2012 Olympics Winner: The American Women?

I've read a lot of talk recently about how this is the first Olympics where women have really stolen the show.  There are some pretty clear indicators (this is the first Olympics where every competing country had at least one female athlete), but some are a little more tricky to draw conclusions from.  For example, in terms of USA medal count, more women won medals than men (58 to 45)*.

I want to keep this first post fairly simple, so my first thought was simply "given the number of medals won by US athletes, is this difference in medals significant?"

The actual proportions for those medal counts are .437 for men and .563 for women (close to the actual counts due to the fact that the US has, for the past few Olympics, tended to win right around 100 medals).  If there was no difference between men and women athletes, we would expect that those proportions would be .50 and .50.  With just over 100 medals, are these proportions different enough from a 50/50 split?

Another way to think about this question would be to rephrase it.  If you tossed a coin 103 times, how unlikely would it be for it to come up heads 58 times and tails 45 times?  Well, it turns out that there's slightly more than a 20% chance of that outcome occurring by...well, chance.  That is to say that we *can't* say that American women won statistically more medals than their male counterparts at the London Olympics, just that they won more. 

That's hardly the end of the story, though.  One nice thing about the Olympics is the longitudinal aspect of the data.  Medal data is readily available for over 100 years.  Looking back too far would certainly produce a large gender gap, and looking at certain years (e.g. 1980, 1984) would likely bias US data.  With that in mind I looked at the past 6 Olympic competitions, from 1992-2012. 

I mentioned that I wanted to keep this post simple, so with that in mind let's look at the following chart in a purely descriptive way:
 

From the graph, then, there does appear to be a period of relative stability around a 60/40 split from 1992 up to 2004, with a shift starting in 2008 and a reversal in 2012.  We can examine if the proportions are different across different years - keeping it as simple as possible a Fisher's exact test fails to show an association of year and proportion between 2008 and 2012, but does reveal a difference in proportions between 2004 and 2012.  Thus, something does seem to be changing in terms of proportions between those years, and it does seem that American women have at least negated male dominance at the Olympic podium, and at best surpassed it.  Should be interesting to see what happens to these proportions in 2016. 

There are a few other factors I'd like to examine in this data in future posts, but if you think of any other things that could be examined as a follow-up to this data do feel free to let me know.  I figure it's something I'll come back to every once in a while, as Olympic data is just pretty fun.



*Note: the careful reader will notice that this is one medal shy of the 104 medals won by the US this year.  For the purposes of this analysis the missing medal is a bronze won in mixed doubles tennis.  This medal which must be excluded or double counted in terms of a gender breakdown.  I chose to exclude it rather than double count it.  Similar events occurred in each of the Olympics examined.