# 3.01 Measuring techniques and data handling

## General considerations

The results of measurements that we make can vary with different environmental conditions. E.g. metals expand and contract as the temperature changes, the dimensions of an object may be measured when it is being subjected to some stress or strain which will compress or stretch the object etc. Therefore it is often important to measure and record the relevant conditions under which the main measurement is carried out. (e.g. the length of a copper rod was 10.03cm when the temperature was 28oC etc.)

## Objectives

The objective of this section is to learn the meaning of all the terms written in bold type

## Measurement value and true value

Two important terms that we must be clear on from the beginning are measurement value and true value. The measurement value (which is sometimes referred to simply as the measurement) is the value given by a measuring instrument and the true value is the actual value of the property being measured.

We must appreciate that it is possible for poor quality measurements to be taken that produce measurement values that do not adequately reflect the true value.(The true value is sometimes also referred to as the measured value, however this term will be avoided in this text to avoid any possible confusion with the measurement value)

## Quality of measurement

The quality of a measurement can be described using terms such as uncertainty, precision, error and accuracy.

## Uncertainty

It is impossible to take a perfect measurement i.e. one that would give an exact true value for the property being measured. In practice the best we can do is to determine the upper and lower limits of a range of values within which the true value lies. (For example we may determine that the length of an object is somewhere between 5mm and 6mm). We call this range of values an uncertainty interval (or sometimes simple the uncertainty). To express the measurement we write down the value at the midpoint of the uncertainty interval along with the difference to the upper and lower limits e.g. if the uncertainty interval was from 99cm to 101cm we would write the measurement as 100 +/- 1cm.
The value at the midpoint of the uncertainty interval is sometimes referred to as the nominal value

## Precision

Precision is a description of how exact the measurement value is. It depends on the uncertainty in the measurement, the smaller the uncertainty is then the more precise the measurement value is.

## Example

A common example to illustrate precision and uncertainty is to consider two possible responses to the question what time is it? One response may be about quarter past twelve or alternatively you could be told it is 12.16.

Clearly the second response is more precise and has less uncertainty. (i.e. It is more exact and has less lee way than the first.)
(To say the time is about quarter past twelve would probably be taken to mean that the time could be anywhere between say 12:13 to 12:17.
However if the time is stated as 12:16 then (as you will see later) this would be taken to mean that the time is within +/- 30 seconds of 12:16.)

## Error

Error in measurement theory does not refer to mistakes as such. An error in a measurement is simply any difference between the measurement value and the true value. (It is true that poor measurement skills can introduce or increase errors in measurement values, but errors will be present in any measurement regardless of how skilfully it is taken. This is due to a range of factors that will be considered later. )

Note
We have stated that error is the difference between the measurement value and the true value. However we have also made it very clear that a measurement actually covers a range of values. Therefore when determining the error in the measurement we must take the maximum error in order to take into account the full range of values specified by the uncertainty. Therefore the error is the difference between the true value and the furthest limit of the uncertainty interval.

## Accuracy

Accuracy is a description of how close the measurement value is to the true value of the property being measured. (The smaller the error the more accurate the measurement value will be).

Note there is an important difference between the definition of error used on the science-campus compared to many other internet sources. This difference is stated clearly below and will be justified at the end of this section on measurement.

## Error

Here error has been defined as the difference between the true value and the furthest limit of the uncertainty interval. In many other texts the error is defined as the difference between the true value and the centre of the uncertainty interval!

This second definition has significant flaws and it leads to some paradoxical interpretations of what is meant by accuracy. The Justification of this statement is presented at the end of the section on measurement. So to clarify, this text specifies the error as the difference between the true value and the furthest limit of the uncertainty interval!