Measurement, uncertainty, and evidence
Learn how a careful observation becomes a defensible scientific claim.
Build the habits used throughout the curriculum: define what is measured, record uncertainty, compare explanations, and say what result would change your mind.
Interactive model
Explore before calculating
Live laboratory
Uncertainty composer
Change two input uncertainties and their correlation. The interval shows why correlated errors do not always add by ordinary quadrature.
Result: σ = 0.500. Independent inputs combine in quadrature.
Level 1 · Foundations teaching kit
Record the investigation. Teach the reasoning.
A learner-facing lab record and a course-specific instructor guide turn the live model into a repeatable classroom investigation.
Learner record
Correlated uncertainty investigation
How does shared movement between two inputs change the uncertainty of a combined result?
Download learner recordInstructor guide
Teach for evidence, not button pushing
Learners distinguish independent quadrature from correlated uncertainty and defend a comparison using controlled variables.
Download instructor guideLesson 1 of 3
Observation is not explanation
What did the instrument record, and what story are we adding afterward?
An observation is a recorded event: a thermometer reads 22.4 °C, a detector counts 17 pulses, or a shadow moves 3 cm. An interpretation explains why it happened.
Several interpretations can fit one observation. Science advances by asking which interpretation makes a distinct prediction that another does not.
Worked example
A sealed box loses 2 g on a kitchen scale after warming. Does that prove mass vanished?
- 1. Record the observation: the displayed mass changed by 2 g.
- 2. List alternatives: scale drift, air buoyancy, evaporation through a leak, vibration, or a true mass change.
- 3. Design discriminating checks: use a calibration weight, a second scale, temperature controls, and leak testing.
The display change is real data; the cause remains undecided until competing explanations are tested.
Try it
Claim-sorting notebook
Materials: Paper and any short science-news paragraph.
- 1. Underline direct observations.
- 2. Circle interpretations.
- 3. Write one alternative explanation.
- 4. Write one measurement that would separate the explanations.
Notice: Most headlines mix data and explanation. Separating them makes the next experiment obvious.
Check your understanding: A camera records a bright streak. Which statement is an observation: ‘the object used exotic propulsion’ or ‘a 14-pixel streak crossed the frame in 0.2 seconds’ ?
Answer: The 14-pixel streak crossing the frame in 0.2 seconds.
It reports what the instrument recorded without assigning a cause.
Lesson 2 of 3
Every number has a neighborhood
How precisely do we actually know a measured value?
No instrument gives infinitely precise knowledge. Resolution, calibration, environment, and repeated variation create a range around every result.
Reporting 12.3 ± 0.2 cm says more than reporting 12.3 cm because it tells another person what differences the experiment can resolve.
Worked example
Five pendulum periods are 1.8, 1.9, 1.8, 2.0, and 1.9 seconds. Summarize them.
- 1. Add the measurements: 9.4 s.
- 2. Divide by five: the mean is 1.88 s.
- 3. Use half the observed range, about 0.1 s, as a simple classroom uncertainty estimate.
Report approximately 1.9 ± 0.1 seconds and describe how the timing was performed.
Try it
Reaction-time uncertainty
Materials: A stopwatch and a partner, or a phone timer.
- 1. Time the same short event five times.
- 2. Compute the mean.
- 3. Find the range.
- 4. Compare your spread with a partner's.
Notice: Human timing creates variation even when the event is unchanged; repetition reveals it.
Check your understanding: Two lengths are 10.0 ± 0.5 cm and 10.2 ± 0.5 cm. Has the experiment clearly resolved a difference?
Answer: No.
The uncertainty ranges overlap strongly, so the apparent 0.2 cm difference is smaller than the measurement precision.
Lesson 3 of 3
From source to independent test
What changes when a claim moves from an idea to an independently reproduced result?
A coherent idea is not yet a measurement. A single measurement is not yet a stable effect. Independent replication asks whether the result survives new people, instruments, and assumptions.
A useful report states the measured quantity, calibration, controls and uncertainty. Compare its proposed explanation with alternatives, then specify a measurement that could distinguish them.
Worked example
A device appears to produce thrust on one laboratory balance.
- 1. State the proposed mechanism and the force it predicts.
- 2. Record the signal, calibration, uncertainty and controls.
- 3. Ask another laboratory to repeat the test with different equipment.
- 4. Compare the new results with the prediction and examine any disagreement.
Describe the measured force and uncertainty, the controls performed, and the results of independent tests.
Try it
Read a report the way a reviewer does
Materials: One published experimental report — a paper, a preprint, or a company's own announcement — and a sheet of paper.
- 1. Write down what was actually measured, in one line.
- 2. List the calibration and the controls the report states.
- 3. Name one alternative explanation the report does not rule out.
- 4. Say what an independent laboratory would have to do next.
Notice: The report's measurements and controls show what was tested; an alternative explanation helps identify the next experiment.
Check your understanding: What is the main value of independent replication?
Answer: It tests whether the result survives different investigators, equipment, and hidden assumptions.
Replication reduces the chance that a signal came from one apparatus, analysis choice, or unnoticed bias.
Continue into the evidence