UPDATE: Study does have several controls including importantly mother’s education and BMI. It also attempts to measure intra-family effects. My previous analysis is invalid.
Television viewing may be a sedentary activity, but it is not for that reason that it is associated with obesity in children. The relationship between television viewing and obesity among children is limited to commercial television viewing and probably operates through the effect of advertising obesogenic foods on television.
There is a well known correlation between TV watching and childhood obesity. The study seeks to control for activity level and the type of TV watch by using time-diaries. Their results show that type of TV watched is a predictor of childhood obesity but activity level is not. Kids who watched commercial free television were less likely to be obese.
However, as far as I can tell they make no attempt to control for exogenous family characteristics. No socioeconomic factors. No family dummies. No randomization.
The simplest story then, is that parents who are conscientious are going to both monitor what their children watch on TV and what they eat. I, of course, would be sympathetic to more complex stories involving backwards causation from obesity to type of TV watching.
When looking at childhood obesity we need to keep a few facts in the forefront of our minds. First, children and parents share the same genes and given the results of previous research we should be very conscious of potential genetic links between parent and child life outcomes.
Second, human personality is to a large extent determined by the interaction of the genes with the social hierarchy. In some sense we can think of much of human behavior as the genes doing the best they can with what they got, in an effort to climb the social ladder.
Obesity has strong social effects. Thus we should expect it to have strong effects on behavior. A fat kid is not going to face the same social incentive structure as a thin kid. A fat parent is not going to face the same social incentive structure as a thin parent. And a parent of a fat kid is not going to face the same social incentive structure as the parent of a thin kid.
Thus we should expect obesity in children to have strong effects on how the parents see themselves and how they interact with their children.