> Using a transformation of the h-index as our indicator of research output, we find male research output to be 0.35 standard deviations (p < 0.001) above female research output. However, the gap falls to 0.13 standard deviations (p < 0.001) when years publishing is controlled for.
What does this mean? What does "years publishing is controlled for" means?
Now consider what happens if men are (on average) more experienced because up until recently more men entered the field than women, but then the trend reversed. If you just compared female to male research output you could come to the wrong conclusion; the difference in experience could overwhelm the difference between sexes.
So there are various statistical tools you can use to measure the difference due to experience, and subtract it out from the difference between sexes to get a more accurate measure of the difference due to sex. Doing this is called "controlling for a variable"
So they effectively compare women-with-1-year vs men-with-1-year, etc. etc, rather than 'women with h-index 5' vs 'men with h-index 5'
edit: should be "Women with h-index of X after Y years" rather than just "Women with h-index of X" (e.g. they control for Y years' publishing between men and women, assuming that time-in-academia is correlated with h-index. Quick glance at the paper suggests that time-in-academia has R2 of 0.62 with h-index)