Re: Introducing a 3rd variable makes the correlation coefficient non-significant. What's happening?

monopsony wrote:
I have two latent constructs in an SEM model. Each construct is
measured by 5 idicators. If I estimate the relationship between the two
constructs A-->B, the correlation is .20.

This would be SIMPLE correlation coefficient between A and B.

But when I introduce another
independent variable (C) pointing to the dependent variable B (that is,
C-->B and A-->B), the correlation between A-->B drops to about .04,

Not sure of what you mean by your terminology. If you mean you add
anothere independent variable C to the model with dependent variable
B, and another independent variable A, then your model becomes

B = a A + c C (with or without a constant term),

I think by "correlation" between A --> B, you mean standardized
coefficient a of A, which is no longer the SIMPLE correlation between
A and B, but the partial correlation between A and B, GIVEN C (or
in the presence of C).

This is a very common misconception in a regression with more than
one independent variable -- that the regression coefficients are NO
LONGER interpretable as the simple correlations between the dep
variable and THAT independent variable, but the partial correlation
given ALL OTHER variables in the equation.


which is non-significant. What is happening here? Why does it do that?
I want to reject the null hypothesis that A isn't related to B.

You could test it with the correlation or the simple regression
coefficient.


But I
do that with C in the model, which makes the relationship
non-significant.

That means in the PRESENCE of C in the model, the relation between
A and B is no longer significant.


The null hypothesis is rejected without C, but not rejected with C.

Without C, the relation between A and B is statistically significant.
But as soon as C is brought into the equation, it takes away whatever
relation there was between A and B, so to speak.

The above is a straightforward (once you get used to the notion of
PARTIAL correlational information) consequence of the meaning of
the regression coefficients in MULTIPLE regression.

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