The dartboard that makes it click
Picture a dartboard. Accuracy is about *being close to the bullseye* — close to the true value. Precision is about *the darts landing close to each other* — repeatable, clustered, regardless of where the cluster sits. These two are completely independent, and that is the whole insight. You can have one without the other, and a beginner who keeps them separate has already avoided the field's most common confusion.
- Accurate and precise: a tight cluster right on the bullseye. The dream — close to true and repeatable.
- Precise but not accurate: a tight cluster, but off in one corner. Beautifully repeatable, and consistently wrong — a classic warning sign.
- Accurate but not precise: darts scattered all around, but averaging out near the centre. Right on average, but no single throw is reliable.
- Neither: scattered and off-centre too. The worst case — and at least it is honest about being a mess.
Putting a size on 'how wrong': absolute error
Accuracy is a feeling until you make it a number. The simplest measure is the absolute error: how far your measured value sits from the true value, in the same units as the measurement. If a certified standard truly contains 50.0 mg of iron and you measure 50.3 mg, your absolute error is +0.3 mg. The sign matters — plus means you read too high, minus too low. Absolute error speaks in the natural units of the thing you measured, which makes it concrete and easy to picture.
But absolute error alone can mislead. Is a 0.3 mg error big or small? It depends entirely on what you were measuring. Being off by 0.3 mg when the true amount is 50 mg is a tiny slip. Being off by 0.3 mg when the true amount is only 0.5 mg is a catastrophe. The bare number cannot tell the two apart — which is exactly why we need a second way of looking at it.
Error in proportion: relative error
The fix is relative error: the absolute error compared to the size of the true value, usually written as a percentage. You take the absolute error and divide it by the true value. For the 50 mg case, 0.3 ÷ 50 is 0.6% — small. For the 0.5 mg case, 0.3 ÷ 0.5 is 60% — alarming. Same absolute error, wildly different relative errors, and only the relative version tells you which result you can actually trust.
This is why relative error is the language analysts usually reach for when comparing how good two methods are, or how well a result holds up at different concentrations. Absolute error answers "by how many milligrams was I off?"; relative error answers "was that a big deal, given what I was measuring?" Both are useful, but it is the relative one that lets you compare a blood-glucose result against a river-pollutant result on a fair footing.
When the error always leans the same way: bias
Go back to the 'precise but not accurate' dartboard — the tight cluster sitting off to one side. That sideways offset has a name: bias. Bias is a consistent lean in your results, always in the same direction, that does not wash out no matter how many times you repeat the measurement. If your balance always reads 0.2 g heavy, every single weighing carries that same +0.2 g bias. Averaging more readings just gives you a very precise wrong answer.
Bias is the enemy of accuracy, and it is sneaky precisely because repeatability cannot expose it. The clean numbers feel reassuring. The only way to catch bias is to compare against something you trust to be true — a certified standard, a second independent method, another lab. The next guide opens up *where* bias comes from by sorting all measurement errors into a few honest families.