When we measure things, we face some restrictions. These limits come from either the tool we use or changes in what we're measuring. The uncertainty is the amount that the measured value can differ from the actual value. It could be a tiny difference a big one. These are called physical limitations in measurements.

Limitations due to the instrument’s accuracy

Sometimes, the measuring instruments we use can limit our measurements. These limitations can make it difficult to get accurate results. There are two reasons for these limitations: instrumental accuracy and instrumental functioning.

Instrumental accuracy happens when the thing we want to measure is smaller than what our instrument can measure. For example, if we want to measure an object that is 19.5mm long, but our ruler only has centimetre marks, our measurement will only be an estimate, like 2cm, which isn't the true value.

Instrumental functioning happens when our instrument has a problem or has become inaccurate over time. For instance, if we use a digital thermometer that's off by 2 degrees Celsius, then all temperature readings will be off by 2 degrees.

How does data deviate and produce ‘errors’?

Whenever we take measurements or read data, there's always a chance for errors. These errors can come from the instrument we use, the person taking the measurement, or the system we're working with. The errors can be grouped into two categories: systematic and random errors.

Systematic errors are caused by a consistent problem with the instrument, person, or system. For example, if a scale always reads 2 pounds heavier than the actual weight, that's a systematic error.

Random errors, on the other hand, happen by chance and are unpredictable. They can come from factors like environmental conditions or human error, like reading a gauge incorrectly.

Finally, gaffe errors happen when something goes wrong with the instrument itself, like a broken sensor or a misreading.

Systematic errors

Systematic errors are not accidental and are caused by the instrument or system. These errors occur consistently in every measurement. Common sources of these errors include using the instrument incorrectly, deviation within the instrument, or issues with the system used to analyze the data.

There are three main sources of systematic errors:

1. Instruments: These errors occur when the measuring instrument adds, subtracts, or modifies the measured data during each measurement, leading to a consistent deviation in the data.
2. Systems: This error source is a defect in the system used for the measurements, such as a malfunctioning computer program or a faulty sensor.
3. Observations: This error type occurs due to discrepancies between the measured value and how the individual reads that value. Also known as "observational error," it can result from mistakes made by the person taking the measurement, such as making a parallax error when measuring length with a ruler. In this case, the measured length may differ from the true length due to the experimenter looking at the ruler markings from an angle.

Random errors

Random errors are caused by chance and can occur due to various factors. They are not consistent, and their presence can cause sudden deviations in measured values. There are two main sources of random errors:

1. Systems: An error can be produced by a defect in the system, such as the sudden malfunction of a sensor. This type of random error is not consistent and occurs as a one-off event.
2. Observations: In contrast to systematic errors, random errors in observations are just blunders, such as a wrong reading. They occur unexpectedly and are not consistent.

Random errors are unavoidable and can be reduced by taking multiple measurements and averaging the results, which can help to smooth out any deviations caused by random errors.

What are precision and accuracy?

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

Precision

Precision refers to the consistency and repeatability of measured values. If a measuring instrument is precise, it will produce measurements that are consistently close to one another. This means that if we measure the weight of an object that should weigh 4.3kg, we will get results that are very close to 4.3kg every time we measure it.

However, precision does not necessarily mean that the measurements are accurate. An instrument can be precise but still consistently deviate from the true value. For example, a scale might consistently produce measurements that are close to 4.0kg for an object that actually weighs 4.3kg. This type of error is called a systematic error and can be a result of a defect in the instrument or an error in the measurement process.

Therefore, it is important to ensure both precision and accuracy in measurements to obtain reliable and valid data.

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.

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When taking measurements, it is important to understand that there will always be limitations and uncertainties due to physical limitations of the instruments or the user. These limitations can lead to differences between the measured values and the real ones, which are called errors. Errors can be either systematic or random, and both can affect the accuracy and precision of the measurements.

Accuracy refers to how closely the measured value corresponds to the true value, while precision refers to how consistently the same value can be measured. An instrument can be accurate but not precise if it consistently produces values close to the true value but with a large variation in the measurements. On the other hand, an instrument can be precise but not accurate if it consistently produces the same value but with a consistent deviation from the true value.

It is important to consider both accuracy and precision when interpreting measurement results. Any deviation of measured values from the real ones due to limitations in measurements are called uncertainties, and they should be taken into account when making decisions based on the measured values.

Limitations of Measurements

What are physical measurements?

Physical measurements are measurements of an object’s physical properties, such as its length, mass, luminous intensity, electrical charge, temperature, particle quantity, and time. Also, any combination of the seven elemental physical properties can be measured.

What limitations are there in measuring physical properties?

When measuring any property, limitations are present in the instruments or in how the user reads the measured values. Other limitations can come from the theory or the system used to measure physical properties.

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