1.9: Uncertainty in Measurement: Accuracy and Precision
Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.
Suppose a quality control chemist at a pharmaceutical company is tasked with checking the accuracy and precision of three different machines, meant to dispense 500 mL of cough syrup into storage bottles. The chemist proceeds to use each machine to fill five bottles and then carefully determines the actual volume dispensed, as reported in Table 1.
|Table 1. Volume (mL) of Cough Syrup Delivered by 500 mL Dispensers|
|Dispenser #1||Dispenser #2||Dispenser #3|
Considering these results, the chemist reported that dispenser #1 is precise but not accurate. All the values from dispense #1 are close to each other, but none of the values are close to the target value of 500 mL. Results for dispenser #2 showed improved accuracy (values are close to 500 mL) but worse precision (not close to one another). Finally, the chemist reported that dispenser #3 is working well, and it is dispensing cough syrup both accurately (all volumes are within 0.2 mL of the target volume) and precisely (volumes differ from each other by no more than 0.2 mL).
Highly accurate measurements tend to be precise, too. However, highly precise measurements may not necessarily be accurate. For example, an improperly calibrated thermometer or a faulty weighing balance may give precise readings that are inaccurate.
Random and Systematic Errors
Scientists always try their best to record their measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors may be random or systematic.
Random errors are observed due to the inconsistency or fluctuation in the measurement process or variations in the quantity itself that is being measured. Such errors fluctuate from too high or too low from the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a ruler. Random error in this measuring process might be the result of the inconsistent method in which the scientist reads the scales, or if the earthworm isn’t still and its body movements might pose difficulty in taking correct length measurements. Random error cannot be avoided; however, it can be averaged out with repeated trials.
Systematic errors arise from a persistent issue and result in a consistent discrepancy in measurement. These errors tend to be consistently either too high or too low from the true value. These are predictable and are mostly instrumental in nature. For instance, an improperly calibrated weighing balance may consistently weigh objects heavier than their true value. However, unlike random error, systemic errors cannot average out with repeated measurements.
This text is adapted from Openstax, Chemistry 2e, Section 1.5: Measurement Uncertainty, Accuracy, and Precision.