Gilson and Voss - Voss Associates

COUNTING STATISTICS
COUNTING STATISTICS
2
Minimum Detectable Activity k + 2kRB x t
S+B
x (1+t
S+B/t B)
(MDA) MDA = t x Eff
Minimum Detectable Count Rate
2
LLD = L = MDCR k + 2kR x t x (1+t /t )
S+B
D B S+B S+B B
t S+B
2
Minimum Detectable Activity k + 2kRB x t
S+B
x (1+t
S+B/t B)
(MDA) MDA = t x Eff
Minimum Detectable Count Rate
2
LLD = L = MDCR k + 2kR x t x (1+t /t )
S+B
D B S+B S+B B
t S+B
L
C
= k x R
B
x t
S+B
+ R
B
x tB
k = 1.645 (for 95% Confidence Level)
t
S+B
= sample count time
t
B
= background count time
R
B
= background count rate
Eff = efficiency of the detector (expressed as a decimal)
R
S+B
= sample count rate
LLD is Lower Limit of Detection
L
D
is the Decision Level
L
C
is the Critical Level and generally expressed as counts (or
signal level) above background
K 0.674 1 1.645 1.96 2.58 3.00
% C.L. 50 68.3 90 95 99 99.7
If R
B
is in DPM it must be converted to CPM before using the
above equations.
A ‘k’ of 1.645 is used as the 95% confidence level for a twotailed
distribution.
Gaussian statistics should be used for > 30 counts and Poisson
statistics for < 30 counts. The typical formulas such as those
above are an attempt to blend the two statistical models.
Page 107
L
C
= k x R
B
x t
S+B
+ R
B
x tB
k = 1.645 (for 95% Confidence Level)
t
S+B
= sample count time
t
B
= background count time
R
B
= background count rate
Eff = efficiency of the detector (expressed as a decimal)
R
S+B
= sample count rate
LLD is Lower Limit of Detection
L
D
is the Decision Level
L
C
is the Critical Level and generally expressed as counts (or
signal level) above background
K 0.674 1 1.645 1.96 2.58 3.00
% C.L. 50 68.3 90 95 99 99.7
If R
B
is in DPM it must be converted to CPM before using the
above equations.
A ‘k’ of 1.645 is used as the 95% confidence level for a twotailed
distribution.
Gaussian statistics should be used for > 30 counts and Poisson
statistics for < 30 counts. The typical formulas such as those
above are an attempt to blend the two statistical models.
Page 107
COUNTING STATISTICS
COUNTING STATISTICS
2
Minimum Detectable Activity k + 2kRB x t
S+B
x (1+t
S+B/t B)
(MDA) MDA = t x Eff
Minimum Detectable Count Rate
2
LLD = L = MDCR k + 2kR x t x (1+t /t )
S+B
D B S+B S+B B
t S+B
2
Minimum Detectable Activity k + 2kRB x t
S+B
x (1+t
S+B/t B)
(MDA) MDA = t x Eff
Minimum Detectable Count Rate
2
LLD = L = MDCR k + 2kR x t x (1+t /t )
S+B
D B S+B S+B B
t S+B
L
C
= k x R
B
x t
S+B
+ R
B
x tB
k = 1.645 (for 95% Confidence Level)
t
S+B
= sample count time
t
B
= background count time
R
B
= background count rate
Eff = efficiency of the detector (expressed as a decimal)
R
S+B
= sample count rate
LLD is Lower Limit of Detection
L
D
is the Decision Level
L
C
is the Critical Level and generally expressed as counts (or
signal level) above background
K 0.674 1 1.645 1.96 2.58 3.00
% C.L. 50 68.3 90 95 99 99.7
If R
B
is in DPM it must be converted to CPM before using the
above equations.
A ‘k’ of 1.645 is used as the 95% confidence level for a twotailed
distribution.
Gaussian statistics should be used for > 30 counts and Poisson
statistics for < 30 counts. The typical formulas such as those
above are an attempt to blend the two statistical models.
Page 107
L
C
= k x R
B
x t
S+B
+ R
B
x tB
k = 1.645 (for 95% Confidence Level)
t
S+B
= sample count time
t
B
= background count time
R
B
= background count rate
Eff = efficiency of the detector (expressed as a decimal)
R
S+B
= sample count rate
LLD is Lower Limit of Detection
L
D
is the Decision Level
L
C
is the Critical Level and generally expressed as counts (or
signal level) above background
K 0.674 1 1.645 1.96 2.58 3.00
% C.L. 50 68.3 90 95 99 99.7
B
If R is in DPM it must be converted to CPM before using the
above equations.
A ‘k’ of 1.645 is used as the 95% confidence level for a twotailed
distribution.
Gaussian statistics should be used for > 30 counts and Poisson
statistics for < 30 counts. The typical formulas such as those
above are an attempt to blend the two statistical models.
Page 107