Today is my birthday. It’s also the birthday of a close friend. What an incredible coincidence! Or wait, may be is just expected. One more time R comes into our help, because it has a built-in function to answer our question.

Which is the probability of two coincident anniversaries among a group of 17 people? (yes we have a mailing list, so I can count my friends semi-objectively without the fear of not counting them all). Just type:

`pbirthday(n= 17, classes = 365, coincident = 2)`

The answer is approximately 0.3, that is 3 of every 10 friend groups (of that size) have at least two anniversaries that coincide. Not that impressive, isn’t it?. But the beauty of stats is that **stats are here to correct your intuition.** To have an impressive coincidence (and statistical significant) you will need a group of 47 people, none of them with coinciding birthdays. And then, probably nobody will be amazed.

`qbirthday(prob = 0.95, classes = 365, coincident = 2)`

Anyway, happy birthday to all readers celebrating today (if any)!

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Actually, I think the effect of the birthday problem on intuition is that a surprisingly *small* group of people has a surprisingly *large* chance of having a shared birthday. So for your group of 17 people, an intuitive guess at the probability might be 1/20 (17/365), and the real answer is six times bigger than that. I am surprised by how large it is.

I don’t think statistical significance has any relevance here – what is your null hypothesis? What parameter are you estimating?

My “I learned this today” is that the birthday distribution is in R. I never knew that before. Thank you for sharing this.

Yes, I was also surprised that R has this function implemented in the basic stats package.

Sorry for the “statistically significant” part. I am not fond of p-values, but I am a frequentist by training, so I can’t help. I was just referring to the fact that the probability of not having any coincidence on a 47 people group is 0.05.

Fair enough. I just tend to think of the birthday problem as a piece of probability,

Nice post and nice function. I wrote about this last year using ggplot2: http://jason.bryer.org/posts/2012-01-31/given-a-room-with-n-people-in-it-what-is-the-probability-any-two-will-have-the-same-birthday.html

I like your figure! very clear.