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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 Moisture absorption. Events. 33. Error Reduction. Peer Check STAR Procedure Use and Adherence.

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Counting Statistics

HPT001.011

Revision 3

Page of 45

31

statistical accuracy
HPT001.011

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32

Statistical Accuracy
  • Factors that affect statistical accuracy:
  • Count rate
  • Count time
  • Background
  • Equipment efficiency
  • Sample vol.
  • Geometry
  • Moisture absorption
error reduction

Events

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33

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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