PSLE-SCI-REALITY-0460
Wait, What? One Small Percentage Is Doing Too Many Jobs
A sensor datasheet says Linearity: ±0.2% of full scale. A learner reads the specification and says, “Excellent. Every measurement from this sensor must be accurate to within 0.2%.”
That is too strong. A linearity specification describes how closely the instrument’s response follows an expected straight-line relationship over a stated range and method. It is one performance characteristic. Total measurement quality can also depend on calibration, offset, repeatability, hysteresis, resolution, environmental conditions, reference quality and other uncertainty contributions.
This Reality Lab teaches one evidence-transfer job: do not turn a component specification into a guarantee about the whole measurement.
Quick Answer
- Linearity describes deviation from an expected linear input-output relationship under stated conditions.
- It is not automatically the same thing as total accuracy.
- The percentage may be expressed relative to full scale, reading or another defined basis; read the datasheet carefully.
- An instrument can have excellent linearity but still be shifted by an offset or calibration error.
- It can also be repeatable but nonlinear, or linear over one range but not another.
- To judge a measurement claim, combine the relevant specifications instead of promoting one number into a universal guarantee.
The Exact Learner Job This Reality Lab Owns
Owned learner job: evaluating a datasheet, comparison chart or laboratory report that gives a linearity or nonlinearity specification and deciding what that number actually says about the instrument’s response.
Not owned here: general calibration, accuracy versus precision, sensor sensitivity, hysteresis, full-scale percentages, uncertainty calculations or choosing measuring instruments. Those concepts already have their owners. This page applies them to a specific communication object: a small linearity percentage that can be mistaken for total accuracy.
Why This Belongs in PSLE Science
The current 2026 PSLE Science assessment is based on the 2023 Primary Science syllabus. Its scientific-inquiry objectives include interpreting and analysing information, evaluating observations, information and methods, and communicating explanations and reasoning. A datasheet is scientific information. The learner’s job is to identify what quantity a specification describes and avoid extending the conclusion beyond that quantity.
NIST measurement guidance defines linearity, more precisely nonlinearity, as deviation of instrument output from a linear dependence on input. NIST calibration guidance also treats calibration models, bias and measurement uncertainty as separate issues. That separation is the heart of this article.
Rebuild the Object: The Pressure Sensor
Imagine a fictional pressure sensor intended to respond from 0 to 100 units. An ideal simple relationship would be:
| Reference input | Ideal output | Actual output |
|---|---|---|
| 0 | 0.0 | 1.0 |
| 25 | 25.0 | 26.1 |
| 50 | 50.0 | 51.0 |
| 75 | 75.0 | 75.9 |
| 100 | 100.0 | 101.0 |
The response is almost a straight line. Yet every reading is shifted upward by about one unit. Good straight-line behaviour does not remove the offset. If the linearity calculation is made relative to the best fitted line, the nonlinearity can be small even while the instrument has a systematic shift relative to the reference.
Straight Does Not Automatically Mean Correct
Imagine drawing a perfectly straight ruler line on a page, but placing the ruler one centimetre too high. The line can be straight and still be in the wrong position. Linearity asks about the shape of the response. Accuracy relative to a reference asks a different question.
This is why a statement such as “linearity ±0.2%” cannot safely be translated into “every reading is within ±0.2% of truth”. The specification needs its own definition and must be combined with other relevant evidence.
Observed, Specified, Inferred
| Layer | Example | Scientific meaning |
|---|---|---|
| Observed | Output values across several reference inputs | Evidence about response behaviour |
| Specified | Linearity ±0.2% FS | A stated bound on deviation from a defined linear relationship |
| Careful inference | The response is close to the stated line under tested conditions | Matches the specification’s job |
| Overclaim | Every future measurement is accurate to ±0.2% | Requires additional performance evidence |
Worked Case 1: Excellent Linearity, Wrong Zero
A fictional temperature instrument produces 2, 12, 22, 32 and 42 units when references are 0, 10, 20, 30 and 40. The spacing is beautifully linear: every increase of 10 in the reference produces an increase of 10 in the reading. But the instrument is shifted upward by 2 units.
The sensor can therefore have strong linear behaviour and still need an offset correction. The example separates two properties that advertisements sometimes blur together.
