# Learner lab record: Correlated uncertainty investigation

Course: Measurement, uncertainty, and evidence

Name: ____________________  Date: ____________________  Group: ____________________

## Investigation question

How does shared movement between two inputs change the uncertainty of a combined result?

## Setup

Use the live uncertainty composer. Change one control at a time, keep a record of every setting, and treat correlation as a declared relationship rather than a guess.

## Variables

| Variable | Role | Unit |
| --- | --- | --- |
| Input uncertainty σx | independent | chosen measurement unit |
| Input uncertainty σy | independent | same unit as σx |
| Correlation ρ | independent | unitless |
| Combined uncertainty σ | dependent | chosen measurement unit |

## Predict before changing controls

1. Predict the result when ρ=0.

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2. Predict whether positive or negative correlation makes the combined interval wider.

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## Observation table

| σx | σy | ρ | combined σ | what changed? |
| --- | --- | --- | --- | --- |
|   |   |   |   |   |
|   |   |   |   |   |
|   |   |   |   |   |
|   |   |   |   |   |
|   |   |   |   |   |
|   |   |   |   |   |

## Analyze

1. Which run reproduced ordinary quadrature?

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2. Which pair of runs isolates correlation?

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3. What assumption would make your comparison invalid?

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4. State the result with units and an uncertainty interval.

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## Evidence-bounded conclusion

When ___ stayed fixed and ρ changed from ___ to ___, combined uncertainty changed from ___ to ___ because ___.

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