It seems like your real beef here is with journalism (even the higher-than-average quality journalism that normally appears in the Economist). The fact that some news magazine doesn't include citations for claims in an article[1] has nothing to do with the sketchiness (or non-sketchiness) of "social science."
It is too bad though that the Economist doesn't provide citations for claims like this. Did they pull "10%" out of thin air? Are 10% of new medical doctorates currently earned by Muslims? Did they include all kinds of doctorates (PhD, etc) in the calculation? A simple link to the source for this number would clear that all up...
[1] http://www.economist.com/news/united-states/21679823-despite...
Paper: "We put three women and three men in a room for 10 minutes and they brainstormed 1.3 extra ideas than a room of 6 men."
Article: "Study proves gender balance leads to better meetings!"
But here's something interesting: I've tracked down a source for the 10% claim, and it's absolutely bonkers:
* An editorial[1] in the Detroit Free Press makes the following claim:
| "an analysis of statistics provided by the American Medical Association indicates that 10% of all American physicians are Muslims"
That certainly makes it sound like the AMA thinks that 10% of American physicians are Muslims.
* The source provided for this claim, "Muslim Doctors Abundant, But Muslim Hospitals Non-Existent"[2] is a 2008 post on a site called The Muslim Link.
Here's how that post arrived at the 10% claim:
* 113,585 Physicians in the US (2006)
* 7,000 current and retired physicians are members of the Association of Physicians of Pakistani Descent of North America
* 5.9% of African Americans are Muslim; 3.5% of physicians are African American; therefore there are 2000 African American Muslim physicians
* 7000 + 2000 = 9000; 9000 is just about 10% of 113,585
I shit you not, that's the most straightforward reading of the analysis at [2]. Now it's in the Economist. I seriously hope they got that number somewhere else.
[1] http://www.freep.com/article/20140128/OPINION05/301280121/da...
[2] http://www.muslimlinkpaper.com/myjumla/index.php?option=com_...
Apparently ~2.7% as measured by this study in 2005. Surprised I could not find department of labor statistics on the question. I would say that it is very possible that the proportion has increased drastically since 2005: Many of the people who have fled Iraq and Syria since then are skilled professionals including doctors.
As much as I hate Trump, I don't think this is possible.
https://www.aamc.org/download/426242/data/ihsreportdownload....
So that takes the coarse estimate down to 25 years.
Not any more than any other science that relies on sampling humans (I'm looking at medicine). Both start yielding stronger results when they explore the effect of mechanisms that are already known, and have a bad record of discovering "surprising" effects.
The antidote is simple: never rely on a single study, or even two.