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Paper: Revisiting a 90-year-old debate: the advantages of the mean deviation
Actually im busy doing an exam paper for linguistics class, but it turned out to be not so difficult, so i spent som time on Khan Academy doing probability and statistics courses. i want to master that stuff, especially the stuff i dont currently know the details about, like regression.
anyway, i stumpled into a comment asking about the way the standard deviation is calculated. why not just use the absolute value insted of squaring stuff and taking the square root after? i actually tried that once, and it gives different results! i tried it out becus the teacher's notes said that it wud giv the same results. pretty neat discovery IMO.
anyway, the other one has a name as well: https://en.wikipedia.org/wiki/Absolute_deviation
here's a paper that argues that we shud really return to the MD (mean deviation). i didnt understand all the math, but it sure is easier to calculate and the meaning of it easier to grasp, altho its probably too difficult to switch now that most of statistics is based on the SD. still cool tho.
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.
Keywords: variance, measuring variation, political arithmetic, mean deviation, standard deviation, social construction of statistics
it also has a new odd use of "social construction" which annoyed me when reading it.