Applied statistics

Applied statistics provide both a familiar source of information and a notorious source of error and misinformation. Errors commonly arise from misplaced confidence in an intuitive interpretations, but some of the most serious have arisen from misuse by mathematicians and other professionals. Deliberate misinterpretation of statistics by politicians and marketing professionals is so much a popular commonplace that its genuine use is often treated with suspicion. To those unfamiliar with it, statistics can seem impenetrably arcane, but its pitfalls can be avoided given a grasp of a few readily understood concepts.

(terms shown in italics are defined in the glossary on the related articles subpage).

Overview: the basics

Statistics are observations that are recorded in numerical form. It is essential to their successful handling to accept that statistics are not facts and therefore incontrovertible, but observations about facts and therefore fallible. The reliability of the information that they provide depends not only upon their successful interpretation, but also upon the accuracy with which the facts are observed and the extent to which they truly represent the subject matter of that information. An appreciation of the means by which statistics are collected is thus an essential part of the understanding of statistics and is least as important as a familiarity with the tools that are used in its interpretation.

Although the derivation of those tools involved advanced mathematics, the laws of chance on which much of statistics theory is based are no more than a formalisation of intuitive concepts, and the use of the resulting algorithms and computer software requires only a grasp of basic mathematical principles

The collection of statistics

The methodology adopted for the collection of observations has a profound influence upon the problem of extracting useful information from the resulting statistics. That problem is at its easiest when the collecting authority can minimise disturbing influences by conducting a "controlled experiment". A range of more complex methodologies (and associated software packages) referred to as "the design of experiments" is available for use when the collecting authority has various lesser degrees of control. The object of the design in each case is to facilitate the testing of an hypothesis by helping to remove the influence of factors that the hypothesis does not take into account. At the furthest extreme from the controlled experiment, no such help can be provided through the physical elimination of extraneous influences - and, if they are to be eliminated, it must be done after they have been identified by a purely analytical technique termed the "analysis of variance". For example, the rôle of the authorities that collect economic statistics is necessarily passive, and the testing of economic hypotheses involves the use of a version of the analysis of variance termed "econometrics" (sometimes confused with economic modelling, which is a purely deterministic technique).

Statistical inference

Popular errors

An eminent authority has claimed that the results of most medical research are flawed because of statistical misinterpretation