An observational error is the difference between the result of a measurement and true value of a quantity to the extent that such a thing exists. Note that the term error doesn’t imply there is anything wrong with this, it is not a mistake. It is only a mistake if we take the observed value to be the true value. Observational errors occur for a number of reasons such as
- Measurement Errors – Any measuring device will have some limit to its accuracy and possibly some bias in its readings. For example a clock which is only accurate to seconds or a scale that is only sensitive to 0.1 grams. These also include human errors the difference between what a person tries to do and actually does.
- Statistical Errors – Errors introduced because you sample only part of a population. Measuring the masses of 1000 pennies instead of all pennies. Performing an experiment 10 times, instead of an infinite number of times.
- Model Errors – These are errors that are caused by elements missing from the model of what is going on. Dropping a ball, but ignoring air resistance. Measuring a voltage but ignoring the internal resistance of the measuring device. The good thing is that these can be reduced by a better physical understanding of what is going on. However, it many cases to be very accurate requires knowing what is going on with incredible accuracy.
This page on Measurement Error from Statistics How To contains more information on the topic.
