http://www.nytimes.com/2009/11/26/garden/26cousins.html?pagewanted=all

“For the most part, scientists studying the phenomenon worldwide are finding evidence that the risk of birth defects and mortality is less significant than previously thought. A widely disseminated study published in The Journal of Genetic Counseling in 2002 said that the risk of serious genetic defects like spina bifida and cystic fibrosis in the children of first cousins indeed exists but that it is rather small, 1.7 to 2.8 percentage points higher than for children of unrelated parents, who face a 3 to 4 percent risk — or about the equivalent of that in children of women giving birth in their early 40s. The study also said the risk of mortality for children of first cousins was 4.4 percentage points higher.”

The first problem is that this paragraph completely confuses the statistical issue because of the way it describes the percentages. “1.7-2.8 percentage points higher than for children of unrelated parents, who face a 3 to 4 percent risk” - now does that mean 1.7-2.8% of the 3-4% risk? In other words, low-end, 0.03 * 1.017 = 0.0305 or 3.05% to high-end 0.04 * 1.028 = 0.0411 or 4.1%?

No, probably not. But because of the way it’s stated that’s how it sounds. What they almost certainly mean is for the percentages to be added - that is, a range of 3 + 1.7 = 4.7 percent to 6.8 percent. That’s a much easier statistic to grasp and it’s easier to compare: 3-4% and 4.7-6.8%

Put that way, the quoted comment later in the article that “Even the small average risk of defects reported in the 2002 study represents nearly double the risk to children of unrelated parents” is much easier to see in the statistics.

The second problem is that an increased rate for mortality is quoted without the normal rate being given. “The study also said the risk of mortality for children of first cousins was 4.4 percentage points higher.” But what’s the normal infant mortality rate? If it’s 25%, that 4.4% doesn’t look so significant. But it’s not. The US infant mortality rate is 0.67% (6.7/1000). And here again the same problem as before comes in. Is the rate 4.4% higher than the normal rate - 0.0067 * 1.044 = 0.0070 or 0.70% - or is it, like the other statistics appear to mean, saying that the rate is 0.67 + 4.4 = 5.07 percent? I am assuming the latter - but if so, this sentence massively fails to communicate that we are talking about a mortality rate that means that a child of first cousins is 5.07 / 0.67 = 7.57 times more likely to die in infancy. Because the baseline US infant mortality rate is missing, and because the quoted increase is unclear, it’s impossible to get that piece of information from the article. But if the latter interpretation is correct, the increase in percentage terms over the baseline rate is 4.4 / 0.67 * 100 = 657%

4.4%. 657%. These are different kinds of numbers. It would be good if the article made that a little bit clearer.