Accuracy, Precision and Trueness

Introduction

Repeated measurements may cluster tightly and still be wrong. Another set may scatter widely around a reference value. These patterns call for different diagnoses. Precision describes agreement among repeated results; trueness concerns systematic closeness of their average to a reference; accuracy describes closeness of a result to the intended value in ordinary analytical discussion. Reliable conclusions need attention to both scatter and bias.

Core explanation

Precision is about spread under stated conditions. If repeated measurements of one solution are 9.98, 10.01 and 10.00 mg L⁻¹, they are closely grouped. Precision can be quantified by standard deviation or relative standard deviation. Repeatability refers to results under nearly unchanged conditions over a short period; intermediate precision and reproducibility describe progressively broader changes such as days, operators or laboratories. A precision statement should say which conditions were varied.

Trueness concerns how the mean of many measurements compares with a reference or accepted value. If a certified reference material contains 10.00 mg L⁻¹ but a method repeatedly returns about 9.50 mg L⁻¹, the method is precise yet biased low. The bias might arise from incomplete extraction, a calibration error, matrix suppression or a lost dilution factor. Correcting it requires identifying and validating the cause, not merely adjusting a result until it matches a preferred number.

Accuracy is often used to describe closeness of an individual result to the measurand's value, incorporating both random variation and bias. Exact true values are rarely known for real samples, so a certified reference value with stated uncertainty supplies evidence rather than magical certainty.

A target diagram illustrates possible patterns: tight cluster at centre means good precision and trueness; tight cluster off centre means precise but biased; broad cluster centred roughly on target means poor precision but little apparent average bias; broad cluster off centre is poor in both respects. This is a teaching picture, not a substitute for numerical analysis or uncertainty estimates. A small sample of repeats can appear centred by chance.

Reference materials, spikes and independent methods help assess trueness. Replicates assess precision. Blanks test contamination. A method can perform differently in a clean standard solution and a complex sample matrix, so validation should use materials resembling the real samples. Crucially, excellent analytical precision for one bottle does not establish that it was representative of a river; sampling quality remains a separate requirement.

Step-by-step reasoning

1. Specify the measurand and measurement conditions. 2. Collect independent replicate results appropriate to the precision question. 3. Calculate mean and spread without discarding inconvenient data without justification. 4. Compare with a suitable reference value, accounting for its uncertainty. 5. Diagnose bias separately from random scatter and include sampling limitations.

Visual explanation

Draw four target circles with three or more dots in each. Put dots tightly centred, tightly displaced, widely distributed around centre and widely displaced. Label the horizontal distinction as average bias and the vertical distinction as scatter. Add a note that a certified reference value itself has uncertainty, so the centre is an accepted reference rather than an unknowable perfect truth.

Real-world analogy

An archer firing arrows into a target provides a useful analogy. A narrow group away from the bullseye is precise but has a sighting bias; a loose group around the bullseye has poor precision. In chemistry, the “bullseye” must be defined by a trustworthy reference, and sampling can move the whole target before the arrows are shot.

Real-world example

Two laboratories measure a quality-control solution certified at 50.0 mg L⁻¹. Lab A obtains 48.9, 49.0 and 49.1; Lab B obtains 49.0, 50.0 and 51.0. A has much smaller spread but a lower mean; B has a mean matching the reference but greater scatter. Neither pattern should be called simply “better” without stating required tolerance and uncertainty.

Why?

Why do many repeat readings not remove systematic bias? Averaging reduces the influence of random fluctuations, but an error common to every reading remains in the average. If a pipette delivers 1% less than its assumed volume each time, more repetitions can produce an increasingly precise estimate of the wrong value.

Common misconception

“Precise means accurate” is the central mistake. A tight cluster can be offset by calibration or preparation bias. Equally, a mean close to a reference based on just a few scattered results does not prove a method is sufficiently precise. Use the correct term and say what evidence supports it.

Worked example

Results of 9.80, 9.82 and 9.81 mg L⁻¹ have mean (9.80 + 9.82 + 9.81)/3 = 9.81 mg L⁻¹ and a small spread. If a suitable reference value is 10.00 mg L⁻¹, the observed bias estimate is 9.81 − 10.00 = −0.19 mg L⁻¹, or −1.9% relative to the reference. The results are precise but show evidence of low trueness. Whether that difference is significant requires uncertainty for the reference and measurement method.

Quick check

1. A method returns 5.01, 5.00 and 5.02 mg L⁻¹ for a reference material certified at 6.00 mg L⁻¹. What can you say? Answer: The readings have good repeat precision but are strongly biased low relative to the reference. The cause could lie in calibration, recovery or interference and should be investigated.

Exam focus

Use replicate spread to discuss precision and comparison with a reference to discuss trueness. Calculate a mean and signed bias correctly when data are supplied. Do not say a result is truly accurate solely because its digits agree with an expected answer; assess method, reference and uncertainty. Keep sampling representativeness distinct from instrument precision.

Advanced insight

Measurement uncertainty combines quantified contributions from random effects and imperfect knowledge of systematic effects. Bias correction may be appropriate when a stable, well-characterised cause is known, but correction itself carries uncertainty. Reporting a corrected value without that uncertainty can overstate confidence.

Summary

Precision describes how closely replicate results agree; trueness describes how a mean relates to an accepted reference; accuracy concerns closeness of results to the measurand. Replicates, reference materials and blanks address different failure modes. A reliable analysis also requires a representative sample and a transparent uncertainty statement.

Practice questions

1. What evidence would help detect a shared low bias in a method? Answer: Analyse a suitable certified reference material or compare with an independent validated method. Replicate readings alone cannot reveal a shared offset.

2. Three results have little scatter but their average differs from the reference. Which property is strong and which is questionable? Answer: Precision is strong because the results agree. Trueness is questionable because their mean is displaced from the reference, subject to the relevant uncertainties.

3. Can a result be accurate by chance when a method is imprecise? Answer: An individual measurement may happen to lie near the reference, but an imprecise method gives a wide range of possible results. One lucky value does not establish reliable accuracy.