A non-detect is not an exact numerical zero. When an analytical table mixes measured values with less-than qualifiers, an ordinary mean cannot be calculated without deciding how to handle the incomplete numerical information. That decision can change the answer substantially, especially in small datasets.
Identify the missing numerical information
A reported value of less than 2 ng/mL supplies different information from a measured value of 2 ng/mL. It also differs from a blank cell, which may indicate that no result was obtained at all.
In a USGS-hosted research summary, Dennis Helsel explains that substituting fractions of detection limits can distort estimates and obscure or create apparent relationships. Methods designed for censored data offer alternatives to routine substitution.USGS / D. R. Helsel — Fabricating data: How substituting values for nondetects can ruin results, and what can be done about it (opens in a new tab)
The relevant lesson for a report reader is not to choose a fashionable statistical method from its name. First establish what each qualifier means, why it was assigned and whether the limits are expressed on comparable sample bases.
Compare three common shortcuts
Consider four hypothetical results on the same basis: 6 ng/mL, 10 ng/mL, less than 2 ng/mL and less than 2 ng/mL. Replacing both qualified entries with zero gives a mean of 16 ÷ 4 = 4 ng/mL.
| Rule | Calculated mean |
|---|---|
| Replace each <2 with 0 | 4.0 ng/mL |
| Replace each <2 with 1 | 4.5 ng/mL |
| Omit both qualified entries | 8.0 ng/mL among the two retained results |
The last calculation answers a different question: the average among the retained quantified results. It should not be labelled the average across all four samples without explaining the exclusions.
None of these calculations identifies the two unreported concentrations. A precise-looking decimal produced by the spreadsheet does not reduce that missing information.
Use a limited interval illustration carefully
For arithmetic illustration only, assume each less-than entry represents an unknown non-negative value strictly below 2, and treat the two quantified values as fixed. Under those assumptions, the four-value mean lies from 4 ng/mL up to, but not including, 5 ng/mL.
This is a bound on the simplified input values, not a confidence interval for the true population mean. It does not include uncertainty in the quantified results, sampling variation or imperfect detection classification.
In actual measurements a reporting limit is not an infallible upper bound on the true concentration. The method’s uncertainty and detection behaviour still matter. State the simplifying assumption rather than promoting the arithmetic bound into an analytical guarantee.
If one sample instead has a higher reporting limit because it was diluted, the information available for that sample is different. Replacing every non-detect with the same number would conceal that difference.
Choose a summary that fits the available evidence
A useful initial summary can give the number of samples, number quantified, range of reporting limits and distribution of quantified values. This preserves important information even when the data do not support a reliable estimate of the overall mean.
For formal estimation, the appropriate censored-data method depends on the sample size, fraction censored, limit pattern, distribution assumptions and question being asked. A four-sample illustration is not enough to validate a complex model.
Document the chosen approach before using the summary to support a conclusion. If different reasonable treatments change that conclusion, report the sensitivity instead of selecting the one that produces the preferred result.
Keep original laboratory values and qualifiers in the source table. Derived replacements, exclusions or model estimates belong in clearly identified analysis fields so the calculation can be reconstructed.
Sources and further detail
- USGS / D. R. Helsel — Fabricating data: How substituting values for nondetects can ruin results, and what can be done about it (opens in a new tab)
Chemosphere, 2006; DOI 10.1016/j.chemosphere.2006.04.051. Official indexed abstract read; full journal text was not used. The four-sample example and conditional interval calculation are original.
Sources checked 19 September 2026. Worked examples are illustrative unless a supplied report is explicitly identified. This article has not undergone independent scientific peer review.