SCIENCE · INVESTIGATE AND EXPLAIN

Choose evidence that separates explanations

Design a useful test under instrument limits.

Learning outcome: Compare prediction separation with measurement error before collecting data.

Starting recap

An error bound gives an interval of possible measurement outcomes; it is not a probability.

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Try

Two models predict 4 and 6 cm, but the instrument may be wrong by 1 cm in either direction.

Open the experiment

Predict

Will an input that separates exact predictions still separate uncertain readings?

Your prediction and reason

Experiment

Keep time at 3 seconds. Compare error bounds 0.25, 1 and 2 cm. Then choose a stronger input.

Choose a discriminating input

Worked teaching model · synthetic values · Model A predicts 4 cm; model B predicts 2 cm/s × input time. Each prediction has a bounded measurement interval, not a probabilistic confidence interval.

Input setting: 2 s Absolute measurement error bound: 0.5 cm

Reset keeps your prediction, captures and practice history.

Calculated values on the same fixed scale
Row	Quantity	Value (cm)
1	Model A prediction	4
2	Model B prediction	4
3	Prediction separation	0
4	Combined interval half-widths	1

The bounded prediction intervals overlap.

A test separates these bounded predictions only when |4 − 2t| > 2 × error bound. A larger gap helps only within the stated model domains. Neither model is established as true by choosing this input.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

An instrument can blur a good theoretical comparison

Suppose model A predicts 4 cm and model B predicts 6 cm. With an absolute measurement error no larger than 0.5 cm, A permits readings from 3.5 to 4.5 cm and B permits 5.5 to 6.5 cm. Those ranges are disjoint.

With an error bound of 1 cm, the ranges become 3–5 and 5–7 cm. A reading of 5 cm is compatible with both. Touching is not the same as being disjoint.

For two predictions, a sufficient separation condition is absolute prediction difference > twice the error bound, when both use the same bound. In the lab, the difference is the absolute value of 4 − 2t, where t is time in seconds. Both quantities being compared have units of centimetres.

Bounds are assumptions

The error bound is not a confidence level. It says that values outside the stated interval are excluded by the assumed measurement model. If the instrument has an additional unknown bias, that assumption may fail.

Choose a time that separates the models at the current resolution. Then increase the bound without changing the time. Your conclusion can change even though the exact predictions do not.

Real model discrimination also needs an observation, a valid measurement procedure and a defensible model domain. The activity teaches test selection, not proof that either candidate describes reality.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

State the inequality that makes the bounded intervals disjoint, and a condition under which the test is inconclusive.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Ask a question that can be tested Next: Read an instrument with units

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