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A cosa serve? Lo spiega Galton...



Disegno di Galton del quinconce del 1877Francis Galton presenta un dispositivo simile a quello descritto in Natural Inheritance già nel 1877 in un suo intervento ai Proceedings of the Royal Institution, pubblicato successivamente sulla rivista Nature, dove lo utilizza per illustrare il fenomeno della regressione alla media.

In Natural Inheritance, invece, Galton utilizza l'apparecchio per illustrare in modo meccanico la genesi della curva normale:

"The Curve of Frequency, and that of Distribution, are convertible: therefore if the genesis of either of them can be made clear, that of the other becomes also intelligible. I shall now illustrate the origin of the Curve of Frequency, by means of an apparatus shown in Fig. 7, that mimics in a very pretty way the conditions on which Deviation depends.

[...]

The outline of the columns of shot that accumulate in the successive compartments approximates to the Curve of Frequency, and is closely of the same shape however often the experiment is repeated. The outline of the columns would become more nearly identical with the Normal Curve of Frequency, if the rows of pins were much more numerous, the shot smaller, and the compartments narrower; also if a larger quantity of shot was used.

Disegno di Galton della sua macchinaThe principle on which the action of the apparatus depends is, that a number of small and independent accidents befall each shot in its career.

In rare cases, a long run of luck continues to favour the course of a particular shot towards either outside place, but in the large majority of instances the number of accidents that cause Deviation to the right, balance in a greater or less degree those that cause Deviation to the left.

Therefore most of the shot finds its way into the compartments that are situated near to a perpendicular line drawn from the outlet of the funnel, and the Frequency with which shots stray to different distances to the right or left of that line diminishes in a much faster ratio than those distances increase.

This illustrates and explains the reason why mediocrity is so common."

Galton[1889], pp 63-65


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