OK, that's great, you say, but it doesn't prove anything: They could genuinely be changing their minds to start believing what they think God believes, in which case it's no wonder they correlate well.
Ah, but that's where they get tricky:
... We investigated this in Study 5 by
influencing participants’ own attitudes about affirmative action
through exposure to persuasive arguments. In a pro-policy
condition, participants read one strong argument supporting
affirmative action and one weak argument opposing it. In an
anti-policy condition, participants read one weak argument
supporting affirmative action and one strong argument opposing
it (see SI Text). Participants then rated the strength of each
argument they received. Finally, participants reported their
attitude about affirmative action and did the same for God, the
average American, Gates, and Bush. ...
They have the subject read a paper designed to shift their view in some point, and administer the survey again. The paper does indeed shift the opinions of the subject, and it also shifts what they think God's opinions are, and what they think Bill Gate's are (though to a lesser extent), but not Bush or the average american.
In another study,
Study 6 sought convergent evidence by using a
different experimental manipulation that relied on internally
generated arguments rather than on externally provided ones. In
particular, participants were asked to write and deliver a speech
either consistent or inconsistent with their own preexisting
beliefs in front of a video camera. Under these circumstances,
people tend to shift their attitudes in a direction consistent with
the speech they deliver (21, 22). Participants first reported (in a
dichotomous choice task) whether they generally supported or
opposed the death penalty, among other issues. Approximately
30 min later, a new experimenter told participants that videotapes
were needed for another study of people evaluating
speeches about the death penalty. Participants were then asked,
depending on random assignment, if they would be willing to
deliver a speech in favor of or opposed to the death penalty. This
meant delivering a speech consistent with preexisting attitudes
for some participants and inconsistent with preexisting attitudes
for the other participants. All but five participants (two in the
consistent condition, three in the inconsistent condition) agreed
to the experimenter’s request. After delivering the speech,
participants reported their own attitude about the death penalty,
and then did the same for God, Gates, Bush, and the average
They did a similar thing, only with a different method of modifying the participants' beliefs, with the same result.
Finally, they did a comparison in an fMRI which confirmed that people use the same brain areas to process questions about their own beliefs and God's beliefs-- but they use different areas to process other people's beliefs. (In my mind, until we know more about the brain, this sort of thing is of limited use in proving anything)
So what does this prove, and what doesn't it prove?
They do seem to have shown fairly convincingly that these people do not maintain separate categories in their mind for their own opinions and God's opinions. This implies that these people are or could be serving as their own God: their perception of God's opinions are probably just echo boxes for their own opinions.
OK, so the sample sizes are adequate but not huge; I'd be willing to bet that there's one personality type that would probably break this mold, at least occasionally: the theology geek and/or pastor. The sort of person who would say something like "I wish I didn't have to believe this, but the bible says blah blah blah..."
I suspect a common Christian response to this will take the general form of claiming that that the individuals in the study were not *good* Christians, that, in fact, the majority of Christians in the country are not good Christians and do tend to remake God in their own image. So the people in the studies were sinful/backslidden/uninformed/idolatrous/fake Christians. I find this to be a very unpalatable response; what reason do we have for supposing those who propose this kind of argument are actually among the good/real Christians?
So how do you know if you are doing this yourself? I can only speculate, but chances would seem pretty good that if there's nothing you and God disagree on, you're doing this.
Here are two other takes on this study. I'll add other links to responses to the study if you have them and they're interesting.