Approximate Confidence Intervals for Paired Counting Utilizing Half-Integer Corrected Gaussian Distributions
W. E. Potter
In the past exact Neyman-Pearson confidence intervals, for paired counting, of the form [yy.yy, xx.xx] were discussed. Also codes that can compute these exact confidence intervals were discussed. Confidence intervals are useful in describing the results of measurements that can arise in both air sampling and bioassay analysis. Confidence intervals provide a way to interpret negative net counts. Approximate confidence intervals follow from the Neyman-Pearson principle with half-integer corrected Gaussian distributions used in place of the exact probability distributions. The resultant approximate confidence limits can be calculated without a computer. For many low-level activity measurements yy.yy is zero or taken to be zero and xx.xx is the quantity of interest. Numerical experimentation yields the following conservative property of the approximate value for xx.xx: the approximate value for xx.xx is equal to or greater than the exact value when the confidence level is 90%, 95%, 97.5%, 99%, and 99.9%. The half-integer corrected value for yy.yy can be both smaller and larger than the exact value. The half-integer corrected values for both xx.xx and yy.yy are superior to other approximate confidence intervals using Gaussian distributions. In the above it is assumed that a good estimate is available for the expected blank count. If there is concern, then utilizing a confidence interval for the expected blank count allows the determination of a modified confidence interval for the expected net count.
This abstract was presented at the 37th Annual Midyear Meeting, "Air Monitoring and Internal Dosimetry", Late Submissions Session, 2/8/2004 - 2/11/2004, held in Augusta, GA.