Counting Data and T-test Evaluation of Detection Limits and Their Effect on Data-Group Similarities

Four arbitrary collections of detrital zircons were analyzed by EMP, using high beam currents and long counting times to produce calculated 1-sigma detection limits (DL) for U, Th, and Pb of 174, 129, and 97 ppm, respectively. The spectrometer background position was determined by qualitative scans across element peaks. 300 analyses were collected: 100 for two collections and 50 for the others, and data manipulation and Student's t-test calculations for the groups were made using a spreadsheet program. The compositional results were U: 0-3.6 wt. %, Th: 0-0.32 wt. %, and below-DL for Pb. It was assumed that below-DL net-count results should cluster around 0. Histograms of net counts below-DL had non-zero means for all three elements, suggesting that the background measurements were incorrect: the maxima were offset from 0 by +20 cts/sec/nA for U and Th, and - 80 cts/sec/nA for Pb (negative net counts were reported, but below-DL results were returned as 0 wt. % by the EMP software). Above-DL wt. % data were regressed against count rates, all the net counts were shifted to set the below-DL mean at zero counts, and the overall (+ and -) wt. % values were recalculated according to the regression. The non-zero means for U and Th were thus reduced by 40 and 9 ppm, respectively. The mean Pb was -3.2 wt. %, calculated from the net counts and Pb (ca. 64 wt. %) of the crocoite standard; this result was unreasonable, but the count-rate data (containing no compositional interpretation) for Pb was used for t-tests. The difference between t-test results from data including 0 wt. % values and from count-rate values was significant. For example, the inclusion of numerous 0 wt. % data in a group with low U concentrations biased the mean and standard deviation to suggest that the group was distinct, but the use of net count rates showed that the group was similar to another group with low but detectible U. Wt. % results for Pb were meaningless due to the calibration error, but the net-count data allowed comparison and discrimination between groups based on t- test calculations.