Retain information in nondetects without fabricating values

Define the evidence question

A reported nondetect does not establish that a substance is absent. It means the measurement did not quantify a value above a specified reporting limit under the method used. The limit and detection/quantification convention must be retained with the observation rather than replacing every censored result with an exact invented number.

Reconstruct the observation or physical model

The original finite sample contains quantified concentrations 2,4,6 µg/L and two nonnegative values below separate limits L1 and L2. The sample sum is at least 12 and strictly below 12+L1+L2. Dividing by five gives a lower bound and an upper supremum for this sample mean. The strict upper endpoint is not attained under the stated below-limit convention.

Separate the competing interpretations

Half-limit substitution gives one number within those bounds, but the measurement supplies no probability distribution making that number unbiased. Different limits across time can create apparent trends if censoring is handled inconsistently. More suitable statistical methods depend on the sampling design, distributions and censoring structure.

Challenge uncertainty and identification

These arithmetic bounds are not confidence intervals for a population and do not determine regulatory compliance or safety. Measurement error in quantified results and uncertainty in the limits are deliberately omitted. The exercise preserves what the packet actually says while identifying what additional evidence a statistical analysis would require.

Worked original packet

With limits 2 and 4, the sample mean lies from 2.4 inclusive to 3.6 exclusive µg/L. Half-limit substitution gives 3.0, but that is a chosen assumption rather than five measured concentrations.

Investigation

Compare two low limits with two high limits while leaving quantified observations unchanged. Report the interval and explain why a changing substitution mean does not demonstrate a physical concentration trend.

Changed-case transfer

With limits 1 and 5, calculate the mean bounds and half-limit result. Is the result a population confidence interval?

Feedback

Bounds remain[2.4,3.6) µg/L and half-limit mean 3.0 because the limit sum remains 6. No population sampling or probability model was supplied, so these are finite-sample bounds, not confidence limits.

Sources and evidence boundary

Original prose, numerical packets and exercises. Primary method/mechanism source, checked 30 October 2026. No current measured climate values, personal risk estimates, exposure limits or regulatory conclusions are inferred from these fictional cases. Retain first reasoning and critique in the course workspace. No physical pollutant exposure or environmental intervention is requested.