Uncertainty & measurement
Agreement within uncertainty
Compare two values using their uncertainty intervals.
Your measurements
Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
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Result & working
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Interpretation & assumptions
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Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Values in the same unit. | |
| Non-negative interval half-widths with an explained meaning. |
Worked example
- Measured value a
- 9.7
- Absolute uncertainty in a
- 0.2
- Reference / second value b
- 9.81
- Absolute uncertainty in b
- 0
- Common unit
- m/s²
The stated intervals overlap.
Follow the example steps
- A = 9.7 ± 0.2 m/s²; B = 9.81 ± 0 m/s².
- Separation = |9.7 − (9.81)| = 0.11 m/s².
- Sum of interval half-widths = 0.2 + 0 = 0.2 m/s².
- 0.11 ≤ 0.2: The stated intervals overlap.
Common mistakes
Overlapping intervals do not prove a model.
Incorrect approach
10 ± 1 and 11 ± 1: the model is proven.
Correct approach
[9, 11] and [10, 12] overlap; the values are compatible under this interval convention.
More checks before you submit
- Do not claim that overlap proves the theory.
- Compare quantities in matching units.
- Keep systematic effects in view even when the random spread is small.
Method notes
Use interval overlap as a simple school-lab consistency check. A touching endpoint counts as overlap. A result can have a small percentage error yet fail this check if its claimed uncertainty is very small.
Overlap means the measurements can share a value within these stated bounds. It does not prove equality or validate the apparatus. Non-overlap suggests investigating the model and uncertainty estimates.
This is not a hypothesis test, p-value or confidence-level calculation. Standard-deviation bars need a statistical interpretation before using them as interval bounds.