Evaluating and Drawing Conclusions

A conclusion answers the original question — and goes no further. Say what the data show, quote the quantity you measured with its uncertainty, and state whether it supports the hypothesis. Resist conclusions your data cannot carry.

Precision — how closely repeated readings agree with one another. Precision is limited by random error and by the resolution of your instruments.

Accuracy — how close a reading is to the true value. Accuracy is limited by systematic error.

The two are independent, and confusing them is the most common mistake in evaluation. A balance with a zero error of +2 g gives beautifully repeatable readings that are all wrong by the same amount: precise, but not accurate.

Example: three measurements of 4.51 s, 4.52 s and 4.51 s are precise. If the stopwatch runs 5% slow, every one of them is inaccurate, and no amount of repeating will reveal it. Only comparison with a known standard would.

Repeatability — the same experimenter, using the same method and apparatus, gets the same results.

Reproducibility — a different experimenter, with different apparatus, gets the same results. Reproducibility is the stronger claim and the one that matters for publication.

Validity — whether the experiment actually tests what it claims to. An experiment can be precise, accurate and repeatable, and still invalid if a control variable was left free. Validity is decided by the design, not by the quality of the readings.

Judging the result against its uncertainty — comparison is only meaningful once uncertainty is included. A measured Young modulus of 2.3 × 10¹¹ Pa ± 0.4 × 10¹¹ Pa is consistent with an accepted value of 2.0 × 10¹¹ Pa, because the accepted value lies inside the range. Quoting the measurement alone makes the two look further apart than the data can justify.

Suggesting improvements — an improvement must attack an identified weakness and be more than "be more careful" or "take more readings". Say what the limitation was, and what specific change addresses it.

Example: "the largest uncertainty was in the wire's diameter, measured with a ruler; using a micrometer would reduce it from about 10% to about 0.5%" identifies the dominant source and fixes it. "Repeat the experiment more times" would not, because repeats do nothing about a systematic error in the diameter.

Anomalies in the evaluation — say which readings you excluded and why. If several anomalies cluster at one end of the range, that is evidence of something systematic — apparatus reaching a limit, or an assumption breaking down — and is worth more than a tidy graph.