We can use a lot of methods to try to minimize our errors, but we can
never eliminate them. For the purposes of working with errors, we can divide
them into three groups: gross, systematic and random errors. This division
is based on what causes the errors and how we deal with them, rather than
any other aspect of their nature. You will see other classification
schemes, but this one is both comprehensive and useful.
are those which we can also call `blunders'. They can be of any size or nature, and tend to occur through carelessness. Writing down the wrong value, reading the instrument incorrectly, measuring to the wrong mark; these are gross errors. They can be caused by people, machinery, weather conditions and various other things. We deal with gross errors by
careful procedures and relentless checking of our work.
are those which we can model mathematically and therefore correct. They are caused by the mathematical model of the procedure that we are using being different to what is going on in the real world. We reduce and compute with measurements on the basis of models and if the models are not complete, we will have discrepancies. For example, if we measure a distance without allowing for the slope of the tape, we will have a systematic error, which can be eliminated if we use the correct model of the measurement process. We can eliminate, or at least minimize, systematic errors by careful work, using the appropriate model for the process in use, and by using checks that will reveal systematic errors in measurements. Note that checks that use the same measurement processes may not detect some systematic errors, so you have to be fairly creative in developing methods for detecting systematic errors.
are those which have no apparent cause, but are a consequence of the measurement process itself. All measurements have to be done to some limit of precision and we cannot predict the exact measurement we will obtain. However, random errors have very definite statistical behavior and so can be dealt with by statistical methods. Random errors are the small differences between repeated measurements of the same quantity, often of the order of the finest division in the measuring scale. We can eliminate or minimize the effects of
random errors by statistical procedures: for example we can adopt the mean of a set of measurements as the value to be used in later calculations. With the idea of the ubiquity of errors in all our measurements and everything we do, we can
now look at one measurement process and see how errors affect it. We will begin by looking at linear measurements, such as those we make with tapes and such equipment as EDM.