PSLE-SCI-REALITY-0130
Wait, What? “Not Detected” Is Not the Same Sentence as “There Was None”
A monitoring report contains five results: 12, 9, ND, 8 and ND. Someone preparing a neat infographic replaces both “ND” entries with 0, calculates an average, and publishes the result as though every zero were an actual measurement.
The arithmetic may be tidy. The scientific meaning may not be.
“ND” usually means the measurement system did not detect the target above a stated detection or reporting limit under the conditions of that test. The real amount might be zero. It might also be a small positive amount below the method’s ability to distinguish or quantify reliably. Those possibilities are scientifically different.
This Reality Lab asks a narrow but powerful question: when a dataset contains non-detects, what happens to the scientific story if we silently turn them into zero before calculating an average, drawing a graph or comparing two places?
Quick Answer
- Find the detection or reporting limit attached to each non-detect.
- Do not read “not detected” as a direct observation of zero unless the method and scientific context justify that interpretation.
- Check how the report handles values below the limit before calculating summaries.
- Ask whether replacing non-detects with zero pushes an average, trend or comparison downward.
- Keep the conclusion inside the evidence. If the method cannot resolve the exact low value, the scientific statement should preserve that uncertainty rather than invent precision.
The Exact Learner Job This Page Owns
This page owns one real-world evidence-transfer job: evaluating a chart, table, dashboard or report that converts measurements below a detection limit into numerical zeros before summarising the data.
It does not replace the canonical PSLE Science owners for averages, graphs, measurement, uncertainty or evidence selection. It applies those skills to a scientific communication object that learners can meet in environmental monitoring, laboratory reports and public data.
- Reality Lab Vol No.094: “Detected” — Does That Tell You How Much Is There?
- Reality Lab Vol No.111: Can a Method Prove a Claim Below Its Reporting Limit?
- Reality Lab Vol No.112: Is an Estimated Result the Same Kind of Number as an Ordinary Result?
- Scientific Method, Evidence & Measurement | How Science Knows
Original Reality Lab Case: The Five Rainwater Samples
This is an original composite case using constructed data. It is not copied from an examination or real risk assessment.
A fictional laboratory measures Indicator R in five rainwater samples. Its reporting limit is 5 units. Results are:
| Sample | Laboratory report |
|---|---|
| A | 12 units |
| B | 9 units |
| C | ND, reporting limit 5 |
| D | 8 units |
| E | ND, reporting limit 5 |
A social-media post rewrites the results as 12, 9, 0, 8 and 0. The reported mean becomes 5.8 units.
But what if the two non-detect samples actually contained 4 units each? The mean would be 7.4 units. What if they contained 1 unit each? The mean would be 6.2 units. The laboratory did not tell us which exact low values were present. It told us that those samples were not detected above the relevant limit.
The problem is not that zero can never be used in any scientific analysis. The problem is pretending that the substitution is an observation rather than an analytical choice.
Observed, Reported, Substituted and Inferred
| Layer | What happened |
|---|---|
| Observed by the method | No signal was resolved above the method’s stated lower limit for Samples C and E. |
| Reported | ND with a reporting limit of 5 units. |
| Substituted later | The infographic author entered 0 for each ND. |
| Calculated | A mean based on those substituted zeros. |
| Possible overclaim | “The average amount measured in the five samples was exactly 5.8 units.” |
The scientific skill is to keep these layers separate. A calculated number can look objective even when one of its inputs was a decision rather than a direct measurement.
What “Below the Detection Limit” Actually Protects You From Saying
Suppose a method cannot reliably distinguish values below 5 units from background noise. A result below that threshold does not tell you whether the sample contains 0, 1, 2, 3 or 4 units. The exact interpretation depends on the method and how its lower limits are defined, but the central reasoning rule is durable: lack of detection above a limit is not direct proof of absence.
U.S. EPA guidance on data near detection limits explicitly warns against unjustified treatment of non-detects as zero. Another EPA statistical quality-assurance guide explains that a non-detect can represent a value somewhere between zero and the detection limit and that no single analysis procedure is appropriate for every dataset.
