How do I test for lower variability induced by systematic missings? In my data, some individuals have missing data on the central predictor (father missed the intake assessment). Comparing the DVs' means for those with a missing/non-missing predictor yielded some sizeable effects.
Now I want to find out whether the systematic missings may have led me to underestimate the size of the OLS regression coefficients. What's a good way to do this?
Simply comparing the variances of the DVs in the group without missings to the group with missings is easy to do?
But conceptually I want to know whether the whole sample has significantly less variability when I leave the group with missings (and significantly-lower-than-average-scores) out, not whether the two groups (with missings and without missings) have different variances.
All that I found so far was about independent samples, not about subsets.
Also, just to bring me up to speed: heteroscedasticity is usually used in the context of residual variance, right? What's a good term for constricted variance that would give me better luck with google?
 A: I think you have posed two different questions: one which asks about bias in your coefficients and another which talks about variance.  
Bias
As far as I can tell, the general solution to attempting to understand the likely bias in coefficient estimates is to explicitly model the cause of the missing data.  However, in most situations that I have come across such information is not available and there is instead a need to do something a little more pragmatic (but imperfect).  The following should tell you if you have bias:


*

*Recode the missing data on the central predictor by assigning the
mean to each observation.

*Create a new binary variable which has a 1 when respondents are
missing data and a 0 otherwise.

*Re-estimate your models with these two independent variables
replacing the central predictor.


The coefficient of the binary variable will capture the phenomena of missing group having a different mean on the dependent variables.  You can assess bias by comparing the coefficients obtained with the models I have just described with the models you were obtaining with the smaller sample size.
Variance
A priori, adding in the respondents with the missing data is going to increase your variance.  If they were the same as everybody else then your variance wouldn't change, but you know they are not the same as everybody else so your variance should increase.  However, I doubt this is so relevant to solving your problem as your interest is the conditional variance (i.e., the relationship between the predictors and your dependent variables) rather than the variance per se.
