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SARAD
GmbH
T(slow) = N / (C
* S) = 100 cts / (0.2 kBq/m³ * 8 cts/(min*kBq/m³) = 62.5 min.
Rn
That looks pretty but makes no sense because of the longer response time. So we will set
the interval to 120 Minutes and ask for the statistical error in this case:
N(slow) = C
* T * S = 0.2 kBq/m³ * 120 min * 8 cts/(min*Bq/m³) = 192 cts
Rn
E(1σ) = 100 % * 1 * √(N) / N = 100 % * 1 * √(192) / 192 = 7.22 %
Now one could say 68.3% is not sure enough, I want to choose 2σ confidence interval to get
a more trustable result:
E(2σ) = 100 % * 2 * √(N) / N = 100 % * 2 * √(192) / 192 = 14.44 %
For interpretation look at the begin of this chapter.
Is an observed concentration change statistical significant or not?
If you have a look at the acquired time distribution you will see variations of the concentration
from point to point. The question is now: Is it a real change in the Radon concentration or
only a statistical fluctuation?
The test is very simple: Define a confidence level with respect to your needs and look at the
statistical error bands of the two points of interest. If the error bands do not overlap each
other, the change in the Radon concentration is significant otherwise it "can be or not can
be".
Example 1:
Reading 1: 1500 Bq/m³ ± 10%
Reading 2: 1300 Bq/m³ ± 13%
The upper limit of the error band of the reading 2 is higher than the lower limit of the error
band of reading 1. Because the "true" value could be placed within 1350 Bq/m³ and 1469
Bq/m³, the variation of both readings is not statistical significant.
Example 2:
Reading 1: 1500 Bq/m³ ± 10%
Reading 2: 1000 Bq/m³ ± 15%
The error bands of the readings do not overlap each other. Therefore, a statistical significant
concentration change is given.
Two arbitrary points of a measurement series may be considered using this test. It is not
necessary that the points are direct neighbours.
Detection Limit
The term Detection Limit defines the smallest value of the Radon concentration which
delivers a non-zero reading of the instrument within a given integration interval (at least 1
decay per interval). Because of the statistical behaviour a related confidence interval has to
be stated.
Why is it necessary to know the Detection Limit? If the set integration interval is short and the
Radon concentration low, the expected "true" value of the number of detected decays may
be around or less than 1. Because of the statistical variations, intervals without any detected
decay will appear frequently. The most extreme situation would be a measurement series
with a lot of "zero" intervals and only one interval with one detected decay (because a decay
cannot be split).
When calculating the Radon concentration by the given formula, the concentration value for
the interval with the one count is much to high while all other values show zero. Then, all
Manual_ThoronScout_EN_02-07-15.doc
Thoron-Scout
error band [1350 ... 1650 Bq/m³]
error band [1131 ... 1469 Bq/m³]
error band [1350 ... 1650 Bq/m³]
error band [850 ... 1150 Bq/m³]
10
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