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"Ivan Balduci" <[EMAIL PROTECTED]> wrote in message =
news:[EMAIL PROTECTED]
Hi Dr J Williams, Dr David Heiser, Dr Rich Ulrich, Dr Dawson, Dr =
Auslenders and all members
Thanks for your answers
=
.......................................................................
Now, I would like to know what I can to know more to explain for my =
students about the Galton Board (quicunx) more than this=20
explanation of this site =
http://www.stattucino.com/berrie/dsl/Galton.html
-------------------------------------------------------------
I went to your site. I think you short-changed Galton and the historic =
importance of his effort. You should have read his famous book, "Natural =
Inheritance" by Francis Galton, F.R.S. , 1889 (Republished by Genetics =
Heritage Press, 1997, Placitas, New Mexico).=20
Chapter 5 of the book covers the ideas. It (the device on page 63) has =
to do with an illustration of his law of error and the origin of the =
Curve of Frequency. He says, "The principle on which the action of the =
apparatus depends is, that a number of small and independent accidents =
befall each shot in its career.........Whenever a large sample of =
chaotic elements are taken in hand and marshaled in order of their =
magnitude, an unsuspected and most beautiful form of regularity proves =
to have been latent all along."=20
The shot not only interacts with the pins, but interact with each =
other. The shot is not made up of perfect spheres. All the natural =
irregularity of the shape and weight of each ball, imprecise placing of =
the pins, variable stiffness of the pins, etc., result in a normal =
distribution (as the limit of the total effect of innumerable small =
forces).
The events are all a normal distribution, not binomial. The computer =
program you generated does not deal with a lot of impacts of balls of =
different sizes and weights. Galton was illustrating the facts of nature =
in that deviation from the median (center) comes from all kinds of =
unobservable and immeasurable events acting on a measurable =
characteristic.
Our term "regression" for fitting an equation to data, comes from his =
observation that the heights of offspring is on the average less than =
the heights of either parent. In other words, there is a regression of =
the parents height.
David Heiser
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<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
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<DIV>"Ivan Balduci" <<A=20
href=3D"mailto:[EMAIL PROTECTED]">[EMAIL PROTECTED]</A>> wrote =
in message=20
<A=20
=
href=3D"news:[EMAIL PROTECTED]">news:5=
[EMAIL PROTECTED]</A>...</DIV>
<DIV>Hi Dr J Williams, Dr David Heiser, Dr Rich Ulrich, Dr Dawson, Dr=20
Auslenders and all members<BR>Thanks for your=20
=
answers<BR>..............................................................=
.........<BR>Now,=20
I would like to know what I can to know more to explain for my =
students about=20
the Galton Board (quicunx) more than this <BR>explanation of this site =
<A=20
=
href=3D"http://www.stattucino.com/berrie/dsl/Galton.html";>http://www.stat=
tucino.com/berrie/dsl/Galton.html</A></DIV>
=
<DIV>-------------------------------------------------------------</DIV>
<DIV>I went to your site. I think you short-changed Galton and the =
historic=20
importance of his effort. You should have read his famous book, =
"Natural=20
Inheritance" by Francis Galton, F.R.S. , 1889 (Republished by Genetics =
Heritage Press, 1997, Placitas, New Mexico). </DIV>
<DIV> </DIV>
<DIV>Chapter 5 of the book covers the ideas. It (the device on page =
63) has to=20
do with an illustration of his law of error and the origin of the =
Curve of=20
Frequency. He says, "The principle on which the action of the =
apparatus=20
depends is, that a number of small and independent accidents befall =
each shot=20
in its career.........Whenever a large sample of chaotic elements are =
taken in=20
hand and marshaled in order of their magnitude, an unsuspected and =
most=20
beautiful form of regularity proves to have been latent all along." =
</DIV>
<DIV> </DIV>
<DIV>The shot not only interacts with the pins, but interact with each =
other.=20
The shot is not made up of perfect spheres. All the natural =
irregularity of=20
the shape and weight of each ball, imprecise placing of the pins, =
variable=20
stiffness of the pins, etc., result in a normal distribution (as the =
limit of=20
the total effect of innumerable small forces).</DIV>
<DIV> </DIV>
<DIV>The events are all a normal distribution, not binomial. The =
computer=20
program you generated does not deal with a lot of impacts of balls of=20
different sizes and weights. Galton was illustrating the facts of =
nature in=20
that deviation from the median (center) comes from all kinds of =
unobservable=20
and immeasurable events acting on a measurable characteristic.</DIV>
<DIV> </DIV>
<DIV>Our term "regression" for fitting an equation to data, comes from =
his=20
observation that the heights of offspring is on the average less than =
the=20
heights of either parent. In other words, there is a regression of the =
parents=20
height.</DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>David Heiser</FONT></DIV>
<DIV><FONT face=3DArial =
size=3D2></FONT> </DIV></BLOCKQUOTE></BODY></HTML>
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