I have a question regarding my mediated model.
My unstand. B in R3 (-0.015) is not lower than B in R1 (-0.17), but the 3 regressions showed that each is significant (p-values of R1, R2, and R3 are less than .001). This shows that there is no mediation? What's going on?
And when I put this into the Sobel's test (for negative betas), the test statistic shows to be -8.48, but the p-value is 0. So there's a significant level of mediation, right?
These two results are not supporting one another.
Another question: for the Sobel's test statistic, do I regress Mediator (M) to Outcome (O) separately to find the B and SE? Or do I just use the M and O figures from my R3, which is (P and M on O)?
Thanks!
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K, so I know I'm not a TA, but I think I have the answer for this. You can refer to a TA's comment after it though.
The B you reported in regression 3 IS actually "lower" in magnitude than in regression 1 for your predictor. If you compare the standardized betas, you will notice (I think) that the regression 1 beta will be higher both in magnitude and in numerical value than in regression 3, thus revealing that your relationship for the beta did indeed change.
Also, Sobel's can certainly be negative, since it is a Z score. What matters is the significance of this score, p <.....
For Sobel's, you will need the B and SE from regression 2 (if you look at the diagram on the website, you can see which Bs and SEs you will need) and from regression 3 (the predictor to outcome).
"My unstand. B in R3 (-0.015) is not lower than B in R1 (-0.17), but the 3 regressions showed that each is significant (p-values of R1, R2, and R3 are less than .001). This shows that there is no mediation? What's going on?"
I'm not entirely certain about a couple of things you have typed above, so please help me understand.
The first one may be a typo. -0.015 is in fact quite a bit smaller in magnitude (i.e., absolute value) than is -0.170. The difference is .155, or over 10 times the smaller value. (Of course, if you meant to type -0.150 instead of -0.015, this may be moot.)
If all three regressions showed significant values as expected (regression 1, predictor predicts outcome is significant; regression 2, predictor predicts mediator is significant; regression 3, mediator predicts outcome even when predictor is in equation), then you have satisfied the three preconditions for regression. It sounds like from above that this is what happened, so I don't understand your comment about "This shows that there is no mediation?" These three regressions, by themselves, do not show mediation--they simply provide the test of whether or not mediation could have occurred--they are the preconditions. You appear to have satisfied the preconditions, assuming that the mediator predicts the outcome even while controlling for the predictor.
If the values of -0.015 and -0.170 are correct, then you have passed the comparison piece of mediation. (If it were a typo, and the real values were -0.15 and -0.17, then you have a significant additive model in which both predictor and "mediator" are really both predictors of the outcome, and computing the Sobel test would not be appropriate in such an instance.)
"And when I put this into the Sobel's test (for negative betas), the test statistic shows to be -8.48, but the p-value is 0. So there's a significant level of mediation, right?"
Your Sobel test is significant, which also indicates that you have mediation. (BTW, the probability level printed by the calculator may show up as .000, but in your write up, a clear acknowledgment that the probability is not EXACTLY 0 is needed, so p < .001.)
"Another question: for the Sobel's test statistic, do I regress Mediator (M) to Outcome (O) separately to find the B and SE? Or do I just use the M and O figures from my R3, which is (P and M on O)?"
Finally, as mentioned with the mediated homework, all of the necessary values for computing the Sobel test are available from the three regressions that you compute in this process. Do not compute a different regression to come up with a value for this test. As a reminder, you may find it very useful to draw the entire model, and plug in all values from the regressions, including both values for the unlabeled path between predictor and outcome.
Thanks, Chris!
-0.015 is higher than -0.17 because everything's in negative... Like, -1 is higher than -2? Or am I confusing a lot of things?
My stand. beta is R1 is -.305, and in R3 is -.027, so again, the figure in R1 is lower...
Yes, it is a -.015 and not -.150. Do I read the unstandardized betas in absolute term?
"If you compare the standardized betas, you will notice (I think) that the regression 1 beta will be higher both in magnitude and in numerical value than in regression 3, thus revealing that your relationship for the beta did indeed change."
-this was wrong, I forgot that standardized betas could be negative.
Referring to the "magnitude" of your unstandardized B from Regression 1 to Regression 3 (-.17 to -.015): does it make sense that -.015 is lower in magnitude than -.17 (meaning that that -.015 is closer to 0 than -.17)? The sign (negative) of the unstandardized B is not so much an issue as the size of the B, because this tells you the relative change in your outcome variable from that predictor. So, thinking of the example of -2 to -1, -1 IS actually "lower" because the relationship changed (it is less negative than before, and closer to 0). Does this make sense?
Mari, I hope I'm not muddling things up. If this is unhelpful you can delete.
Thanks Chris. I understood your explanation (so I hope it's not wrong :)).
The sign of a beta (standardized or unstandardized) refers only to the DIRECTION of the relation between those to variables. That is, a negative beta indicates that as X goes UP, Y goes DOWN (and vice versa--as X goes DOWN, Y goes UP).
The STRENGTH of the relationship (i.e., the magnitude) is measured by the absolute value. That is, a relationship of +1 is exactly as strong as a relationship of -1.
Thus (from my first reply): -0.015 is in fact quite a bit smaller in magnitude (i.e., absolute value) than is -0.170. The difference is .155, or over 10 times the smaller value.
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