the same lines in the gamma-ray spectrum. The results for ^{232}Th and ^{228}Ra should be comparable because both are actually based on measuring gamma-rays from the decay product ^{228}Ac. The

results for rays from

238 234 U and Th.

^{234}Th should be comparable because both are actually based on the gamma-

For both of these statistical tests, each sample for which one or both labs failed to detect and measure the radionuclide of interest was omitted from the data set.

Test 1: For the first test, each difference was normalized by dividing it by its standard uncertainty (i.e., an estimated standard deviation).^{5 }A two-sided t-test was then performed on the normalized differences to test whether the mean normalized difference was different from zero at the 5 % level of significance. For ^{226}Ra, ^{40}K, and ^{238}U/234Th no significant differences were detected. However, a statistically significant difference was found for ^{232}Th/^{228}Ra. NAREL’s

results for ^{228}Ra were significantly higher than FDOH’s results for based on the activity of the gamma-emitting decay product ^{228}Ac).

^{232}Th (both of which were

Test 2: For the second test, the differences were not normalized. A two-sided t-test was performed on the unnormalized differences to test whether the mean difference was different from zero at the 5 % level of significance. Test 2 produced the same conclusions as Test 1 for all four radionuclides. A statistically significant difference (at the 5 % level) was found only for

^{232}Th/_{228}Ra.

The “relative percent differences” (RPD) between NAREL’s results and FDOH’s results were also calculated and averaged by nuclide. The RPD is defined as follows

RPD =

N–F (N + F)/2

× 100 %

where N = NAREL’s result for a particular sample and F = FDOH’s result for the same sample. Although the sample-by-sample RPD values vary from less than 100 % to more than +100 %, the average RPD is large (37 %) only for ^{232}Th/^{228}Ra.

232

228 Th/ Ra

238

234 U/ Th

226 40 Nuclide Ra K

RPD +4.2 %

0.5 % +37.0 % +6.8 %

Note: Some of the normalized differences for particular samples and nuclides are unusually large. If there were no systematic differences between the labs and if the measurement uncertainties were realistic, one would expect nearly all the normalized differences to fall between 3 and +3. In fact several of the normalized differences exceed ±3 and one of them exceeds +5. The large difference between the two ^{40}K results for sample 90675-04963 is particularly hard to explain, since ^{40}K is generally considered to be easy to measure. NAREL double-checked its result for this sample, which is similar to the ^{40}K results for other samples. FDOH’s result for this sample is smaller than the ^{40}K result for any other sample in the group.

5 The uncertainties reported with the FDOH results represent counting uncertainty only. The uncertainties reported by NAREL include counting uncertainty and other uncertainty components.

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8/10/2009