By 1901 the great Karl Pearson was devoting himself to full time research and teaching in the new mathematical field of statistics, with a grant from the Worshipful Company of Drapers which enabled him to establish the biometric laboratory at University College, London. Projects ranged from advances in statistical methodology to the analysis of data on heredity and physical anthropology as well as work on non-biological topics such as astronomy and dam construction which demonstrated the wide applicability of his new analytical techniques.
The first recorded mentions in print of heteroscedasticity & homoscedasticity, words coined by Pearson, came in 1905, in the pleasingly named Drapers’ Company Research Memoirs (Biometric Series):
If all arrays are equally scattered about their means, I shall speak of the system as a homoscedastic system, otherwise it is a heteroscedastic system.
Scedastic comes from the Greek σκεδαστ-ός,’ capable of being scattered’ & so heteroscedastic means 'of unequal scatter or variation; having different variances.' The word has only ever been applied to statistics.
The use of the word scatter left me wondering what measure was being used – when did standard deviation or variance come into use.
According to the OED the word deviation was first used by W. W. Greener in 1858 in his book on one of the most popular sporting pastimes of the day, Scientific Gunnery:
The mean deviation on the target from the centre of the group of 10 hits being only •85 of a foot at 500 yards' range.
but Pearson gave the first rigorous definition in 1894 in Philosophical Transactions of the Royal Society:
Then σ will be termed its standard-deviation (error of mean square).
It appears to have been left to R. A. Fisher in 1918, in Transactions of the Royal Society of Edinburgh, to introduce variance as a formal technical term in statistics:
It is desirable in analysing the causes of variability to deal with the square of the standard deviation as the measure of variability. We shall term this quantity the Variance.
