Random or Systematic: Two Ways to Be Wrong, and Only One of Them Averages Away

PRECISION is how closely your repeats agree with each other. ACCURACY is how close they are to the real value. They are independent, and you can have either without the other. Tight repeats prove precision and say nothing about accuracy. That is the whole problem: the evidence you can gather by yourself only ever speaks to the first one, so a systematic error is invisible from the inside. So the question to ask of a set of readings is not "do they agree?" but "what would make them all wrong in the same direction?" A caliper that does not close to zero. A thermometer immersed too shallow. A stopwatch always started late. Each produces perfect agreement on the wrong number.

Four families cover most of them. A ZERO that is off, which the previous rung deals with. A SCALE that is stretched or squashed, so the error grows with the reading. An instrument used OUTSIDE its assumptions — a thermometer not immersed deep enough, an infrared reading taken off a shiny surface. And the OBSERVER: reading a scale from an angle, always rounding the same way, starting a watch late. Each has a signature. A zero offset shifts everything by the same amount; a scale error shifts small readings a little and large ones a lot; an assumption failure appears only in certain conditions. Measuring two known values, one small and one large, separates the first two immediately. The pyrometer rung is a worked example of the third: polished steel at 900 degrees reads hundreds of degrees cold, not because the instrument is faulty but because its emissivity assumption is wrong for that surface.

The practical method is to make two things disagree. Measure the same object with two different instruments. Have two people measure it. Measure it, turn it round, and measure it again. Each disagreement is a systematic error becoming visible. Agreement is evidence too, and it is worth recording. "Checked against the second caliper, agreed to 0.02 mm" is a line that makes a later reader trust everything around it — and saves you repeating the check in six months. Quote what you could not rule out, plainly. A result that says "2.08 plus or minus 0.02 s; the stopwatch was not checked against a known interval, so a start-delay bias of up to about 0.1 s may be present" is far more useful than a confident 2.08, and it tells the next person exactly what to do first.