1.2.9Development of Practical Skills in Physics

Precision, Accuracy and Experimental Limitations

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1.2.9 Precision, Accuracy and Experimental Limitations — OCR A Level Physics A notes: Distinguish precision, accuracy, resolution, repeatability and reproducibility, and identify the limitations that affect a practical result.In everyday speech the two words are used loosely, but…

Random errors
Systematic errors
Worked example 1
not accurate
Worked example 2
reproducible

Section 1 of 9Precision and accuracy are different ideas

In everyday speech the two words are used loosely, but in physics they mean different things.

Accuracy

Accuracy how close a measurement is to the true value. High accuracy means small systematic error.

Precision

Precision how close repeated measurements are to each other. High precision means small random scatter.

Imagine four darts thrown at a target.

Tightly grouped around the centre: precise and accurate.

Tightly grouped but far from the centre: precise but not accurate, a sign of a systematic error.

Widely spread around the centre: accurate on average but not precise.

Widely spread and off-centre: neither.

A result can be precise without being accurate; for example, a stopwatch that gains 0.5 s every minute will give very consistent but wrong times.

Section 2 of 9Resolution, repeatability and reproducibility

Resolution is the smallest change in a quantity that an instrument can detect. A digital balance reading to 0.01 g has a resolution of 0.01 g. High resolution is necessary for high precision, but it does not guarantee accuracy: a balance that has a zero error of 0.3 g still displays to 0.01 g.

Repeatability describes how close results are when the same person repeats the measurement with the same apparatus and method over a short time. Reproducibility describes how close results are when a different person, apparatus or laboratory carries out the experiment. Agreement between independent groups is strong evidence that a result is real and not a quirk of one set-up.

Section 3 of 9Sources of error and how they appear

Random errors arise from unpredictable variation: fluctuating readings, difficulties in judging the exact moment to stop a timer, small changes in room conditions. They scatter results both sides of the true value. Averaging many readings reduces them, and they are shown on a graph by points scattering on both sides of the best-fit line.

Systematic errors always push readings the same way: zero errors, poorly calibrated meters, a metre rule worn at the end, an object's temperature changing the resistance.

Sources of error and how they appear

They produce a displaced line, often with a wrong intercept, and cannot be reduced by averaging.

They can be found by calibration against a standard, by checking zero readings and by comparing two different methods.

A mistake (misreading, wrong unit, wrongly recorded number) is neither random nor systematic and is removed by care and checking.

Section 4 of 9Experimental limitations

A limitation is a feature of the method or apparatus that restricts the quality of the result.

Experimental limitations

Typical examples are: instrument resolution too coarse for the quantity (a 1 mm rule for a wire diameter), human reaction time in timing, energy losses to the surroundings in calorimetry, air resistance in a falling-object experiment, internal resistance of a power supply, and too small a range or too few points.

In an evaluation, name the limitation, say which result it affects and in which direction (“heat loss makes the measured specific heat capacity too high because less temperature rise is observed for the electrical energy supplied”), and suggest a fix.

Quantify wherever possible. Comparing percentage uncertainties shows which limitation matters most, so effort goes where it improves the result most; see Analysing Quantitative Data (1.2.2).

Section 5 of 9Practical consequences

When designing an experiment, balance the aims.

Increase precision by repeating, by using larger quantities and by choosing instruments with finer resolution.

Improve accuracy by calibrating, zeroing and controlling variables.

Report precision using the uncertainty and judge accuracy by comparing with an accepted value.

The two are connected in the final conclusion: a result with a small uncertainty that disagrees with theory implies an unidentified systematic error, whereas a result with a large uncertainty that agrees with theory is correct but not impressive.

These ideas are applied in Methods to Increase Accuracy (1.2.11).

Section 6 of 9Linking to the whole investigation

Treat precision and accuracy as two separate questions when you review any practical. Ask how big the scatter is, then ask whether the average sits where theory says it should. Both answers belong in the evaluation.

Section 7 of 9Worked examples

Five measurements of a 100.0 g standard mass on a balance read 100.8, 100.9, 100.8, 100.7 and 100.8 g. Comment on the precision and accuracy.
A student measures the period of a pendulum as 1.52 s, 1.55 s and 1.49 s. A second student using the same apparatus gets 1.60 s, 1.62 s and 1.61 s. Discuss the repeatability and reproducibility.
A 20 cm ruler with a worn end is used to measure a 12.0 cm length. The worn end means the zero mark is 1 mm in from the end and the student places the end at the edge of the object. What is the systematic error and its percentage?

Section 8 of 9Key terms

Term	Meaning
Accuracy	Closeness of a measurement to the true value.
Precision	Closeness of repeated measurements to each other.
Resolution	The smallest change an instrument can detect.
Repeatability	Agreement when the same observer repeats the experiment with the same equipment.
Reproducibility	Agreement when different observers or equipment give the result.
Systematic error	A consistent offset in all readings in one direction.

Section 9 of 9Exam technique

Using ‘accurate’ and ‘precise’ as synonyms.

Claiming that averaging many readings removes a zero error.

Confusing resolution with accuracya very fine scale can still be wrong.

Quoting ‘human error’ as a limitation instead of a specific cause such as reaction time.

Describing a limitation without saying which way it moves the result.