Detection limits for samples that give rise to counting data with extra-Poisson variance

Detection limits are presented for duplicate background samples that produced counting data with extra-Poisson variance that was attributed to a nonuniform activity distribution in the background sample medium. The presence of extra-Poisson variance was detected using the chi-squared test, where the presumed change in baseline activity from sample to sample was interpreted as an increase in experimental population variance. The runs test and Wilk-Shapiro test verified, respectively, the acceptable randomness of the data and the hypothesis that the data are normally distributed. Confidence intervals for detection limits therefore were based on the normal and t-distributions. The reduced chi-squared statistic was incorporated into the equations for the critical level and lower limit of detection to account for experimental variance beyond the expected Poisson value. The incorporation of extra-Poisson variance increased these detection limits for a well-defined background by a factor of 2.3 compared to the expected values for the paired-sample method which were derived under the assumption of Poisson variance, where the 30 background measurements have a reduced chi-squared statistic of 9.44.