Smoking in pregnancy and low weight babies: a statistical consideration.

A previously published article tries to account for the higher mortality of low birth weight babies born to mothers who do not smoke by a hypothesis concerning the mean birth weights below an arbitrary level based on the nature of the normal distribution. It claims that if the birth weights of babies born to mothers either smokers or nonsmokers are distributed as normal distributions of equal variance then under certain conditions one would expect on mathematical grounds that the average weight of low weight babies would be greater if their mothers smoked than if they did not despite the fact that overall the mean birth weight of babies born to mothers who do not smoke is highest. If low weight babies born to mothers who smoke are on average heavier than those born to mothers who do not smoke the mortality of such a group (other things being equal) would be lower. However this argument is not mathematically justified and is based on a false premise since if there are two normal distributions of equal variance but different means the average value of the variable in question in any given fixed range will always be greater in the distribution with the higher mean. Thus the published article is correct in stating that in practice the difference in mean birth weights of low weight babies is likely to be small but it is incorrect in proposing that a reversal of mean weights may in certain conditions occur if birth weights are distributed normally.