An interaction effect is a change in the simple main effect of one variable over levels of the second. When the effect of one factor depends on the level of the other factor you can use the interaction plot to see possible interactions. This is most commonly found in the analysis of ANOVA.
I found an example online that was a simple example. Interaction plot for % of moisture in relation to cereal grains being dry enough before packaging them. The cereal grain must be dry to be packaged so looking at data to find what would be the best oven temperature to oven baking time will help identify the best process to increase the effectiveness of packaging the grains.
This visual graph shows baking time to baking temperature. This shows an interaction between the oven temperature and oven time. The grains have a lower percentage of moisture when they are baked for a time of 60 minutes as opposed to 30 minutes at 125-130 degrees. However, when the temperature is 135 degrees the grain has lower moisture percentage when baked for 30 minutes.
You could use this method with many different things in the everyday world. In the medical field, you could use this method with medication side effects, utilizing a certain procedure over others etc.
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