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PMT statistics issue

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

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  1. mook Johnson

    mook Johnson Guest

    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  Larkin

    John Larkin Guest


    Poisson statistics, right?

    John
     
  3. mook Johnson

    mook Johnson Guest

    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. Genome

    Genome Guest

    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 Thompson

    Jim Thompson Guest

    100% ?:)

    ...Jim Thompson
     
  7. Genome

    Genome Guest

    Bugger!

    DNA
     
  8. mook Johnson

    mook Johnson Guest

    What about conecutive 45 sample means?
     

  9. 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 Johnson

    mook Johnson Guest

    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
    about the tricky stuff.
     
  12. Mook Johnson

    Mook Johnson Guest

    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 Johnson

    Mook Johnson Guest


    Now that is crystal clear.

    Thanks.
     
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