Well, I only know a modest amount of econometrics, so here's my translation for the "Chinese."
Because of the design of the GSS, not all participants were asked all of the variables that make up the outcomes of interest in this study.
The survey (GSS) asks a core set of questions while participants were randomly selected to answer the more specific questions. (I had to figure this out from context from an earlier section).
Consequently, it was not possible in this case to conduct a multivariate analysis of variance (MANOVA) to control for the inflated Type 1 error that occurs when multiple statistical tests are conducted.
Since each participant did not answer all of the questions we desired, we had to conduct several regression analysis instead of a single, traditional multi-variate analysis. A multi-variate analysis would have less error.
First, the association between pornography use and feminist identification was assessed using... blahblahblah binary regression... blahblah blahblah... that controlled for the first year of the survey.
We ran a binary regressions to determine the other factors we really cared about. These factors include: feminist identification, views on traditional family, attitude towards women in power, women in the workplace, and abortion. (Basically a binary regression is a statistical method that uses several variables to return a "yes" or "no" response, e.g. reg Is_Snarks_Cool post_counts sexiness other_stuff where the dependent variable Is_Snarks_Cool returns a 1 or 0. In the case of the study, they use a more complicated set up that has 2*(binary result 1) * 2 (binary result 2) for whatever reason, which is why we have numbers higher than 1 in Table 2, I think.)
To control for inflated Type 1 error we employed Bonferroni corrections to all of our analyses, which conservatively adjusted the significance threshold. Each of the analyses described here was also conducted with both weighted (adjusting for the undersampling of adults living in multiple-adult residences) and unweighted samples. The conclusions reached from both sets of analyses were identical, so the unweighted results are presented for the sake of simplicity.
To control for the larger margin of error because we ran a bunch of regressions instead of a single one, we use Bonferroni corrections on our analysis. (I have no idea what Bonferroni corrections are. Sorry! I'm guessing it's somekind of technique that compensates for errors when doing multiple regressions instead of one). We used weighted and unweighted samples to account for the fact that some of our data came from houses where there were multiple adults in one household. It turns that didn't really matter, so we used the unweighted data for simplicity.
There is this bit later down the line though:
It has long been known that individuals who volunteer for research involving exposure to sexual material differ from those who do not on a number of dimensions. Self-selectionp ressures were much stronger in Hald et al.'s study than the GSS study, which may have contributed to the differential recruitment of individuals who seek to avoid exposure to pornography. Arguably, the samples obtained by the GSS are more likely to contain individuals who were both less likely to consume pornography and as well as more likely to hold non egalitarian attitudes than the sample obtained by Half and colleagues.
So it doesn't really seem like they control for cause-effect relationships. Instead, it seems like this study defends that position by saying the GSS is less biased sample set than previous studies.
