Simpsonโs paradox is a statistical phenomenon where the relationship between two variables changes if the population is divided into subcategories. In the following animation, we can see how the linear relationship between two variables is inversed, if we take into account a third categorical variable. Simpson's paradox highlights the fact that analysts should be diligent to avoid mistakes.
How to identify this phenomenon in SmartPLS?
Hello Rasoul,
My understanding of Simpson's paradox is that it is a function of the subgroup proportions changing. That being the case, one could control for this by forcing constant proportions of cases throughout the range of the second variable (whether it's time/occasion, or something else).
In general, though, if you suspected a third variable, wouldn't testing this be as simple as including (a) the suspected third variable; and (b) the interaction of the third variable with the designated IV as predictors in the model? This is referred to as moderation in a lot of the literature.
Good luck with your work.
Hi Rasoul,
the fact that an estimated relationship changes when stratifying (=controlling or adjusting!) a third variable, doesn't tell you anything as the key issue is whether this variable acts as a confounder (common cause auf X and Y) or collider (a common effect of X and Y). Both change the relatinship between X and Y but controlling for the confounder UN-biases the effect but controlling for the collider biases the (otherwise unbiased) effect.
I strongly recommend this book that will enlighten you :)
Pearl, J., & MacKenzie, D. (2018). The book of why. Basic books.
HTH
Holger
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