Robbie Low, writing in Touchstone (June 2003), points to an interesting 1994 study in Switzerland about the connection between the churchgoing habits of fathers and mothers and the effect on their children when they are grown.
Here’s a summary:
In short, if a father does not go to church, no matter how faithful his wife’s devotions, only one child in 50 will become a regular worshipper. If a father does go regularly, regardless of the practice of the mother, between two-thirds and three-quarters of their children will become churchgoers (regular and irregular). If a father goes but irregularly to church, regardless of his wife’s devotion, between a half and two-thirds of their offspring will find themselves coming to church regularly or occasionally.
A non-practicing mother with a regular father will see a minimum of two-thirds of her children ending up at church. In contrast, a non-practicing father with a regular mother will see two-thirds of his children never darken the church door. If his wife is similarly negligent that figure rises to 80 percent!
The results are shocking, but they should not be surprising. They are about as politically incorrect as it is possible to be; but they simply confirm what psychologists, criminologists, educationalists, and traditional Christians know. You cannot buck the biology of the created order. Father’s influence, from the determination of a child’s sex by the implantation of his seed to the funerary rites surrounding his passing, is out of all proportion to his allotted, and severely diminished role, in Western liberal society.
... [W]hen a child begins to move into that period of differentiation from home and engagement with the world “out there,” he (and she) looks increasingly to the father for his role model. Where the father is indifferent, inadequate, or just plain absent, that task of differentiation and engagement is much harder. When children see that church is a “women and children” thing, they will respond accordingly—by not going to church, or going much less.
Curiously, both adult women as well as men will conclude subconsciously that Dad’s absence indicates that going to church is not really a “grown-up” activity. In terms of commitment, a mother’s role may be to encourage and confirm, but it is not primary to her adult offspring’s decision. Mothers’ choices have dramatically less effect upon children than their fathers’, and without him she has little effect on the primary lifestyle choices her offspring make in their religious observances.
Her major influence is not on regular attendance at all but on keeping her irregular children from lapsing altogether. This is, needless to say, a vital work, but even then, without the input of the father (regular or irregular), the proportion of regulars to lapsed goes from 60/40 to 40/60.
And of course what is best for kids is not dad simply attending church regularly, but dad loving and leading 7 days a week in response to the gospel's capture of his heart.