We have to get used to living in a world where science — even social science — can detect really small things. Understanding how important really small things are, and how to interpret them, is harder nowadays than just finding them.
One of the great crime stories of the last twenty years is the dramatic decline of sexual assault. Rates are so low in parts of the country — for white women especially — that criminologists can’t plot the numbers on a chart.
Besides being wrong about rape (it has declined a lot, but it’s still high compared with most countries), this was a funny statement about science (I’ve heard we can even plot negative numbers now!). But the point is we have problems understanding, and communicating about, small things.
So, back to names.
In 2009, the peak year for the name Malia in the U.S., 1,681 girls were given that name, according to the Social Security Administration, or .041% of the 4.14 million children born that year (there are no male Malias in the SSA’s public database, meaning they have never recorded more than 4 in one year). That year, 7.5% of women ages 18-44 had a baby. If my arithmetic is right, say you know 100 women ages 18-44, and each of them knows 100 others (and there is no overlap in your network). That would mean there is a 30% chance one of your 10,000 friends of a friend had a baby girl and named her Malia in 2009. But probably there is a lot of overlap; if your friend-of-friend network is only 1,000 women 18-44 then that chance would fall to 3%.
Here is the trend in girls named Malia, relative to the total number of girls born, from 1960 to 2016:
To make it easier to see the Malias, here is the same chart with the y-axis on a log scale.
This shows that Malia has been on a long upward trend, from less than 50 per year in the 1960s to more than 1,000 per year now. And it also shows a pronounced spike in 2009, the year Malia peaked .041%. In that year, the number of people naming daughters Malia jumped 75% before declining over the next three years to resume it’s previous trend. Here is the detail on the figure, just showing the Malia in 2005-2016:
What happened there? We can’t know for sure. Even if you asked everyone why they named their kid what they did, I don’t know what answers you would get. But from what we know about naming patterns, and their responsiveness to names in the news (positive or negative), it’s very likely that the bump in 2009 resulted from the high profile of Barack Obama and his daughter Malia, who was 11 when Obama was elected.
What does a causal statement like that that really mean? In 2009, it looks to me like about 828 more people named their daughters Malia than would have otherwise, taking into account the upward trend before 2008. Here’s the actual trend, with a simulated trend showing no Obama effect:
Of course, Obama’s election changed the world forever, which may explain why the upward trend for Malia accelerated again after 2013. But in this simple simulation, which brings the “no Obama” trend back into line with the actual trend in 2014, there were 1,275 more Malias born than there would have been without the Obama election. This implies that over the years 2008-2013, the Obama election increased the probability of someone naming their daughter Malia by .00011, or .011%.
That is a very small effect. I think it’s real, and very interesting. But what does it mean for anything else in the world? This is not a question of statistical significance, although those tools can help. (These names aren’t a probability sample, it’s a list of all names given.) So this is a question for interpreting research findings now that we have these incredibly powerful tools, and very big data to analyze with them. The number alone doesn’t tell the story.