In scientific measurements, accuracy and precision are two important terms. Both terms indicate the result and performance of one measurement. But what does each of them actually represent? What is the essential difference between the two of them? Next, let us dive into the details of accuracy and precision.
Table of Contents
What is accuracy?
Accuracy is the criterion for evaluating the deviation between the measured value and the true value. If the measurement is closer to the true value, then the measurement is more accurate.
Accuracy calculation formula
The accuracy can be judged by calculating the percentage error between the measured value and the true value or by comparing the deviation between the average of all measured values and the true value:
or:
The closer the measurement is to the true value, the smaller the percentage error and the more accurate the measurement will be. Alternatively, the closer the average value is to the true value, the more accurate the measurement.
What is precision?
Precision is a criterion for assessing the performance among different measurements. If the measured value is closer to other measured values, then the measurement precision is higher.
Precision calculation formula
It can be shows the degree of deviation between different measurements by calculating the standard deviation:
The smaller the standard deviation, the more concentrated the distribution of each measurement, and the higher the precision will be.
Difference between accuracy and precision
A comparison of the two is shown in the table below
| Accuracy | Precision |
| Deviation of the measured value from the true value | Dispersion among measurements |
| Evaluation accuracy of single measurement | Multi-measurement evaluation precision |
Compare the frequency distribution of a set of measurements
Examples of accuracy vs. precision
Examples 1：How to verification of the accuracy and precision of the camera ranging at 38.0cm, the measurements records the following result: 37.9cm, 38.1cm, 37.8cm, 38.2cm, 38.0cm：
Solution：
Accuracy：The calculation is as follows:
The average of the measured values is the same as the expected true value, the camera ranging has a high measuring accuracy.
Precision：The calculation is as follows.
Calculations show that the measured values are all within 0.3cm of each other, indicating a high degree of precision.
Examples 2：Use the target surface to describe accuracy and precision.
Case 1: Displays high accuracy and high precision target hits, as shown in the figure below:
Case 2: Displays high accuracy, but low precision target hits, as shown in the figure below:
Case 3: Displays high precision, but low accuracy target hits, as shown in the figure below:
Case 4: Displays low precision and low accuracy target hits, as shown in the figure below:
Summary
Accuracy: Accuracy is the closeness of the measured value to the true value.
Precision: Precision is the closeness among different measurements to each other.
