Precision, accuracy, and a defensible bias correction

Precision must name the conditions of replication. Repeatability usually holds the procedure, operator, measuring system, location, and short time interval fixed. Intermediate precision changes some conditions within one location; reproducibility changes specified broader conditions, such as laboratories. A small repeatability standard deviation therefore does not promise agreement after transport, a software change, or a new operator. Use a replication design that matches the conditions under which the reported performance will actually matter.

Report whether a standard deviation describes individual observations or an estimated mean. These are different summaries, even in an ideal independent sample. An instrument can give nearly identical readings that are all displaced by a common offset. Improving that repeatability further would barely improve agreement to a reference. Conversely, a mean can agree with a reference by coincidence despite very poor individual-reading precision. Examine both location and spread rather than treating a single attractive statistic as sufficient evidence.

The reference value is itself an estimate with uncertainty. A difference between a measured mean and that reference estimates a bias under the comparison conditions; it does not reveal the exact error relative to an unknowable perfect value. Evaluate the uncertainty of the comparison, including covariance if references or processing are shared. A difference small compared with its uncertainty may provide weak evidence for a nonzero bias, but it does not prove the instrument is unbiased under every condition.

A local bias correction requires a stability and transfer argument. A constant offset found near room temperature may change with temperature, range, orientation, or time. Apply it only where evidence or a physical model supports it. If the effect scales with input, use a scale correction rather than a universal additive offset. Comparing multiple reference values and environmental conditions distinguishes these possibilities. The correction model should become more detailed because evidence demands it, not merely because more parameters are available.

Applying an estimated correction can improve expected agreement, but residual uncertainty remains. Do not add the estimated bias magnitude in quadrature as though it were its standard uncertainty, and do not drop the correction uncertainty after applying it. A bias magnitude describes an estimated signed displacement; an uncertainty describes incomplete knowledge. When an effect cannot be corrected adequately, document the treatment and its justification rather than concealing it inside an unexplained accuracy percentage.

A numerical product specification may use the commercial label accuracy for a maximum permissible error. That is a contractual limit under stated conditions, not automatically a standard uncertainty or a probability distribution. Read the definition and operating conditions before using it in a budget. Verification against a tolerance also needs a decision rule when uncertainty is material. A result close to a limit cannot support the same confident conformity statement as one well inside it without additional information.