A few points:
- All the participants were paid via Mechanical Turk for their participation. This gave me pause. Depending on how this was set up, I was curious how they verified that people didn't give some of their answers just to qualify to get paid.
- The study did not follow individual women and show them to be fluctuating. The study compared groups of women at high and low fertility times and reported their differences.
- The measured political attitudes excluded all fiscal views (because those didn't change much) and focused only on social views.
- The single women assessed for political affiliation had a median income of $15000-25000/year, whereas the married women had incomes of $35000-$50000/year. Interestingly, in the discussion section, this difference is considered relatively small and inconsequential.
- While the study (and articles) mention that they surveyed 275 women for the first experiment, they later clarify that they tossed out nearly half of them because they couldn't reasonably determine where they were in their cycle. The second study started at around 500 and got whittled down the 300. This means the groups being compared were about 75 people each in the first study and 150 each in the second.
- The groups were not controlled for anything. Those income ranges are so big you could drive a truck through them, and nothing was said about what states people came from.
- No woman under 44 was counted, nor were any of them asked if they planned on voting.
Overall, I was less weirded out by this study when I saw the authors. They are all pretty hard core evolutionary psych folks, and pretty much believe everything people do is hooked to mating opportunity (interesting, this includes religion. Apparently women become religious to either stop themselves from cheating or to attempt to impose a social order on others that will keep their mates faithful). Take a look at Kristina Durante's publishing history and you'll see why they never even looked at how any other variables might influence anything. Truthfully, they saw a link where they had already decided there was a link.
With sample sizes as small as they were from a very specific group (people seeking out paid work on the internet), a control for region or income would have been helpful. Additionally, the group studied (18-44) is the least likely group to vote. Even beyond their reproductive years, women still tend to vote Democrat...so there's that. I also thought it interesting that there was no control for historic voting behavior...if women who voted for Obama in 2008 were more likely to change their vote in conjunction with specific times of month, it might have been more interesting. As is though, we have no idea if there's a real shift in individuals or if it's just the groups they picked (a interesting number of their p values did not reach the level of statistical significance, the results were reported in the article without this caveat).