Systematic measurement error and common method variance

[@vucanh7360]

Excellent explanation! I really like the publishing tip at the end of the video.

[@mronkko]

You are welcome.

[@user-ey1dg4xn2u]

Thanks for the video, but How come the correlation can be inflated? I would like to know the proof.

[@mronkko]

Assume X and Y are the quantities of interest and A is a source of systematic error. CoV(X+A, Y+A) = CoV(X, Y) + Con(A) > Cov(X,Y) if Var(A)>0. Follows from calculation rules for covariances.

[@user-ey1dg4xn2u]

@@mronkko I understood that cov is inflated.
But isn't that var(x) and var(y) are also inflated such that correlation equation(cov(x,y) / sd(x)*sd(y)) is not inflated?

[@mronkko]

@@user-ey1dg4xn2u The correlation will be inflated too. Consider the case when cov(x,y) = 0, then cor(x,y) =0 but cov(x+a, y+a) >0 if var(a) >0.

[@user-ey1dg4xn2u]

@@mronkko Thanks for the comment. I got that the correlation can be inflated, but isn't that it can not be as much as you described in the video (by the reason I told you)? I used simulation using R-software and enormously increased the variance of error, however, there was not dramatic change in correlation between x and y.
The code is made as follows;
x

[@mronkko]

@@user-ey1dg4xn2u You are modeling effects of random error, not systematic error. Random error biases a correlation toward zero. This is called attenuation in the literature. If the population correlation is zero, like in your case, attenuation has no effect.