Worked Case 2: Accurate Near the Middle, Curved at the Ends
Another fictional sensor matches the reference closely around 50 units but bends away near 0 and 100. A single-point check at 50 could look excellent while the full-range response is nonlinear.
This shows why the tested range matters. A claim about linearity over 20–80 units does not automatically extend to 0–100 units. The range printed next to a specification is part of the evidence, not decoration.
The Denominator Matters: Percent of What?
Suppose a sensor range is 0–100 units and its linearity is stated as ±0.2% of full scale. The numerical amount corresponding to 0.2% of full scale is 0.2 units. That does not mean every reading has total error below 0.2 units; it means the linearity term is being expressed on that basis.
Another datasheet might define nonlinearity as a percentage of reading, span or best-fit line. Never assume two identical-looking percentages use the same denominator or calculation.
Worked Case 3: Two Sensors, Two Different Specs
| Sensor | Linearity | Offset specification | Repeatability |
|---|---|---|---|
| A | ±0.1% FS | ±2 units | ±0.2 unit |
| B | ±0.3% FS | ±0.3 unit | ±0.2 unit |
A marketing graphic highlights only Sensor A’s smaller linearity number and calls it “three times more accurate”. That conclusion is unsupported. Linearity is only one performance component, and Sensor A’s much larger possible offset may matter for the intended measurement.
The correct comparison begins by defining the task and considering all relevant terms on comparable bases.
Linearity and Sensitivity Are Different
Sensitivity describes how much the output changes when the input changes. A sensor could have a steep sensitivity and still be nonlinear. Another could have a smaller sensitivity but follow a straight relationship extremely well. Reality Lab Vol No.295 owns the sensitivity communication job; this page only reminds you not to swap the terms.
Linearity and Hysteresis Are Different
Hysteresis asks whether the reading at the same input depends on whether the input approached from above or below. An instrument could follow a nearly straight path in each direction while those paths are slightly separated. Reality Lab Vol No.379 owns that job. Again, one specification does not erase another.
Linearity and Repeatability Are Different
Repeated measurements can cluster tightly around a response curve. That tells you about repeatability. If the curve itself bends away from the intended relationship, repeatability does not repair nonlinearity. Conversely, a response may be linear on average but noisy on repeated trials.
Method Check: How Was Linearity Tested?
- What reference inputs were used?
- How many points covered the range?
- Was the comparison made against an ideal line, end-point line or best-fit line?
- What range and environmental conditions applied?
- Was the input increased only, decreased only or both?
- Were repeat measurements included?
- What does the percentage use as its denominator?
The exact technical definitions vary among instruments and industries. A careful learner therefore uses the manufacturer’s or method’s stated definition rather than assuming “linearity” always has one universal calculation.
Worked Case 4: The Product Comparison
“Our sensor has ±0.15% linearity, so it is scientifically proven more accurate than Competitor B at ±0.3%.”
Before accepting that claim, ask whether the two linearity specifications use the same definition and denominator, whether the overall accuracy specifications are known, whether calibration and offset are comparable, and whether the values apply over the same range and conditions.
A lower nonlinearity number can be genuinely useful. It simply cannot carry every other measurement-quality claim by itself.
What Evidence Strengthens the Claim “This Instrument Measures Well Across the Range”?
- Reference comparisons cover the intended range.
- The linearity definition is stated.
- Offset or bias is checked separately.
- Repeatability is characterised.
- Hysteresis is considered when relevant.
- Calibration and reference traceability are documented.
- Environmental conditions match the intended use.
- The conclusion combines relevant uncertainty contributions instead of quoting one favourable number.
What Weakens It?
- A linearity number is relabelled as total accuracy.
- The tested range is hidden.
- The denominator behind the percentage is omitted.
- Only one reference point is checked while a full-range claim is made.
- Offset and hysteresis are ignored.
- Different instruments are compared using different definitions.
