COUNTING STATISTICS
B S+B
S+B
B
Minimum Detectable Activity
k + 2k
%
R x t
x (1+t
/t )
2
S+B
(MDA) MDA =
t
x Eff
Minimum Detectable Count Rate
D
B S+B
S+B
B
LLD
=
L
=
MDCR
k + 2k
%
R x t
x (1+t
/t )
2
S+B
t
C
B S+B
B B
L
=
k x
%
R x t
+ R x t
k
=
1.645 (for 95% Confidence Level)
S+B
t
=
sample count time
B
t
=
background count time
B
R
=
background count rate
Eff
=
efficiency of the detector (expressed as a decimal)
S+B
R
=
sample count rate
LLD is Lower Limit of Detection
D
L is the Decision Level
C
L 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 two-
tailed 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.
COUNTING STATISTICS
B S+B
S+B
B
Minimum Detectable Activity
k + 2k
%
R x t
x (1+t
/t )
2
S+B
(MDA) MDA =
t
x Eff
Minimum Detectable Count Rate
D
B S+B
S+B
B
LLD
=
L
=
MDCR
k + 2k
%
R x t
x (1+t
/t )
2
S+B
t
C
B S+B
B B
L
=
k x
%
R x t
+ R x t
k
=
1.645 (for 95% Confidence Level)
S+B
t
=
sample count time
B
t
=
background count time
B
R
=
background count rate
Eff
=
efficiency of the detector (expressed as a decimal)
S+B
R
=
sample count rate
LLD is Lower Limit of Detection
D
L is the Decision Level
C
L 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 two-
tailed 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.
COUNTING STATISTICS
B S+B
S+B
B
Minimum Detectable Activity
k + 2k
%
R x t
x (1+t
/t )
2
S+B
(MDA) MDA =
t
x Eff
Minimum Detectable Count Rate
D
B S+B
S+B
B
LLD
=
L
=
MDCR
k + 2k
%
R x t
x (1+t
/t )
2
S+B
t
C
B S+B
B B
L
=
k x
%
R x t
+ R x t
k
=
1.645 (for 95% Confidence Level)
S+B
t
=
sample count time
B
t
=
background count time
B
R
=
background count rate
Eff
=
efficiency of the detector (expressed as a decimal)
S+B
R
=
sample count rate
LLD is Lower Limit of Detection
D
L is the Decision Level
C
L 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 two-
tailed 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.
COUNTING STATISTICS
B S+B
S+B
B
Minimum Detectable Activity
k + 2k
%
R x t
x (1+t
/t )
2
S+B
(MDA) MDA =
t
x Eff
Minimum Detectable Count Rate
D
B S+B
S+B
B
LLD
=
L
=
MDCR
k + 2k
%
R x t
x (1+t
/t )
2
S+B
t
C
B S+B
B B
L
=
k x
%
R x t
+ R x t
k
=
1.645 (for 95% Confidence Level)
S+B
t
=
sample count time
B
t
=
background count time
B
R
=
background count rate
Eff
=
efficiency of the detector (expressed as a decimal)
S+B
R
=
sample count rate
LLD is Lower Limit of Detection
D
L is the Decision Level
C
L 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 two-
tailed 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.
