Statistical Measures of the Lower Limit of Detection of a Radioactivity Counter

Abstract

The lower limit of detection of a counter is best expressed statistically in terms of two minimal activities determined by the maximal acceptable risks of making a Type I error (of concluding there is sample activity when there is none) and a Type II error (of concluding there is no activity in the sample when there is some). These threshold activities are designated “the minimum significant measured activity”, defined to be the smallest measurement which is interpreted as meaning there is activity in the sample, and “the minimum detectable true activity”, defined to be the smallest amount of activity required to be in a sample in order that a measurement can be expected to imply correctly the presence of activity with a predetermined degree of confidence. It is to be noted that the former refers to a measurement while the latter refers to the actual activity present. This paper is concerned with the statistical problems of the definition and derivation of these two measures of detection sensitivity. Though either quantity can serve equally well as a measure of detection threshold, it is important to recognize the distinction between the threshold for measured activity and the, threshold for true activity and their different applications the former dealing with measurements meriting being reported as greater than zero and the latter with the amount of actual activity that can be detected with predetermined confidence.