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Why are allowable bias and imprecision separate requirements?

Bias describes how far the average result is from a suitable reference value. Imprecision describes how much repeat results vary. A method can meet the requirement for one and fall short on the other, so each needs an appropriate limit and evidence.

Worked example at a glance

100 units

Assigned value

±2%

Fictional bias limit

≤3% CV

Fictional imprecision limit

Decide what each requirement should control

Bias is an estimate of systematic difference relative to an appropriate reference value. Imprecision describes random variation under specified conditions, such as measurements across days within the laboratory. Analytical performance specifications can set separate requirements because the two affect results in different ways. A persistent shift moves the centre of the results. Greater imprecision increases their scatter. [1] [2]

Both requirements can be percentages and still have different denominators. Relative bias is the difference between the observed mean and reference value, divided by the reference value. The coefficient of variation (CV) is the SD divided by the observed mean. Keep the names, signs and denominators attached to the numbers.

Compare the centre and spread of two methods

A fictional material has a suitably assigned concentration of 100 units. Repeated measurements with method A have a mean of 103 units and an SD of 1.5 units. Method B has a mean of 100.5 units and an SD of 4.5 units. Suppose the laboratory has specified relative bias within ±2% and a within-laboratory CV of 3% or less at this level.

Method A has mean 103 and SD 1.5 units. Method B has mean 100.5 and SD 4.5 units. Method A has a larger difference from the assigned value of 100 but less spread.
Points show means and bars show one SD either side. The bars describe spread rather than uncertainty in the estimated mean. Open the figure full size.

Method A is closer to its own mean on repeat measurements, but its mean is 3 units above the assigned value. Method B has a mean only 0.5 units above the assigned value, but its repeated results are more spread out. The chart shows why a result near the reference value on one occasion provides limited evidence about either characteristic.

Read the two comparisons separately

For method A, (103 − 100) ÷ 100 gives +3.0% bias and 1.5 ÷ 103 gives about 1.5% CV. For method B, (100.5 − 100) ÷ 100 gives +0.5% bias and 4.5 ÷ 100.5 gives about 4.5% CV. Compare each estimate with the requirement that applies to it.

MethodBiasCV
A+3.0%1.5%
B+0.5%4.5%
The observed percentages are rounded. The illustrative requirements are bias within ±2% and CV no greater than 3%.

On the point estimates, method A meets the imprecision requirement but exceeds the bias limit. Method B meets the bias requirement but exceeds the imprecision limit. In a real study, consider uncertainty in the estimated mean, the assigned value and the estimated CV, especially when the result is near a limit. Check that the assigned value is appropriate for the material and method. [2]

Keep the direction of bias in the record. A positive and a negative bias of the same size are equally far from the assigned value, but may have different consequences near a decision threshold. More imprecision can increase the chance of results moving in either direction. The intended use determines which effects matter most. [1]

Say which performance characteristic needs attention

A useful verification record states the two estimates, the requirements and the concentrations tested. Where results are compared with an established routine method, describe the observed difference relative to that method unless there is evidence supporting a stronger reference claim. Evidence at one concentration does not establish either bias or imprecision across the whole measuring range. [2] [3]

Example wordingAt the 100-unit level, method A’s CV estimate was below 3%, but its +3.0% relative bias exceeded the ±2% limit. Method B’s +0.5% relative bias was within the limit, while its CV estimate exceeded 3%. Each conclusion applies to the stated study conditions.

Member Learning

Practise interpreting a proposed specification

Understanding analytical performance specifications (APS) helps you check the evidence behind a proposed specification and explain whether it is suitable.

Sources and related reading

Read what makes a specification fit for purpose · Read what a verification study can tell you

By Stephen MacDonald · Suggest a correction · Back to Find a guide