# Behavioral Illusions: The Basis of a Scientific Revolution

**URL:** <http://discourse.iapct.org/t/behavioral-illusions-the-basis-of-a-scientific-revolution/15614>\
**Category:** Fundamentals\
**Created:** [July 28, 2020, 8:56pm UTC](http://discourse.iapct.org/t/behavioral-illusions-the-basis-of-a-scientific-revolution/15614 "2020-07-28T20:56:47Z")\
**Posts on this page:** 1\
**Showing post:** 118

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**Author:** ![amatic](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/a/13edae/32.png) [@amatic](http://discourse.iapct.org/u/amatic)\
**Post date:** [September 29, 2020, 12:51pm UTC](http://discourse.iapct.org/t/behavioral-illusions-the-basis-of-a-scientific-revolution/15614/118 "2020-09-29T12:51:56Z")

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> RM: No, that is not my “theory”. **Something can be a real phenomenon and a statistical artifact.**

No, it cannot. Name some other examples that are real phenomena and also statistical artifacts.

> RM: But what is seen is a statistical artifact that results from the failure to include the variable D in the regression.

Well, that is your theory then. You prefer to call it a hypothesis? The speed-curvature power law is a statistical artifact that results from the failure to include the variable D in the regression.

Are you saying it is not possible to test weather something is a statistical artifact, but it just has to be because of the algebra?

I’ll just back up a second to establish the terms.

![image](http://discourse.iapct.org/uploads/default/original/2X/6/6616d7a242e33ed4654d828b7e13bf25413ef887.png)

_ **v** _ is the velocity vector, with components x’ and y’  
_ **a** _ is the acceleration vector with components x’’ and y’’  
_ **D** _ is the area closed by _ **a** _ and _ **v** _, calculated as the magnitude of the cross product of a and v, as in (1), or by components of a and v, as in (2)

(1) _ **D** _ = | _ **a** _ x _ **v** _ |  
(2) _ **D** _ = | y’‘x’ - x’‘y’ |

You are saying that the area D closed by vectors _ **a** _ and _ **v** _, should be included in the regression analysis between V (speed, magnitude of _ **v** _, one side of the parallelogram) and C, even though D is directly determined by V?

If _ **a** _ is has constant magnitude, the blue side of the parallelogram is always the same. All of the variance in D is going to come from variance in V. Agreed?

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