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

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).

Improved confidence intervals when the sample is counted an integer times longer than the blank.

Past computer solutions for confidence intervals in paired counting are extended to the case where the ratio of the sample count time to the blank count time is taken to be an integer, IRR. Previously, confidence intervals have been named Neyman-Pearson confidence intervals; more correctly they should have been named Neyman confidence intervals or simply confidence intervals. The technique utilized mimics a technique used by Pearson and Hartley to tabulate confidence intervals for the expected value of the discrete Poisson and Binomial distributions. The blank count and the contribution of the sample to the gross count are assumed to be Poisson distributed. The expected value of the blank count, in the sample count time, is assumed known. The net count, OC, is taken to be the gross count minus the product of IRR with the blank count. The probability density function (PDF) for the net count can be determined in a straightforward manner.

Measurements should not be recorded as less than MDA: an extension.

Sometimes the results of measurements in radioactivity are reported as "less than the minimum detectable activity." Over the years there have been articles informing the reader that it is incorrect to express the results of measurements as less than the minimum detectable activity. A very brief review of past comments on expressing the results of measurements precedes a discussion of why measurements should not be reported as less than the minimum detectable activity. The decision level is the value of the net count above which a measurement process is claimed to have detected activity; it is determined so that the probability of detecting activity, when there is no activity in the sample, is less than or equal to the desired error of the first kind. This article extends previous work restricted to paired counting, where the blank and sample were counted for the same amount of time, to blank count times greater than or equal to the sample count times.