Halloween moves births. The full moon does not.

“Full moon tonight — the ward will be busy.” Even the articles written to debunk it describe the belief as widespread among the people who work on labour wards. The large studies say no — half a million North Carolina births over sixty-two lunar cycles in 2005, around seventy million births in another analysis. And one careful paper says yes, a little: 38.7 million French births over fifty years, with “very small but highly significant” extra births on the full-moon date and the day after (Chambat, Fougères and Elyildirim, 2021). Its authors suspect a self-fulfilling prophecy: if a ward expects the full moon to be busy, a few inductions might land on it.

A null result from somebody else is not something I can check, and “very small” is not a number. So I wrote a rule for fifteen years of US daily births, the Social Security Administration series that FiveThirtyEight published, and committed it before downloading a single count.

The rule, and the gate in front of it

A Sunday in those years has 43 % fewer US births than a Tuesday (7,518 against 13,122 a day on average), and September about ten per cent more than January. So the rule takes all of that out first: log births against year-by-month and year-by-weekday effects, fitted without the holidays. Then it compares what is left on the full-moon date and the day after — the French window — with every other day. The uncertainty comes from two thousand fake moons: a two-day window dropped at a random point in each lunar month, which carries whatever odd structure the data has into the error bar.

• survived if the 95 % interval sits above zero;
• killed if it rules out an excess of +0.5 % — about fifty-five extra babies a day across the whole country, nothing any single ward could notice;
• inconclusive otherwise.

A null is only worth the smallest effect it could have seen, so before the data I ran the rule on synthetic years with known excesses. With no effect it kills the claim more than eight times in ten. With a real +0.5 % it confirms it three times in four or better. And a +0.2 % truth is killed a third of the time — which is not an error, because killed means “below +0.5 %”, but it meant I had to write down in advance that killed would be reported as less than, never as nothing.

Then the part I care about most. An instrument that finds nothing might be an instrument that cannot find anything. So it had to pass a gate first: see a calendar effect already known to exist, in the same data, with the same fit. In 2011 Levy, Chung and Slade reported that US births rise on Valentine’s Day and fall on Halloween — the days people would like a birthday on, and the day they would not. If my fit could not see Valentine’s Day above zero and Halloween below it, the moon’s verdict would be void.

What came out

The gate was not close. Halloween: −12.2 %. Valentine’s Day: +3.4 %.

The full moon: −0.03 %, with an interval from −0.34 % to +0.27 %. Killed. The six earlier years from the other federal source, 1994–1999, say the same: −0.01 %.

So in the United States from 2000 to 2014, whatever the full moon does to the day a baby is born, it is less than about a quarter of a per cent — and the one day a year that children dress as ghosts takes away twelve.

Checking the gate did not flatter itself

The Halloween number is large enough to deserve suspicion, so I checked it after the data without the model at all: each 31 October against the same weekday a week before and a week after. It is lower in all fifteen years, by 11.8 % on average.

Then the years where it is smallest gave the mechanism away. 2004, 2009 and 2010 are the three years it falls on a weekend, and they average −4.5 % against −13.6 % on a weekday. Valentine’s Day does the same in miniature, +2.3 % against +5.1 %. Three weekend years is a thin sample, but the direction is what you would expect if most of the effect is scheduled births — inductions and caesareans — and there are far fewer of those to move off a Sunday.

And the rule itself, on this data: inject a real +0.5 % into the full-moon window of the actual series and it says survived; inject +0.3 % and it says inconclusive. It sees what the table built before the data said it would.

What that leaves

The French paper’s abstract gives no size, so after the verdict I read the paper. On 18,263 days of French births, 1968–2017, about 2,121 a day, the full-moon class and the day after “have average surpluses of more than eight and seven births”. That is roughly a third of a per cent — my arithmetic, not theirs — and it sits just above the top of my interval, +0.27 %. So the two do disagree, modestly: my estimate sits about two and a half standard errors below an excess that size, and if the United States had one from 2000 to 2014 the rule would more likely than not have confirmed it. It may still be real in France. Their methods and their lunar days differ from mine, and they offer a mechanism that need not travel: births track how many staff are on shift, so a few wards putting more staff on for the full moon would be enough to produce it.

That is the gate’s lesson again from the other side. A calendar belief can move births, and Halloween shows how hard. Whether the moon does depends on whether anyone schedules around it, and in fifteen years of four million American births a year, not enough people did to show.

And the belief on the ward? The count here is national and daily, and a ward works in nights. A busy full moon on one ward is a memory with a reason to be kept; the quiet full moon on the next ward is not. Nothing in a daily national total can see a single night shift. What it can say is that across every ward in the country, the nights add up to nothing.

The one thing to keep

Before you trust an instrument that found nothing, point it at something that is definitely there. Here that cost one extra function and two dates, and it turned “no effect” from a shrug into a comparison: the calendar moves births more than forty times as far as the moon possibly could.

The register files the study as killed, with the branches beside it. The rule as committed, the gate, the checks after the data and every number above are in the pack. Daily births: Social Security Administration and the CDC’s National Center for Health Statistics, via FiveThirtyEight.