Significant total effects, non-sig direct and indirect effects, why?

[Cameron Whitley]

I ran an SEM model with gender (exogenous variable) and I get the following for effects:

Direct: -0.13
Indirect: -.042
Total: -.172***

The direct and indirect effects are not significant, so why is the total? This is performed using estat teffects

Thanks.

[Clyde Schechter]

Let me answer your question with a question: why does this puzzle you?

The "non-significance" of the direct and indirect effects separately mean that within the precision with which your data were able to provide an estimate of these effects, they are not distinguishable from zero. It does not mean that the effects are zero, just close enough that we can't be certain they aren't. Well, you add the two of them together and you get a bigger number (in magnitude, actually smaller since we're talking negatives here.) And it may (or may not) be the case that the precision of the estimate for the total is sharper than it is for either the direct or indirect effect alone. So now you're being told that this larger magnitude number is large enough that to the extent of the precision made available by your data, we can say with some confidence that it is not zero.

What is surprising or paradoxical about that?

This is the problem with focusing on "statistical significance." It's a real snake pit of a concept and more often misunderstood than correctly understood. You really are better off not focusing on "significance" when interpreting your results. Look at your estimates (coefficients, marginal effects, whatever) and look at how precisely they are estimated (the standard errors or the 95% confidence intervals are measures of that). Then focus on what you can say about each estimate in light of the precision with which it is estimated. I tell my students that the p-values should only be looked at after you've already interpreted your results, and then only if you have nothing better to do with your time.