What is the difference between relative and absolute uncertainty

Q: What is the difference between relative and absolute uncertainty

The difference is relative uncertainty is expressed in a term relative to the measurand (e.g. percent, part-per-million, etc) while absolute uncertainty is expressed in the same unit of measurement as the measurand.

Short answer: The difference is relative uncertainty is expressed in a term relative to the measurand (e.g. percent, part-per-million, etc) while absolute uncertainty is expressed in the same unit of measurement as the measurand.

Difference Between Relative and Absolute Uncertainty Comparison

ISO/IEC 17025 accredited laboratories and ISO 17034 accredited reference material producers can report measurement uncertainty as an absolute uncertainty or a relative uncertainty.

Either form of measurement uncertainty is recommended by:

ISO/IEC 17025 Requirements for Reporting Uncertainty

Reporting Measurement Uncertainty for Testing Labs

For testing labs, the ISO/IEC 17025 section 7.8.3.1 states: “In addition to the requirements listed in 7.8.2, test reports shall, where necessary for the interpretation of the test results, include the following:
…
c) where applicable, the measurement uncertainty presented in the same unit as that of the measurand or in a term relative to the measurand (e.g. percent) when:
– it is relevant to the validity or application of the test results;
– a customer’s instruction so requires, or
– the measurement uncertainty affects conformity to a specification limit.”

Reporting Measurement Uncertainty for Calibration Labs

For calibration labs, the ISO/IEC 17025 section 7.8.4.1 states: “In addition to the requirements listed in 7.8.2, calibration certificates shall include the following:
a) the measurement uncertainty of the measurement result presented in the same unit as that of the measurand or in a term relative to the measurand (e.g. percent);”

Example

**Example of Absolute and Relative Uncertainty**
Description	Symbol	Value	Unit
Measurand	y	1.00000	V at 60 Hz
Absolute Uncertainty	U_abs	0.00015	V
Absolute Uncertainty	U_abs	150	µV
Relative Uncertainty	U_rel	0.015	%
Relative Uncertainty	U_rel	150	µV/V

FAQ

What is relative uncertainty?

Relative uncertainty is measurement uncertainty divided by the absolute value of the measurement or result so it can expressed in a term relative to the measurand, such as a percentage, parts-per-million, etc.

How to calculate relative standard uncertainty?

Calculate relative uncertainty by dividing the absolute uncertainty by the absolute value of the measurand. For example, a 100 µL pipette with an absolute uncertainty of 0.58 µL could be expressed as a relative uncertainty using the formula: 0.58 µL / 100 µL x 100 = 0.58 %.

How to calculate RSD in chemistry?

In chemistry, RSD is typically expressed as a percentage. To calculate it, first calculate the standard deviation. Next, divide the standard deviation by the absolute value of the result (typically, a concentration). Multiply the result by 100 to get RSD as a percentage.

If RSD needs to be expressed as an expanded uncertainty, determine the desired level of confidence (Typically, 95.45 %). Next, calculate the degrees of freedom and use the t-distribution to find the coverage factor. Then, multiple the percent RSD by the coverage factor.

What is the difference between relative uncertainty and relative standard deviation?

Relative standard uncertainty and relative standard deviation have similar confidence intervals. Both represent a standard deviation with a 68.27 % confidence interval. If either one is to be expressed as an expanded uncertainty (i.e. JCGM 100:2008, ISO 21748, or ISO 19036), they need to be multiplied by a coverage factor that produces a desired level of confidence.

However, relative uncertainty and relative standard deviation can have different confidence intervals. For example, a relative uncertainty can represent an expanded uncertainty with a 95.45 % confidence interval while a relative standard deviation represents a standard deviation with a 68.27 % confidence interval.

What is the difference between relative and absolute accuracy?

According to Fluke and Transmille equipment specifications, absolute accuracy contains all sources of error including the uncertainty of the calibration reference standard while relative accuracy contains all sources of error except the uncertainty of the calibration reference standard. The absolute accuracy is recommended for use if the equipment is calibrated by the respective manufacturer’s calibration facilities while the relative accuracy should be used in combination with the reference standard uncertainty if the equipment is calibrated by a laboratory other than the manufacturer.

What is relative standard uncertainty?

Relative standard uncertainty is a standard deviation of standard uncertainty expressed in relative terms, such as percentage, part-per-million, or equivalent.

Glossary

Measurement Uncertainty: non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used. (Source: JCGM 200:2012, 2.26)
Measurand: quantity intended to be measured. (Source: JCGM 200:2012, 2.3)
Relative Measurement Uncertainty: measurement uncertainty expressed in a term relative to the measurand.
Absolute Measurement Uncertainty: measurement uncertainty expressed in the same unit of measurement as the measurand.
CMC Uncertainty: calibration and measurement capability uncertainty available to customers under normal conditions as described in a laboratory’s scope of accreditation or published in the BIPM key comparison database (KCDB). (Source: ILAC P14:09/2020)