eyc-tech Calculation and Measurement of Accuracy and Precision

What Are Accuracy and Precision?

Meaning and Calculation of Accuracy

Many customers frequently ask how accuracy is calculated and what instrument accuracy actually represents. Our engineers provide a detailed explanation of the concept of accuracy.

Under normal operating conditions, the degree of error in an instrument’s measurement result is defined as accuracy. The smaller the error, the higher the accuracy of the instrument. Measurement error is related to the measurement range of the instrument.

Accuracy

In general, accuracy can be expressed using either absolute error or relative error, which are mathematically defined as follows:

• Absolute Error :
  The error value expressed in the same units as the measured reading.
  
  
• Relative Error :
  The error expressed as a percentage of the measured value.

Accuracy and Precision

Precision is also a statistical concept, referring to the degree of concentration or consistency of data obtained from repeated independent measurements. When multiple measurement results are close to each other, the precision is considered high. Conversely, if the differences among repeated measurements are large, the measurements are regarded as having low precision.

In quantitative analysis, the average of all measurement values is often taken as the measured value. However, this approach does not allow accuracy to be properly evaluated and may cause systematic errors to be overlooked. Therefore, a reference standard with repeatable measurements and good reproducibility must be established. Commonly used reference standards today are provided by institutions such as the National Institute of Standards and Technology (NIST) in the United States.

What Is Systematic Error?

Systematic error, also known as regular error, refers to an error that remains constant in magnitude and sign (positive or negative) when the same parameter is measured repeatedly under identical conditions. Alternatively, it may vary according to a predictable pattern when measurement conditions change.

Systematic error is defined as the difference between the average result of repeated measurements and the true value of the measured quantity. In general, imperfections in measurement procedures can introduce errors, some of which originate from systematic errors and others from random errors. Random errors are assumed to arise from unpredictable influencing factors or random variations in time and space. Like random errors, systematic errors cannot be completely eliminated, but they can usually be reduced when their influence on measurement results can be identified and corrected.

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