# stats 70

Sampling error:
Sampling errors are the errors in the sample selection which can lead to incorrect results. Sampling errors are broadly classified as random errors, error to due bias or systematic errors.

Random Error.
All measurements are subject to error, which can often be broken down into two components: a bias or systematic error, which affects all measurements the same way; and a random error, which is in general different each time a measurement is made, and behaves like a number drawn with replacement from a box of numbered tickets whose average is zero.

Systematic error.
An error that affects all the measurements similarly. For example, if a ruler is too short, everything measured with it will appear to be longer than it really is (ignoring random error). If your watch runs fast, every time interval you measure with it will appear to be longer than it really is (again, ignoring random error). Systematic errors do not tend to average out. Systematic errors can also originate from incorrect sampling procedures.

Standard Error (SE).
The Standard Error of a random variable is a measure of how far it is likely to be from its expected value; that is, its scatter in repeated experiments. The SE of a random variable X is defined to be
SE(X) = sqrt[ E( (X – E(X))2]
That is, the standard error is the standard deviation of the errors.