For example, a very carefully conducted study that was published last year presented time-series data for a whooping 709125 Swedish teenagers in order to investigate if violent behavior among these teenagers was related to whether their mothers had smoked during their pregnancy or not. One of the things the Swedish researchers found was that after controlling for various socio-economic variables and other potentially confounding factors, the risk of conviction for violent crimes increased by a staggering 300 percent for teenagers whose mothers had smoked at least one cigarette a day during their pregnancy.

Another thing they found from their analysis of the very same data, however, seemed to strongly negate the first finding: When the researchers restricted their analysis to sibling-pairs for which the mother had smoked only during her pregnancy with one of the siblings, but not the other, the difference in risk for violent behavior disappeared. If anything, those siblings who were born at a time at which their mothers weren't indulging their smoking habit, were at greater risk for violent behavior.
Both findings are illustrated in the graph below.

Before I offer some additional thoughts on the Swedish study, I will briefly introduce a different, but related study that also considers the effects of smoking during pregnancy. The finding is often referred to as the "low birth-weight paradox":

Children who are below a certain weight at birth are found to be at a higher risk of death during infancy. The link between low birth-weight and infant mortality is so strong, that birth-weight has essentially become the primary unit of measurement to express this risk. In fact, I would guess that, long before scientists established ant statistical correlations between the weight and the health of a new-born, concerned parents around the world were assessing the "strength" of their newborns by asking "how much does s/he weigh?".

Here is the paradox then: Mother's smoking is believed to reduce the health of the infant, but infant mortality among babies from smoking mothers is much lower than it is in the general population. This is not an isolated finding, but one that has been observed and confirmed on various occasions, and has led even behemoths in the field of statistics (like R.A. Fisher), to conclude that smoking during pregnancy may indeed have beneficial effects for babies; at least for those with low birth-weight, who are exactly those at a greater risk of death.

The point I am trying to make by citing these kinds of empirical findings is a simple one; an often overlooked truism: Causal inference from observations demands critical thinking. Regardless of whether particular data can be handled in a statistically straight-forward manner, or whether it requires sophisticated modeling techniques, the final conclusions we would draw from our scientific inquiries do not appear as the unequivocal consequence of the data. There is always the need to reason and justify the explicit and implicit assumptions that went into the construction of the sample and the collection of the data, and that governed the choice of methods employed. Underlying all scientific/and non-scientific inquiries, there are always implicit or explicit theories, models, or simply ideas about how the world works; and these ideas are inevitably invoked and deployed whenever we try to "make sense" of something.

Getting back to the examples of smoking mothers, statistical approaches offer some additional guidance on how to make sense of the observations. In the case of the low birth-weight paradox, I am convinced (and it is generally accepted among today's scientists) that what is actually being observed is a statistical treasure that is itself often referred to as Simpson's paradox. It results from the way our data samples arise in non-experimental settings. It is further influenced by the fact that low birth-weight is not exactly the same thing as the risk of infant mortality (it is only an indicator, and there exist other factors that determine the risk of death, but those may not be related to weight), and that we choose a somewhat arbitrary cut-off for what qualifies as "low birth-weight".

Simpson's paradox achieved pop-culture acclaim as part of the so-called Berkeley Sex-Bias case of 1973 in which it was argued (from empirical data) that women were discriminated against when it came to admission to this prestigious university. To support this claim, plaintiffs showed that out of 8442 male applicants to the university, 44% had been admitted, while only 35% of the 4321 female applicants found admission. A closer look at admissions figures, however, revealed that admissions for any given degree program were actually more in favor of women, and that the aggregate numbers did not present convincing (or even reasonable) evidence of discrimination. Instead, the university-wide 9% discrepancy in admissions had resulted from the fact that women were disproportionately applying to programs with stricter admissions standards. This made women less likely to be accepted to the school as such, but for any given program that a woman applied to, her chances of being admitted were observably at least as high as they were for a man applying to the same program.

In the low-birth weight case, Simpson's paradox plays out more subtly, but it still plays a role: Here it helps to consider the fetus that possess the characteristics that are relevant for survival, and would typically have normal birth-weight. Smoking , by this fetus' mother may reduce the child's health so much that it is born underweight (i.e. it is counted as "low birth-weight to a smoking mother"), but not so much that it dies during infancy (this is especially true, when not all health-related qualities are tied to weight). Likewise there will be children that possess qualities that increase their risk of death during infancy, and that would be born with low birth-weight. Smoking may reduce their health so much that mothers might experience a miscarriage (which also implies that there will not be a "birth-weight" measurement for this particular child; it will not be counted).

As a result of these two health-reducing effects of smoking, our sample of low birth-weight infants born to smoking mothers will include a disproportionate amount of children that have above average other health-related qualities. Additionally, those with extremely poor survival chances to begin with, are entirely absent from the sample of children born to smoking mothers, while they will be just healthy enough to be included in the sample for the non-smoking mothers.

As a combined effect of these two biasing trends, we will see increased survival rates among children born to smoking mothers. Paradoxically this bias in observed survival rates comes about not "despite" the health-reducing effects of smoking, but precisely BECAUSE of the health reducing effects of smoking.

As far as the Swedish study is concerned, I still have to wrap my head around it as much as you might have to. Which piece of evidence is more convincing? In this regard, it is worth noting, that both approaches attempt to control for confounders that rely on their own set of assumptions about what is "unobserved":