In absence of paired blanks and of non-paired blanks all producing LODs, would you agree with the following statements (please explain):

Answer Explanations

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  Expert 3

  Statement	Yes	No
  Only the mean of all test samples can be corrected by the mean of all non-paired blanks	1	0
  The uncertainty in this difference needs to consider both variability in the test and in non-paired blanks	1	0
  Nothing can be inferred from individual test results because individual correction is not possible	1	0

  1) Generally, yes, but this approach does not account for sample-specific contamination, so it may under- or over-correct individual values.
  2) Yes, because variability (Var): Var(corrected)=Var(samples)+Var(blanks)
  3) Again, generally true, but it is not definitve, as individual results that are significantly higher than the maximum blank value or LOD suggest true positives.
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  Expert 9

  Statement	Yes	No
  Only the mean of all test samples can be corrected by the mean of all non-paired blanks	0	1
  The uncertainty in this difference needs to consider both variability in the test and in non-paired blanks	0	1
  Nothing can be inferred from individual test results because individual correction is not possible	0	1

  As stated elsewhere, I am of the view that the best approach is to provide data for all samples and all QC samples (blanks and recovery determination), as this allows other researchers to assess the validity of the data provided. If I understand correctly the statement "Nothing can be inferred from individual test results because individual correction is not possible", then I disagree as its logical conclusion is that unless a lab has "perfect blanks" always, then it cannot report MNP levels in any sample. In my opinion, if a lab can show that the MNP level in a sample exceeds the MDA as defined by either equations 1 or 2 as appropriate, then the MNP level in that sample may be reported - albeit alongside information on the MDA. This is because the MDA values account for the variability in blanks.
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  Expert 2

  Statement	Yes	No
  Only the mean of all test samples can be corrected by the mean of all non-paired blanks	1	0
  The uncertainty in this difference needs to consider both variability in the test and in non-paired blanks	1	0
  Nothing can be inferred from individual test results because individual correction is not possible	0	1

   Only the mean of all test samples can be corrected by the mean of all non-paired blanks. YES
  When paired blanks are not available the ability to perform sample-specific background or contamination corrections is lost.  In such cases, only aggregate-level corrections are feasible. This can be done by subtracting the mean of the non-paired blanks from the mean of the test samples. Nonetheless, this method could be  valid only under the assumption that the background signal is relatively consistent on average and that the available blanks accurately represent the background affecting the test samples. Without knowledge about the specific blank contribution for each sample, an individual level correction is not possible. 
  The uncertainty in this difference needs to consider both variability in the test and in non-paired blanks. YES
  When the difference between the mean test value and the mean blank value is calculated, the total uncertainty in the result comes from both sources of variability: the variability within the test samples themselves (such as the standard deviation of their measurements) and the variability within the blanks (such as the standard deviation of the blank measurements). This is a classic case of uncertainty propagation, in which the variance of the difference is obtained as the sum of the individual variances, assuming that the two components are independent.  By neglecting either source of variability you could have an underestimation of the actual uncertainty associated with the corrected measurement. 
  Nothing can be inferred from individual test results because individual correction is not possible. NO
  Even when the individual blank corrections are not available, it is still possible to obtain important data from individual test results. If a test value is significantly higher than the blank mean plus its associated uncertainty, it may still be considered distinguishable from the background noise. Additionally, the statistical inference from the individual level is still accurate, provided that the distributions of both the blank and test measurements are well defined. A global correction, such as subtracting the mean blank value from all  the test values, can also be applied, after which the individual results can be evaluated to determine if they exceed the limit of detection or a established detection threshold. Therefore, while the absence of individual blank corrections limits the precision and confidence of such analyses, it does not entirely exclude the obtaining of useful interpretation of individual test data. 
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  Expert 4

  Statement	Yes	No
  Only the mean of all test samples can be corrected by the mean of all non-paired blanks	0	1
  The uncertainty in this difference needs to consider both variability in the test and in non-paired blanks	1	0
  Nothing can be inferred from individual test results because individual correction is not possible	0	1

  First of all, variability in the broadest sense needs to be properly considered. Secondly, I think a possible approach is to correct individual samples for the mean of all non-paired blanks whilst still reporting the variability in the non-paired blancs. This would consider at least one type of variability whilst the other sources of variability are uncertain.
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  Expert 1

  Statement	Yes	No
  Only the mean of all test samples can be corrected by the mean of all non-paired blanks	0	1
  The uncertainty in this difference needs to consider both variability in the test and in non-paired blanks	1	0
  Nothing can be inferred from individual test results because individual correction is not possible	0	1

  For several reasons mentioned above with regard to blanks, which vary in MNP concentrations, using mean to correct all non-paired blanks can yield inaccurate data.  Uncertainty should be discussed in every measurement data.  You can still infer some information for individual test results without paired blank correction, but that information should be cautiously presented. 
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  Expert 6

  Statement	Yes	No
  Only the mean of all test samples can be corrected by the mean of all non-paired blanks	1	0
  The uncertainty in this difference needs to consider both variability in the test and in non-paired blanks	1	0
  Nothing can be inferred from individual test results because individual correction is not possible	1	0

  The mean of all non-paired blanks should be statistically compared to the mean of all test sample first, to test if they are significant different. 
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  Expert 8

  Statement	Yes	No
  Only the mean of all test samples can be corrected by the mean of all non-paired blanks	1	0
  The uncertainty in this difference needs to consider both variability in the test and in non-paired blanks	1	0
  Nothing can be inferred from individual test results because individual correction is not possible	0	1

  something can be inferred by the individual test results - such as range and SD.