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"For a more mathematical/numerical reason....
the standard error of the marginal effect is obtained by the delta
method, which means that the standard error for the marginal effect of
one independent variable involves the whole variance-covariance matrix
from the estimation together with the appropriate entries from the
Jacobian. In other words, there is a lot of stuff that goes into the
calculation beyond just the standard error of the coefficient of that
variable, and these other things can cause it to be greater than 0.05,
even when the coefficient standard error is less than 0.05."


Note:  It appears that the marginal effects you are reporting under the
column "margeff" are not the marginal effects at the mean but the mean of
the marginal effects.

. use "http://www.stata-press.com/data/r9/nhanes2f.dta",clear

. qui svy: probit heartatk height weight female black age highbp

. mfx 

Marginal effects after svy:probit
      y  = Pr(heartatk) (predict)
         =  .01018915
---------------------------------------------------------------------------
variable|    dy/dx     Std. Err.     z    P>|z|  [    95% C.I.   ]      X
--------+------------------------------------------------------------------
height  |  -.0002103    .00018   -1.18   0.237  -.000559  .000139   168.465
weight  |   .0001798    .00008    2.21   0.027   .000021  .000339   71.9113
female* |  -.0127414    .00357   -3.57   0.000  -.019744 -.005739   .520313
 black* |  -.0006893    .00221   -0.31   0.756  -.005028   .00365   .095637
   age  |   .0011518    .00008   13.93   0.000    .00099  .001314   42.2387
highbp* |  -.0033818    .00176   -1.93   0.054  -.006824   .00006   .105917
----------------------------------------------------------------------------
(*) dy/dx is for discrete change of dummy variable from 0 to 1

. margeff, at(mean) dummies(female \ black \ highbp)

Marginal effects at means on Prob(heartatk==1) after probit

---------------------------------------------------------------------------
 heartatk |   Coef.    Std. Err.      z    P>|z|     [95% Conf. Interval]
----------+----------------------------------------------------------------
   height |  -.0002103    .000178    -1.18   0.237    -.0005592    .0001385
   weight |   .0001798   .0000812     2.21   0.027     .0000207     .000339
   female |  -.0127414   .0035728    -3.57   0.000     -.019744   -.0057388
    black |  -.0006893   .0022138    -0.31   0.756    -.0050283    .0036497
      age |   .0011518   .0000835    13.80   0.000     .0009882    .0013154
   highbp |  -.0033818   .0017562    -1.93   0.054     -.006824    .0000603
---------------------------------------------------------------------------

. margeff

Average marginal effects on Prob(heartatk==1) after probit

---------------------------------------------------------------------------
 heartatk |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------+----------------------------------------------------------------
   height |  -.0006499   .0005384    -1.21   0.227    -.0017052    .0004053
   weight |   .0005557   .0002374     2.34   0.019     .0000904    .0010209
   female |  -.0373506   .0092254    -4.05   0.000    -.0554321   -.0192692
    black |  -.0021513   .0069901    -0.31   0.758    -.0158517    .0115491
      age |    .003559   .0003089    11.52   0.000     .0029536    .0041644
   highbp |  -.0111666   .0061382    -1.82   0.069    -.0231972     .000864
---------------------------------------------------------------------------


Scott



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