits on the
mean count rate creeps down, but the standard deviation on a single one
second measurement isn't going to change at all (unless you were
unlucky with your first few measurements).

14. ### Mook JohnsonGuest

Now that is crystal clear.

Thanks.  