There are some physical limitations in measurements, which are linked to the instrument used or to changes in the measured quantity. The variation in the value of the measured quantity, which can be small or large, is called ‘uncertainty’.
Limitations due to the instrument’s accuracy
Some limitations in measurements are the result of the measuring instruments. The limitations of the instrument can produce results that differ from the true values. There are two sources for these errors, instrumental accuracy and instrumental functioning, as in the examples below:
Instrumental accuracy: the variation of the property you want to measure is smaller than the scale of your instrument. An example of this is when you measure the length of an object whose total length is 19.5mm, but your ruler only has centimetre marks. In this case, your measurement will only be approximate, i.e., you might get a reading of 2cm, which is a close approximation but not the true value.
Instrumental functioning: your instrument has a defect or has become inaccurate over time. An example of this is using a digital thermometer that differs from the actual temperature by 2 degrees Celsius so that all temperature readings will be off by those 2 degrees.
Figure 1. The scale of the instrument can limit the accuracy of our measurements. Source: Flickr (Public Domain).
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:
- 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.
- Systems: this error source is a defect in the system we are using for our measurements.
- 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:
- 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.
- 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.
Figure 2. The object in this image has a length of 4.25cm. Source: Manuel R. Camacho, StudySmarter.
- 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.
Physical Limitations of Measurements - Key takeaways
- When taking measurements, there will always be limitations. These limitations lead to differences between the measured values and the real ones.
- Limitations in measurements are the product of the instruments or the user.
- Limitations in measurements produce errors in the measured values.
- Any deviation of measured values from the real ones produced by errors or any measurement limitations are ‘uncertainties’.
- Errors can be either systematic or random. Systematic errors have their origin in the instruments or the system, while random errors are the results of pure chance.
- Precision and accuracy describe the quality of measurements. Accuracy is the property of measuring a value close to the real one, while precision is the property of consistently repeating the same value.
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