The Denominator and Limit Check
Before you do anything with an ND, ask:
- What exactly is the lower limit called in this report?
- Is it a detection limit, quantitation limit, reporting limit or another project-specific threshold?
- Is the limit the same for every sample?
- Was any sample diluted, concentrated or otherwise prepared in a way that changes its effective reporting limit?
- Does the scientific decision depend strongly on values that could be hiding below the limit?
This matters because “ND < 1” and “ND < 100” do not carry the same information. Both say “not detected” but one measurement system looked much farther down.
The Representation Check: A Zero on a Graph Looks More Certain Than “Unknown Below 5”
A graph forces a visual decision. If the author plots every ND at zero, the line may appear to touch the horizontal axis. Readers can easily interpret that as “none was present”.
There are more honest ways to communicate the situation. A chart can use a special symbol for non-detects, display the reporting limit, separate detected from non-detected results, or explain the statistical treatment in the caption. The exact design depends on the purpose. The principle is constant: do not make the graphic claim more knowledge than the measurement provides.
The Average Check: A Mean Can Inherit the Assumptions Hidden in Its Inputs
Students often learn that an average is calculated by adding values and dividing by the number of values. That arithmetic is correct only after the inputs have been scientifically defined.
If half the dataset consists of non-detects, replacing all of them with zero can strongly lower the mean. Replacing all of them with the detection limit can push the mean upward. Replacing them with half the limit makes yet another assumption. More advanced methods can treat such data as censored rather than as invented exact numbers.
A Primary 5/6 learner does not need to perform those advanced statistical procedures. The learner needs to recognise that the handling rule changes the result and must therefore be visible.
Worked Case 1: Same Detects, Different Detection Limits
Site X and Site Y each report three non-detects. Site X used a method with a reporting limit of 1 unit. Site Y used a method with a reporting limit of 20 units. A headline says, “Both sites had equally clean results because neither detected the substance.”
The evidence does not support that equality. Site X rules out large values much more strongly. Site Y leaves open a much wider range below 20. The same word “ND” can hide different measurement sensitivity.
Worked Case 2: The Before-and-After Treatment Claim
Before treatment, a sample measures 18 units. After treatment, the laboratory reports ND < 5. An advertisement says, “The treatment removed 100%.”
That overstates the evidence. The post-treatment amount might be zero, but it could also be a small amount below 5. A defensible statement would preserve the method limit, for example that the post-treatment measurement was below the stated reporting limit. A separate removal percentage requires a justified treatment of that bounded low value.
Worked Case 3: The Average That Crosses a Decision Line
A project compares its mean with a decision threshold of 6 units. Detected values are 10, 8 and 7, with two ND < 5 results. If the two non-detects are entered as zero, the mean is 5.0. If the hidden values were 4 and 4, the mean would be 6.6. The scientific conclusion near the threshold therefore depends on information the measurement did not resolve.
The correct response is not to choose whichever substitution gives the preferred answer. It is to report the uncertainty and use a method appropriate to the decision.
Worked Case 4: A Dataset With Mostly Non-Detects
A chart contains 50 samples, but 45 are below the reporting limit. The author plots a smooth average line to two decimal places. That precision can be misleading because most underlying values were not actually quantified. Sometimes the more useful scientific communication is the proportion detected above a defined level rather than an exact-looking mean.
Tempting Reasoning That Fails
- “ND means zero.” ND means the target was not detected above the relevant lower limit under that method.
- “If we cannot measure it, it does not matter.” Whether a low amount matters depends on the scientific question, not simply the instrument limit.
- “Use zero because that is the most conservative choice.” Zero is actually the lowest possible assumption; in some decisions it can make the result look cleaner than the evidence supports.
- “Use the detection limit instead.” Substituting the full limit can bias summaries upward. There is no universal replacement rule.
- “Half the limit is always fair.” It is still an assumption, and its suitability depends on the data and purpose.
What Evidence Would Strengthen the Scientific Claim?
- The report states the relevant lower limit for each sample.
- Non-detects remain visibly distinguishable from measured zeros.