Tempting Reasoning That Fails
| Tempting claim | Why it fails | Better question |
|---|---|---|
| “Linearity ±0.2% means accuracy ±0.2%.” | Linearity is only one response characteristic. | What other error or uncertainty terms apply? |
| “Straight response means correct response.” | A straight line can be shifted by an offset. | How does it compare with a reference? |
| “The smallest linearity number wins.” | The intended task may depend on other specifications. | Which properties matter for this measurement? |
| “0.2% always means 0.2% of the reading.” | The percentage basis may be full scale or another definition. | Percent of what? |
| “One good middle point proves full-range linearity.” | Curvature may appear elsewhere. | Was the whole claimed range tested? |
How Far Can the Conclusion Travel?
A verified linearity specification can support a statement about how closely the response follows the defined straight-line model across the tested range and conditions. It can be important when converting sensor output into physical quantity.
It does not by itself establish the total uncertainty of every future reading, prove zero bias, guarantee repeatability, remove hysteresis or show suitability outside the tested range. Those are separate evidence jobs.
PSLE-Style Transfer Case
A fictional light sensor has a linearity specification of ±0.2% full scale and an offset specification of ±3 units. A student says, “Any reading of 50 units must be correct to within 0.1 unit because 0.2% of 50 is 0.1.” Evaluate the statement.
Reasoned answer: The statement is not supported. First, the linearity term is stated as a percentage of full scale, not a percentage of the reading. Second, linearity is only one performance component; the offset specification and other measurement uncertainties can also affect the reading. The overall accuracy cannot be inferred from the linearity number alone.
Practice 1: Straight but Shifted
Reference values 0, 10, 20 and 30 produce readings 2, 12, 22 and 32. Is the response approximately linear? Is it unbiased?
Answer: The response is highly linear in spacing, but it shows an offset of about +2 relative to the references.
Practice 2: Percent of What?
A sensor says “linearity ±0.5% FS”. What does FS tell you to check?
Answer: FS means full scale in this context. Identify the full-scale range before converting the percentage into physical units.
Practice 3: Range Boundary
Linearity is tested from 10 to 90 units. Can you assume the same behaviour at 120 units?
Answer: No. The claim is supported only over the stated tested range unless additional evidence extends it.
Practice 4: Compare Fairly
Sensor A reports linearity as percent full scale; Sensor B reports maximum deviation from a best-fit line in physical units. Can you compare the printed numbers directly?
Answer: Not until the definitions and units are converted to a comparable basis.
Delayed Independent Return
Later you meet a laboratory graph where signal is almost perfectly proportional to concentration. The same habit transfers: good proportionality supports the calibration relationship, but the final result can still depend on reference values, sample preparation, repeatability and other uncertainties. A component of evidence does not become the whole evidence system.
Routes to Existing Canonical PSLE Science Owners
For the difference between accuracy and precision, see How to Tell Measurement Precision From Accuracy in PSLE Science. For full-scale accuracy wording, see Reality Lab Vol No.388. For sensor sensitivity, see Reality Lab Vol No.295. For hysteresis, see Reality Lab Vol No.379.
Parent and Tutor Teaching Guide
Draw two straight lines on graph paper. Make one pass through the correct origin. Draw the other perfectly parallel but shifted upward. Ask: “Which line is straighter? Which line is closer to the reference?” The child should realise that straightness and correctness are different questions.
Then create five reference inputs and five sensor outputs. First use a constant +2 offset. Next make the offset change with input so the response bends. Ask the learner to identify whether the main problem is shift, curvature or both.
Finally, place three specification cards on the table: linearity, repeatability and offset. Give a product claim that highlights only one card. Ask what additional evidence is needed before making an overall measurement-quality statement. This builds systems thinking without demanding advanced calculation.
Authoritative Sources
- Singapore Examinations and Assessment Board — 2026 PSLE Science syllabus
- Singapore Ministry of Education — 2023 Primary Science Teaching and Learning Syllabus
- NIST — Pressure and Vacuum Measurements, measurement terminology including linearity
- NIST — Calibration
- NIST — Linearity Characterization and Uncertainty Quantification of Spectroradiometers
Quiet Return
A specification becomes misleading when we ask it to answer a question it was never designed to answer.
When you see Linearity = ±0.2%, do not translate it automatically into “accuracy ±0.2%”. Translate it into a better question: How closely does this instrument follow its stated line, over what range, and what other evidence determines the quality of the final measurement?
