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2. Error types

While the source tells us where error comes from, it doesn’t tell us how it behaves; the error type does. There are technically three error types. “Technically” since some people don’t consider mistakes a type of error, but we’ll include it here as it does affect measurements if present.

a. Mistake

A mistake is usually the result of carelessness or misunderstanding. Mistakes are generally isolated and stick out in a measurement set. These are common for people learning to use equipment for the first time - something gets forgotten, a wrong button is pushed, digits are transposed, etc.

b. Systematic

A systematic error is one which conforms to some mathematical or physical principle. Because of this behavior a systematic error can be compensated, provided we have enough information. For example, a steel tape changes length based on temperature. We can correct for this as long as we know the steel’s physical characteristics, a calibration temperature and length, and the temperature at measurement.

In some cases we can compensate a systematic error procedurally. If the centered plate bubble runs two divisions when the instrument is rotated 180°, we bring it back one division. We'll discuss the reason more thoroughly in later Chapters on instruments.

c. Random

Random errors are those left when mistakes are eliminated and systematic errors are compensated. They are the only errors which prevent our knowing the true value of what we’re measuring.

Random errors tend to be small and as likely to be positive as negative. Repeating measurements multiple times give random errors a change to cancel. Statistics are used to model and analyze random error effects.

An example of how random errors tend to cancel is flipping a coin. Disregarding the apparent weight differential between the faces, there’s a 50-50 chance heads will come up. It’s possible that if we flip it twice it will come up heads both times. Flipping it three times we could get none, one, two, or three heads. The more we flip it, the more likely we’ll approach 50-50 on heads coming up. Theoretically, if you flip the coin an infinite number of times, keeping everything else the same, half the time it will come up heads. Don’t believe me? Give it a try, I’ll wait.