- The method for summarising non-detects is explained.
- Sensitivity is sufficient for the scientific decision being made.
- Different reporting limits caused by dilution or sample conditions are preserved.
- Raw or minimally processed values remain available alongside summaries.
- The conclusion is tested for whether a reasonable treatment of non-detects would materially change it.
What Would Weaken It?
- ND values are silently replaced with zero.
- Detection limits are omitted from the table or chart.
- Methods with very different lower limits are compared as though “ND” meant the same thing.
- A mean is reported with many decimal places even though much of the dataset is censored below limits.
- A “100% removed” or “none present” claim is built from non-detects without supporting evidence.
Model and Measurement Limits
Detection and reporting limits are not universal constants. They depend on method, instrument, sample material, preparation, background noise and project rules. Different scientific fields also use related terms differently. That is why a careful reader follows the definition used in the actual report instead of assuming every “limit” means the same thing.
Advanced statistical treatment of censored data can be complex. This article does not teach a single replacement formula because authoritative guidance itself recognises that the appropriate method depends on the amount of censored data and the purpose of the analysis.
How Far Can the Conclusion Travel?
If a sample is reported ND < 5, the strongest simple conclusion is that the method did not detect the target above the stated limit under those conditions. That result can be highly useful. It can rule out large concentrations above the limit. But it does not establish an exact zero, and it does not automatically prove a broad safety, environmental or product claim.
PSLE-Style Transfer Case
A class measures Substance Z in four water samples. The results are 7, 6, ND < 4 and ND < 4. One pupil enters 0 for both ND results and says the average is 3.25 units.
Question: Why should the class not present 3.25 units as though every input were directly measured?
Reasoned answer: The two ND samples were not measured as zero. Their exact values are unresolved below the reporting limit. Replacing them with zero is an assumption that affects the calculated mean, so the treatment must be justified and stated.
Explained Practice
Practice A: “ND < 0.2” and “ND < 20” are both non-detects. Which gives stronger evidence that only a very small amount could be present? The first, because the method resolved much farther down.
Practice B: A graph places every non-detect at zero without explanation. What should you ask? What the reporting limits were and how the zero substitution affects the summary.
Practice C: A product test changes from 10 units before treatment to ND < 2 after treatment. Can you say the final amount is exactly zero? No. You can say it was below the stated limit unless stronger evidence supports more.
Delayed Independent Return: The N-D Check
- N — Not detected: What exactly did the instrument fail to distinguish above background?
- D — Detection or reporting limit: What numerical boundary applies to this sample?
- S — Substitution: Was ND replaced by 0, half a limit, a limit value or another estimate?
- E — Effect: Would that choice change the average, graph or decision?
- B — Boundary: What can the evidence honestly rule out, and what low values remain possible?
Parent and Tutor Teaching Guide
Put five cups on a table. Hide between zero and four counters under two cups and tell the learner only, “The detector can confidently report five or more counters; these two cups were below that limit.” Then ask the learner to calculate the exact average. The learner will quickly discover that an exact average cannot be recovered without making assumptions about the hidden cups.
Next, reveal different hidden values and show how the average changes. The teaching goal is not advanced statistics. It is the scientific habit of refusing to turn an unresolved interval into a made-up exact observation.
Authoritative Sources
- Singapore Examinations and Assessment Board — 2026 PSLE Science Syllabus
- Ministry of Education, Singapore — 2023 Primary Science Teaching and Learning Syllabus
- U.S. EPA — Guidance on Data Near Detection Limits
- U.S. EPA — Data Quality Assessment: Statistical Methods for Practitioners (QA/G-9S)
The official Singapore Science frame fits this problem closely. The 2026 PSLE Science assessment objectives include interpreting and analysing information, evaluating observations, information and methods, and communicating explanations and reasoning. The 2023 Primary Science syllabus also asks pupils to exercise healthy scepticism about assumptions and uncertainty and to understand how Science is presented in different forms and media.
The Quiet Return
Zero is a number.
“Not detected” is a statement about what a measurement system could resolve.
Do not turn one into the other without saying what assumption you made.
