The sociologist Rodney Stark claims that a religion's image of God has an impact on the conduct of adherents. People will watch their behavior more closely if they see God as a ruler rather than a friend.
GSS respondents were asked how likely it is that 1) a friend, 2) a master, or 3) a king come to mind when thinking of God. Answers ranged from very likely to not likely at all.
I calculated the contigency coefficients and p-values for the relationships between the answers to each of the three questions and whether you have ever been arrested for a crime. The sample is 388 white people. The relationship between arrest and seeing God as a friend is not statistically significant, but it is for both seeing God as a master and as a king. People with this type of image are less likely to have ever been arrested. On the other hand, the strength of the connection is weak. The coefficient (which is like a Pearson correlation) is .12 for master and .17 for king.
In sum, imagining God to be a powerful authority predicts less crime. It is possible that the trend among Christians to see God as a buddy works against improving behavior.