Limitations of Measurements

How does data deviate and produce ‘errors’?

Every time we make a measurement or read data, we can introduce errors. The source of the error can be the instrument, the user, or the system. The errors fall into two main categories, systematic errors and random errors. There is a third type of error, known as a gaffe error, which can be a broken sensor or a wrong reading.

Systematic errors

Systematic errors have their origin in the instruments or the system and do not happen accidentally. Systematic errors appear consistently in every measurement we take. These errors come from using an instrument in the wrong way, from a deviation within the instrument, or from the system that analyses the data. Systematic errors are always present in the system.

There are several sources of systematic errors:

1. Instruments: the measuring instrument adds, subtracts, or modifies the measured data during every measurement. There is, therefore, a consistent deviation in the data measured by the instrument.
2. Systems: this error source is a defect in the system we are using for our measurements.
3. Observations: this error type has its source in the user. Also called ‘observational error’, it is a discrepancy between the measured value and how the individual reads that value. One example is when the individual measures length with a ruler and makes a parallax error. In this case, the measurement of an object’s length differs from its true length because the experimenter is looking at the markings on the ruler from an angle.

Random errors

Random errors are the product of chance and present when the data suddenly deviates from the measured values. They can have two sources:

1. Systems: an error may be produced by a defect in the system, such as the sudden malfunction of a sensor. This is not a systematic error but a one-off event as there is no consistent malfunction.
2. Observations: in contrast to a parallax error, these errors are just blunders, such as a wrong reading.

What are precision and accuracy?

Precision and accuracy are two concepts related to measurements. They determine the quality of our measured values.

Precision

Precision indicates how repeatable our measured value is. If our measuring instrument is precise, every measurement it makes will be close to every other measurement. So, measuring the weight of an object whose value is 4.3kg, we will always get a value very close to 4.3kg.

Precision does not mean the measurements are correct. An instrument can be precise but consistently deviate far from the true value. In our example of an object weighing 4.3kg, a scale might consistently produce values close to 4.0kg.

Accuracy

Accuracy means that the instrument delivers a value that is identical or very close to the true one. A highly accurate scale measuring the weight of a 4.3kg object will always produce values very close to 4.3kg, with only very minor variations.

To achieve measurements of high quality, we, therefore, need instruments with high accuracy and high precision.

• The closer we are to the white circle at the centre, the more accurate the measurement is.
• The measurements in purple are precise but not accurate.
• The measurements in dark blue are neither precise nor accurate.
• The measurements in light blue are precise and accurate.