How to tell if my variable is a suppressor? I am analyzing data using path analysis and I am hoping someone here can help.  
In my model, I am looking at predictors of a variable, $Y$. In the path model, $Y$ has 4 significant predictors lets call them $A$, $B$, $C$, and $X$ (path coefficient $X$ to $Y$ is $-.16$ which is significant). Of importance, $X$ is not significantly correlated with $Y$ when tested as a bivariate correlation ($r = .105$, ns). I feared that suppression may be present and so I ran the partial correlation controlling for $A$, $B$, and $C$. The partial correlation between $X$ and $Y$ was $-.209$, which is significant. 
Does this rule out suppression and instead suggest incidental / accidental cancellation may be more likely the issue, or am I missing something? Are there other ways to determine if suppression is the issue?
 A: Simply because the coefficient switched signs and became significant from the bivariate analysis to the multivariate analysis does not guarantee that $X$ is a suppressor.  It certainly could be, what you have is the signature effect of suppression, but there are other possibilities as well.  For example, $X$ could be confounded with another of the variables in the model, causing the sign to change, but the inclusion of the remaining variables accounts for enough of the residual variance as to make the effect significant.  In general, it is hard to ultimately know for sure what the exact relationships are between variables.  The best way to determine if $X$ is a suppressor would be to run a new experiment in which you manipulate $X$ and see if there is an effect on $Y$.  If it is a suppressor, there will be no effect.  (Note that this is an equivalence test, which is more subtle than the prototypical hypothesis testing situation.)  
For more information about these topics, you may want to read the following CV threads:  


*

*There is a great overview of suppression here: Suppression effect in regression: definition and visual explanation/depiction.  

*To understand how the sign of a covariate could change without suppression, see:   Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?

*Regarding equivalence testing, see: 


*

*Is it possible to prove a null hypothesis? 

*How to test hypothesis of no group differences?, and/or

*Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis?


*The partial regression coefficient and the partial correlation coefficient are not typically expected to agree, because they are not standardized in quite the same way, see: 


*

*Are standardized betas in multiple linear regression partial correlations?, and/or 

*Multiple regression or partial correlation?
A: I may be mistaken, but suppression typically refers to a multivariate analysis that reduces the effect of one of the variables in the equation. In this case, it seems the univariate relationship is not significant, while the variable is significant in the multivariate analysis. If anything, this is the opposite of suppression. In essence, it appears that removing error associated with A, B, and C led to an increase in variance in Y attributable to X, which lead to it becoming a significant predictor. 
Note that the significance of the partial correlation and the path coefficient should be identical, unless I am mistaken. 
