11.2 - Accuracy, Precision & Error

Accuracy and precision

• A precise result isn't always accurate.
• For example, weighing a 50.0 g mass on a balance that isn't zeroed might give 52.0 g, 52.1 g, and 52.0 g. These readings are precise (they barely differ) but not accurate (they're all about 2 g too high).

Resolution

• The resolution of an instrument is the smallest change it can detect.
• A balance reading to 0.01 g has a higher resolution than one reading to 0.1 g.
• Describe an instrument as having "higher resolution", not as being "more precise" - precision describes how closely a set of readings cluster, not a single reading.

Repeatable and reproducible

• Repeatable - You get similar results when you repeat the investigation yourself, using the same method and equipment.
• Reproducible - Someone else gets similar results, or you get them using a different method or different equipment.
• Reproducible results give more confidence than repeatable ones, because getting a similar result with a different set-up rules out a fault in one person's technique or one piece of equipment.

Estimating uncertainty from repeats

Repeat readings scatter about a mean, and the size of that scatter determines the uncertainty.

Range and uncertainty

• Range - The largest reading minus the smallest reading in a set of repeats.
• Uncertainty - Half the range, because the true value is expected to lie within half the range on either side of the mean:

• Results are written as mean ± uncertainty.
• A larger range means a larger uncertainty and less precise readings.

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Worked example - Uncertainty of a titration

A titration repeated three times gives titres of 24.50 cm³, 24.60 cm³, and 24.55 cm³. Find the mean and the uncertainty.

Random and systematic error

• Random error - An unpredictable difference between readings, such as slight differences in judgement when reading a scale. Taking repeats and calculating a mean reduces its effect.
• Systematic error - A fault that shifts every reading by the same amount in the same direction, such as a balance not set to zero (a zero error). Taking a mean doesn't reduce it.

Effects on accuracy and precision

• Random error scatters readings, reducing precision.
• Systematic error shifts every reading the same way, reducing accuracy.
• A set of results that is precise but not accurate points to a systematic error.

Anomalous results

• An anomalous result (or outlier) lies well outside the scatter of the rest of the readings.
• Exclude anomalies when calculating the mean.