Accuracy
refers to the degree of agreement between the result of a measurement and the
true value of the quantity being measured. The more accurate the system, the
closer the result is to the true value.
In practice, the true value is not known. Accuracy therefore describes how
close the measurement result is to a reference value, a standard, or a
recognized measurement technique.
Precision refers to the degree to which repeated measurements of the
same quantity yield similar results. These values differ due to random errors.
The greater the precision, the smaller the dispersion of the data.
It is important to understand that accuracy and precision are different
concepts. Classic illustrations of the distinction between accuracy and
precision:
a. Points scattered and far from the center indicate neither accuracy nor
precision.
b. Points scattered but
centered on average indicate accuracy without precision.
c. Points clustered together
but far from the center indicate precision without accuracy.
d. Points clustered tightly at
the center of the target indicate both accuracy and precision.
Assessing accuracy and precision
To
asses accuracy and precision, the same quantity must be measured repeatedly:
🔺 Accuracy is assessed
by comparing the mean of the measurement results to the true value.
🔺Precision is assessed by the standard deviation of the measurements.
Example
You measured a part three times and
obtained:
15.0 in; 15.1 in; 14.9
in
There is precision, and you can write: (15.0 ± 0.01) in
But if the true value is 40.0 cm, is it accurate?
Since 1 inch = 2.54 cm, then 15.0 × 2.54 = 38.1 cm → Lacks accuracy.
Accuracy and precision are distinct attributes
🔺 Accuracy indicates how close
the measurements are to the true (or reference) value.
🔺Precision indicates how close the measurements are to each other, even if
they are far from the true value.
Example
Let’s consider another case of
experimental measurements. A test sample with a true mass of 100 mg is
measured.
If
the results are:
98.5;
98.6; 98.7; 98.5
the measurements are precise, but not
accurate.
If the results are:
99.6; 101.6; 99.6; 100.5
The measurements are accurate, but not
precise.
Instruments are usually precise, but due to wear or mishandling, they may no
longer be calibrated. Therefore, don’t assume a result is correct just because
it is precise – it also needs to be accurate.
To assess accuracy and
precision in measurement results, two statistics are used: bias and standard
deviation.
🔺 Bias is the difference between the reference value and the mean of the
obtained measurements (under the same conditions).
🔺Standard deviation, denoted by s, is a measure of data dispersion
within a sample.
Example (revisited)
15.0 in; 15.1 in; 14.9 in
The mean is 15.0 in. The true value is 40.0 cm = 15.7 in
Bias
= 15.7 – 15.0 = 0.7
To calculate the standard deviation, which measures the spread of the values,
you can use Excel, but the manual calculation is shown in the table below,
remembering that deviation means the difference between each observed value and
the mean.The mean of the measurements is 15. Then, you have:
Theoretical Illustration
🔺 In the first figure, you see the results of an infinite number of
measurements made by two operators. Both obtained accurate results (bias equals
zero), but the one represented by the red curve showed greater precision than
the one represented by the black curve.
🔺 In the second figure, you also see results from two operators. Both achieved
equal precision, but the accuracy of the operator represented by the right-hand
curve is higher — assuming the true value is marked in red.
