The Science Daily article I've linked to here goes on to say
In northern and middle European countries (including Britain and Ireland, the Scandinavian countries, Netherlands, Austria, Belgium, and Germany) there was a "distinct quickening" in the pace of advance in the period spanning the two World Wars and the Great Depression. This is striking because the period largely predates the wide implementation of major breakthroughs in modern medicine and national health services. One possible reason, alongside the crucial decline in infant mortality, for the rapid growth of average male height in this period was that there was a strong downward trend in fertility at the time, and smaller family sizes have already been linked with increasing height.
Other factors in the increase in average male height include an increased income per capita; more sanitary housing and living conditions; better general education about health and nutrition (which led to better care for children and young people within the home); and better social services and health systems.
All well and good. Except one thing. They think that smaller family sizes result in taller children? Um, no. As long as children with genes for height receive plenty of nutritious food to eat and don't suffer from terrible diseases when they're young, they will grow up big and tall regardless of how many brothers and sisters they have. In prosperous countries with plentiful, affordable food, wise eating habits can be practiced in large families just as easily as in small families.
I served an LDS mission in Poland less than ten years after the "Iron Curtain" came down. LDS people, along with Catholics, are known for having larger than average families. The American young men serving missions in Poland were nearly all tall and rather appallingly healthy in contrast to the Poles of the same age who had grown up in want (thanks, communism) and breathing polluted air.
There are so many times that correlation is mistaken for causation. Someone should start a blog dedicated to showcasing examples of that. I'd follow it.