Difference between revisions of "User:IssaRice/Multiplicative process"

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* Arthur Jensen, in ''Bias in Mental Testing'': "If achievement depends on other normally distributed factors in addition to ability, such as motivation, interest, energy, and persistence, and if all these factors act ''multiplicatively'', then theoretically we should expect achievement to show a positively skewed distribution. The greater the number of factors (each normally distributed), the more skewed is the distribution of their products. The products of normally distributed variables are distributed in a skewed way such that the distribution of products can be normalized by a logarithmic transformation. A logarithmic transformation of achievement scores in effect makes the component elements of achievement additive rather than multiplicative. Theoretically a multiplicative effect of ability and motivation (or other traits involved in achievement) makes sense. Imagine the limiting case of zero ability; then regardless of the amount of motivation, achievement would equal zero. Also, with zero motivation, regardless of the amount of ability, achievement would equal zero. Great achievers in any field are always high in a number of relevant traits, the multiplicative interaction of which places their accomplishments far beyond those of the average person—much farther than their standing on any single trait or a mere additive combination of several traits. A superior talent alone does not produce the achievements of a Michelangelo, a Beethoven, or an Einstein. The same can be said of Olympics-level athletic performance, which depends on years of concentrated effort and training as well as certain inborn physical advantages. Thus it is probably more correct to say that a person’s achievements are a ''product'', rather than a ''summation'', of his or her abilities, disposition, and training." (p. 98)
 
* Arthur Jensen, in ''Bias in Mental Testing'': "If achievement depends on other normally distributed factors in addition to ability, such as motivation, interest, energy, and persistence, and if all these factors act ''multiplicatively'', then theoretically we should expect achievement to show a positively skewed distribution. The greater the number of factors (each normally distributed), the more skewed is the distribution of their products. The products of normally distributed variables are distributed in a skewed way such that the distribution of products can be normalized by a logarithmic transformation. A logarithmic transformation of achievement scores in effect makes the component elements of achievement additive rather than multiplicative. Theoretically a multiplicative effect of ability and motivation (or other traits involved in achievement) makes sense. Imagine the limiting case of zero ability; then regardless of the amount of motivation, achievement would equal zero. Also, with zero motivation, regardless of the amount of ability, achievement would equal zero. Great achievers in any field are always high in a number of relevant traits, the multiplicative interaction of which places their accomplishments far beyond those of the average person—much farther than their standing on any single trait or a mere additive combination of several traits. A superior talent alone does not produce the achievements of a Michelangelo, a Beethoven, or an Einstein. The same can be said of Olympics-level athletic performance, which depends on years of concentrated effort and training as well as certain inborn physical advantages. Thus it is probably more correct to say that a person’s achievements are a ''product'', rather than a ''summation'', of his or her abilities, disposition, and training." (p. 98)
 
* Chapter 7 of http://users.cms.caltech.edu/~adamw/heavytails.html
 
* Chapter 7 of http://users.cms.caltech.edu/~adamw/heavytails.html
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* https://www.greaterwrong.com/posts/xs7noq52qYaCYNCws/mark-eichenlaub-how-to-develop-scientific-intuition -- are the scientific heuristics discussed here additive or multiplicative?

Revision as of 08:59, 6 February 2019

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