> 9/11 has a small but noticeable dip compared to the surrounding dates. I wonder if that's people avoiding it or if it's just coincidence

I also see something else: there is a light streak going down the 13th of every month, as if people were having fewer babies that day.

If I want to figure out whether this is an actual pattern or just a coincidence, how would I go about that? I mean, as I understand the general process it's a two-parter:

1. Come up with a model of the situation: say, uniform probability of giving birth any given day.

2. Calculate the probability of getting your actual results based on the model. If these are lower than some threshold you pick, say, 5% or 1%, then you discard your model because you have found something that breaks your assumptions.

But there's lots of nuance here. Is does my model even make sense? Isn't it more useful to define the number of child births on any given day to be normally distributed with mu = average over the year? Are the two equivalent because something something central limit theorem?

Is there a simple and convenient way to do the calculations for the most common models? And say I'm interested only in the streak of the 13th... do I need to consider all other days as well before I discard my model? My intuition says that the streak of the 13th is easier to prove/disprove than the dip of 9/11, because it's 12 data points (is there?) compared to just one -- but I also feel like I'm way off base here...

I'm at a bit of a loss here. I haven't studied a lot of statistics because I've been busy with other things but this is the kind of thing I'd love love love to learn.

I do remember a bit of the Think Bayes book, and I could plug each month into a comouterprogram updating the birth probabilities of each day based on that... but how do I know if I have enough data to get a day-by-day resolving power? Maybe I should look at weekly averages instead?

I mean, I understand this is a whole field of research and not something you learn overnight, but is there not some subset of "countertop hypothesis testing" that you can apply casually over the kitchen table to get you at least somewhere?

TL;DR: I think I see patterns in this data and I want to statistically reject my hypotheses. How do I approach that?

Edit: I guess the reason my question differs slightly from high school stats is because I don't get to design an experiment that will give easily analysable data. And I'm afraid of creatively interpreting the existing data to make it easier to deal with, because I think that will lead me to incorrect conclusions.