Scientists recognize two different sorts of error:
Statistical error: the difference between a computed, estimated, or measured value and the true, specified, or theoretically correct value (see errors and residuals in statistics) that is caused by random, and inherently unpredictable fluctuations in the measurement apparatus.
Systematic error: the difference between a computed, estimated, or measured value and the true, specified, or theoretically correct value that is caused by non-random fluctuations from an unknown source (see uncertainty), and which, once identified, can usually be eliminated.
Statisticians speak of two significant sorts of statistical error. The context is that there is a "null hypothesis" which corresponds to a presumed default "state of nature", e.g., that an individual is free of disease, that an accused is innocent, or that a potential login candidate is not authorized. Corresponding to the null hypothesis is an "alternative hypothesis" which corresponds to the opposite situation, that is, that the individual has the disease, that the accused is guilty, or that the login candidate is an authorized user. The problem is to distinguish accurately between the null hypothesis and the alternative. A test of some sort is conducted (a blood test, a legal trial, a login attempt), and data is obtained. The result of the test may be negative (that is, it does not indicate disease, guilt, or authorized identity). On the other hand, it may be positive (that is, it may indicate disease, guilt, or identity). If the result of the test does not correspond with the actual state of nature, then an error has occurred, but if the result of the test corresponds with the actual state of nature, then a correct decision has been made. There are two kinds of error, classified as "Type I error" and "Type II error," depending upon which hypothesis has incorrectly been identified as the true state of nature.
Type I error, also known as an "error of the first kind", an α error, or a "false positive": the error of rejecting a null hypothesis when it is the true state of nature. In other words, this is the error of accepting an alternative hypothesis (the real hypothesis of interest) when an observation is due to chance. Plainly speaking, it occurs when we are observing a difference when in truth there is none.
Type II error, also known as an "error of the second kind", a β error, or a "false negative": the error of not rejecting a null hypothesis when the alternative hypothesis is the true state of nature. In other words, this is the error of failing to accept an alternative hypothesis when you don't have adequate power. Plainly speaking, it occurs when we are failing to observe a difference when there is one.
