Small amounts of radioactivity in samples are determined by measuring the rate at which radiations emitted by the radioactivity produce responses in a radiation detector. The rate measurement is a count of the number of response events that occur within the measurement time period.
Usually, the detector is also sensitive to background radiation that was not emitted by the sample. This requires that the measurement be interpreted to decide if the sample contains radioactivity, and if so, how much.
The accumulation of counts during a radioactivity measurement is a random process, and the interpretation of the results requires an estimate of the probability that the result of the measurement occurred by chance alone. To completely understand a measurement, the following questions should be answered:
What was the process for making the detection decision?
What is the probability of a false positive result for the detection decision process?
For results determined to be not detected, what is the probability of a false negative result for that determination?
For results determined to be not detected, or what is the largest amount of radioactivity that could be present?
For results determined to be detected, what does the stated value represent? Is it the result with the highest probability, the result that has a 50/50 chance of being exceeded, or as some result that lies midway between the upper and lower limits of probable results?
For results determined to be detected, what does the stated range of possible values represent? What is the probability that the true result could be outside the stated range?
Whenever we count a sample, there is an implied decision as to whether the observed result is due to background alone, or to a combination of background and sample radioactivity. We will make this decision by comparing the sample count result to some (as yet undefined) decision value related to the background and, if the result is higher than that decision value, deciding that radioactivity was detected in the sample. When the sample results are significantly larger than those that could be due to background, the decision is easy (even if the decision value is not precisely calculated). However, when the sample results are close to those that could be due to background, the decision is more difficult, and the decision value should be determined in a predictable and defendable manner.
This decision is a two-step sequential process. First, we determine the Maximum Probable Background (MPB). This is the largest count result that could be due to background, such that the chance of a larger number due to background is unlikely . Then, we compare this to the actual counting result, and decide if any radioactivity was detected. This gives us the following possible outcomes:
The sample does not actually contain radioactivity, but the background produces more counts than expected from the mean count rate (i.e., the gross sample count exceeds the MPB).
We incorrectly conclude that the sample contains radioactivity. (False Positive Decision).
The sample does not actually contain radioactivity, but the background produces fewer counts than expected from the mean count rate (i.e., the gross sample count does not exceed the MPB). We correctly conclude (for the wrong reason) that the sample does not contain radioactivity.
The sample actually contains radioactivity, but during the counting period, the background and the sample radioactivity together produce fewer counts than expected from the combined mean count rate (i.e., the gross sample count does not exceed the MPB).
We incorrectly conclude that the sample does not contain radioactivity. (False Negative Decision).
The sample actually contains radioactivity, and during the counting period, the background and the sample radioactivity together produce more counts than expected from the combined mean count rate (i.e., the gross sample count exceeds the MPB). We correctly conclude that the sample contains radioactivity.
And… It’s not complete – maybe this year (2016)
I wonder if this will ever be finished?
Nope, probably not!