## Are you more likely to give birth on a full moon? Revised

In my previous post Ratbag and Roland pointed out that there seems to be a slight increase in probability in the birth rate for the week after a full moon and they suggested I carry out a significance test. I returned to the original data and found that the assumption that birth is equally likely on all days is in  significant disagreement with the data: could it be that the moon actually has an effect on the probability of birth? Luckily, if I correct my assumptions by noting that births are less likely on weekends, the influence of the full moon disappears again. So you are not more likely to give birth on a full moon, but you are more likely to give birth during the week.

In order to make a significance test it is necessary to have  a model of the underlying probability. In this case, we need to make some assumption about the probability of being born at a certain number of days distance from the nearest full moon. The most naive assumption is that babies are born with equal probability on each day of the year. In 1969 there were 13 full moons. Of the 12 intervals between each full moon, 6 were 29 days long and 6 were 30 days  long. Thus, assuming each day of the year is equally probable for birth, we can compute that the  probability of a baby being born between -14 and +14 days from a full moon is 0.03391 (to 4 s.f.) and  that  the probability of a baby being born 15 days from a full moon is 0.01667 (to 4 s.f.). The variance of a binomial distribution is $v=p(1-p)n$, where p is the probability of an even and n is the number of events considered. Since about 1.8 million births is the sample size used, this leads to a standard deviation $\sigma=0.000135$. Since any deviations from the probabilities of more than $3~\sigma$ would be significant, the increase in probability in the ten days after full moons seems significant.

This result surprised me: are women’s wombs really in tune to the music of the spheres? To make my mind up, I decided to look at the distribution of births as a function of day of the year, which is shown in the graph below.

Every 7 days there seems to be an event which leads to a significant reduction in births. This event happens on Saturdays and Sundays.  I am not sure why, but I reckon that doctors and nurses being on holidays might have something to do with it :D.

A better model for the probability of being born a certain number of days away from the full moon, must take this variation into account. If I do this, I obtain the curve shown in green in the graph below.

The error bars on the green and red line show the 99.7% confidence interval (3 $\sigma$) . Notice that they match the data very closely indeed.

So the bottom line is that you are certainly more likely to give birth during the week, but the moon has nothing to do with it.