Keep in mind that tests from other eras (let's say the 80s and backwards, just for simplicity) were significantly skewed towards male-oriented views of intelligence. I'm not saying they were sexist: Just that in some cases the men writing the tests couldn't conceive how the correct answer could be other than the one they intended. We have a lot more studies now showing different methods of thinking, and a lot more respect for intelligence in social situations as well as academic ones. My mother, for example, scored 78 on an IQ test back in the 1970s, despite a grade average of A's and B's. Her most recent attempt at an IQ test landed her somewhere in the 130 range, I think. Her teacher back in 70-something told her the the test was total bunk and to ignore it, because he intended to.
It's not just limited to IQ tests, but essentially, generations of women have grown up thinking they're less "intelligent" than men... but with a very academic definition of intelligence.
If someone wants to launch a counter-study, try replacing the term "intelligence" in this study with "common sense". I'd be willing to bet the results would be sharply reversed, even among men reporting their own levels of "common sense". Just a hunch.