Precision of measurements with arbitrary confidence levels when samples are counted equal to or longer than blanks by...

Past computer solutions for confidence intervals, both in paired counting and when the sample is counted an integer number of times more than the blank, are extended to computing the precision of the measurement. The blank count and the contribution of the sample to the gross count are assumed to be Poisson distributed. While the standard deviation and the probability density function of the net count are readily computed, the name and properties of the probability density function are unknown. Hence, the uncertainty of the net count is unknown. However, both the upper and lower confidence limits, at a given confidence level, can be computed. In general, the difference between the upper limit and the observed net count is greater than the difference between the observed net count and the lower confidence limit. So the bound on the uncertainty is taken to be the difference between the upper confidence limit and the observed net count. Then the precision can be taken to be the bound on the uncertainty divided by the observed net count (relative bound on the uncertainty).