What is an Interaction?

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*Interactions are when the effect of two, or more, variables is not simply additive. This page describes the interaction between two variables. It is possible to examine the interactions of three or more variables but this is beyond the scope of this page.
*Interactions are when the effect of two, or more, variables is not simply additive. This page describes the interaction between two variables. It is possible to examine the interactions of three or more variables but this is beyond the scope of this page.
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==Examples==
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==Interactions and Main Effects==
*Imagine a study about the effect of energy bars and energy drinks on time to run the 1500 meters. The quantity of energy bars and energy drinks represent two variables. The dependent variable is the time taken to run 1500 meters.  
*Imagine a study about the effect of energy bars and energy drinks on time to run the 1500 meters. The quantity of energy bars and energy drinks represent two variables. The dependent variable is the time taken to run 1500 meters.  
*# ''Example 1'' - An interaction occurs if running speed improves by more than just the additive effect of having either an energy bar or an energy drink. For example, imagine eating a certain amount of energy bars increases running speed by 3 seconds, and drinking energy drinks increases running speed by 2 seconds. An interaction occurs if the joint effect of energy bars and energy drinks increases running speed by more than 5 seconds, such as liquid in the drink amplifying the ability to digest the energy in the bar leading to faster times.  
*# ''Example 1'' - An interaction occurs if running speed improves by more than just the additive effect of having either an energy bar or an energy drink. For example, imagine eating a certain amount of energy bars increases running speed by 3 seconds, and drinking energy drinks increases running speed by 2 seconds. An interaction occurs if the joint effect of energy bars and energy drinks increases running speed by more than 5 seconds, such as liquid in the drink amplifying the ability to digest the energy in the bar leading to faster times.  
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==Graphical representations of interactions==
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==Graphical representations of Interactions==
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[[Image:IMEb.JPG]]  
[[Image:IMEb.JPG]]  
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[[Image:NoIMEd.JPG]]
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==Statistical formula behind Interactions==
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==Statistical formula behind interactions==
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*For those more technically minded, here is the algebra. An interaction effect reflects the effect of the interaction controlling for the two predictors themselves.  
*For those more technically minded, here is the algebra. An interaction effect reflects the effect of the interaction controlling for the two predictors themselves.  
*#In the following examples:  
*#In the following examples:  

Revision as of 04:12, 29 June 2007


Contents


Interactions and Main Effects


Graphical representations of Interactions

NoI2MEc.JPG

I2ME.JPG

NoINoME.JPG

INoME.JPG

NoIMEb.JPG

IMEb.JPG

NoIMEd.JPG

IMEd.JPG



Statistical formula behind Interactions

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