| Abstract: | ABSTRACT: This paper discusses the reliance of numerical analysis on the concept of the standard deviation, and its close relative the variance. It suggests that the original reasons why the standard deviation concept has permeated traditional statistics are no longer clearly valid, if they ever were. The absolute mean deviation, it is argued here, has many advantages over the standard deviation. It is more efficient as an estimate of a population parameter in the real-life situation where the data contain tiny errors, or do not form a completely perfect normal distribution. It is easier to use, and more tolerant of extreme values, in the majority of real-life situations where population parameters are not required. It is easier for new researchers to learn about and understand, and also closely linked to a number of arithmetic techniques already used in the sociology of education and elsewhere. We could continue to use the standard deviation instead, as we do presently, because so much of the rest of traditional statistics is based upon it (effect sizes, and the F-test, for example). However, we should weigh the convenience of this solution for some against the possibility of creating a much simpler and more widespread form of numeric analysis for many. |
