ABSTRACT
Since the time of De Moivre, the variables that have been examined by workers in the field of probability have expressed measurements as multiples of a variety of basic units that reflect the dispersion of the range of possible scores. Today the chosen units are units of standard deviation, and the scores obtained are called standard scores or z scores. Karl Pearson used the term standard deviation and gave it the symbol σ (the lower case Greek letter sigma) in 1894, but the unit was known (although not in its present-day form) to De Moivre. It corresponds to that point on the abscissa of a normal distribution such that an ordinate erected from it would cut the curve at its point of inflection, or, in simple terms, the point where the curvature of the function changes from concave to convex. Sir George Airy (1801–1892) named σ √ 2 the modulus (although this term had been used, in passing, for √ n by De Moivre as early as 1733) and described a variety of other possible measures, including the probable error, in 1875. 1 This latter was the unit chosen by Gallon (whose work is discussed later), although he objected strongly to the name:
It is astonishing that mathematicians, who are the most precise and perspicacious of men, have not long since revolted against this cumbrous, slip-shod, and misleading phrase Moreover the term Probable Error is absurd when applied to the subjects now in hand, such as Stature, Eye-colour, Artistic Faculty, or Disease. I shall therefore usually speak of Prob. Deviation. (Galton, 1889, p. 58)
