In what way could MNAR data affect the results of correlations? I am studying the effects of exercise non-adherence in a pain sample (n=70). 
Pearson's correlations showed a moderate, negative, relationship between baseline pain and adherence behaviour at 3 months. A moderate, positive relationship was found between baseline disability and adherence behaviour. 
It is likely that those who dropped out of the study (i.e. did NOT complete adherence data at 3 months) are also less adherent to exercise in general. Therefore, my data may be MNAR.
My question is: If my data were MNAR, how might this affect the estimated correlation?
Thank you very much in advance for any help!
 A: The effect on the correlation depends on whether the dropouts had pain and disability values consistent with what you observed in the non-dropouts.
It may be helpful to think in graphical terms: imagine a scatter plot of pain (y) vs adherence (x). The negative correlation means that if we plot a linear regression trendline through the points, the line has a negative slope. 
Now consider the missing points due to the dropouts. These missing points have a small x value and an unknown y value. What we want to know is, what would have happened if these individuals did not drop out and we had actually observed these points?
There are three possible cases, depending on the typical y values of the dropout population:


*

*If the dropouts had y values consistent with your trendline, you would get about the same slope whether you had those points or not. 

*If they had y values much lower than your trendline, you might get a different, more positive slope if those points were included.

*If they had y values much higher than your trendline, you might get a different, more negative slope if those points were included.


To determine the most likely scenario you have to engage in some speculation - is it likely that the dropouts had higher or lower pain than the non-dropouts with low adherence?
The question about the disability-adherence correlation can be analyzed in the same way.
