Counting Statistics
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Counting Statistics. 31. 32. Statistical Accuracy. Factors that affect statistical accuracy :. Count rate Count time Background Equipment efficiency. Sample vol. Geometry Moistureabsorption. Events. 33. Error Reduction. Peer Check STAR Procedure Use and Adherence.

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Counting Statistics

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Counting statistics

Counting Statistics

HPT001.011

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31


Statistical accuracy

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32

Statistical Accuracy

  • Factors that affect statistical accuracy:

  • Count rate

  • Count time

  • Background

  • Equipment efficiency

  • Sample vol.

  • Geometry

  • Moistureabsorption


Error reduction

Events

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Error Reduction

  • Peer Check

  • STAR

  • Procedure Use and Adherence


Accuracy and precision

Accuracy and Precision

34

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Standard deviation

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Standard Deviation

Where’s the mean?

  • Represented by the Greek symbol sigma 

  • One  is the distance from the peak out to a vertical line enclosing 34.15% of the total area under the curve


Frequency distribution

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Frequency Distribution

  • Data is plotted on a histogram

  • Height of bar represents frequency of occurrence


Poisson distribution

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Poisson Distribution

  • Probability of “success” is low

  • Number of trials is high


Gaussian distribution

Gaussian Distribution

38

  • Symmetrical about the mean

  • One  includes 68.3% of area under curve

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Confidence level

Confidence Level

39

1 = 68.3 % confidence level

2 = 95.4 % confidence level

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Minimum detectable count rate

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Minimum Detectable Count Rate

  • Calculated using the equation:

MDC = 2.71 + 3.3 [B(tb+ts)/tb]1/2

where:MDC is the minimum dectectable counts;

B is the background counts;

tb is the background counting time, minutes;

ts is the sample counting time, minutes.

MDCR = MDC/ts


Mdcr application

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MDCR Application

  • If gross count rate is > (Bkd + MDCR):

It may be concluded with 95% confidence that radioactivity is present above natural background. Calculate results using normal processes.


Mdcr application cont d

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MDCR Application (cont’d)

  • If gross count rate is < (Bkd + MDCR):

record as

"< MDA".


Lower limit of detection

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Lower Limit of Detection

  • Calculated using the equation:

LLD (Ci/cc) = 4.66 b

(2.22E6)(E)(V)(Y)(D)

where:V is the sample volume in cc;

E is the counter efficiency (cts/dis);

Y is the chemical yield if applicable;

D is the decay correction for delayed count on sample.

2.22E6 is a conversion factor - dpm per Ci


Chi square test

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Chi-Square Test

  • Calculated using the equation:

x2 = (n-)2

where:n = the data for each count;

 = the average of the individual counts;

 = n/N

N = the number of observations (usually 21)


Chi square test1

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Chi-Square Test


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