Which Question Cannot Be Answered Through Making Measurements

Emma’s Thoughts: “Precision”, “Accuracy” and “Uncertainty” – what’s the difference?

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Have you ever started writing a lab report and wondered whether or not you should describe your measurement in terms of “accuracy” or “precision”? What about describing the error in your experiment as a measure of “accuracy” or “uncertainty”?

You’re not alone! Precision, accuracy and uncertainty all relate to error, but have different meanings. To clarify these terms, I think it is useful to study them side-by-side.

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• Precision refers to how close your measurements are to each other when you repeat a measurement multiple times. If the values obtained are close to one another, your measurements are precise. For example, say you were measuring the rebound height of a basketball, dropped from a fixed height. After performing the measurement multiple times, you find that the measured rebound heights are very close in value to each other. You could then report that “After repeating our measurement multiple times, the values that we obtained were very close together. Our measurements were precise!”. Of course, you have to specify what you mean by “close” (perhaps in terms of the divisions on the ruler that you used to measure rebound height).
• Accuracy measures the agreement between a measured value and its true value. If the measured value is close to the true value, your measured value is accurate. For example, say that you developed a model for the distance covered by a rock thrown with a slingshot. If you find that the measured value is close to the predicted value, you would say that your model is accurate, “Our model value was very close to the value that we measured – our model was accurate.” Again, you have to specify what you mean by “close”, usually in terms of the uncertainty on your measured value.
• Uncertainty is an estimate of the amount that a measurement will differ from a true value. In science, we aim to lower the uncertainty in our measurements, so that we can test models and theories with more precision. Let’s say that you are measuring the number of rotations of a spinning top during a certain period of time. Your measurements are close together, but have a fixed range of values. This would be an example where you could calculate the uncertainty in your measurements. It would be sensible to say “After multiple measurements, we’ve found that our values are similar and our uncertainty captures the range of values that we measured.”

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