On Aug 18 2018 Kofi Anan died. A famous politician.
On Aug 25, 2018 John McCain died. A famous politician.
On Aug 26, 2018 Neil Simon died, a famous playwright.
For 12 famous people who died between Aug 5 and Aug 26 see here (be careful- there are a few more on the list who died in August but a different year).
One could group those 12 into four sets of three and claim the rule of threes that celebrities die in threes. There was an episode of 30 Rock where two celebrities had died and Tracy Jordan (a celeb) tried to kill a third one so he would not be a victim of the rule of threes. (see the short video clip: here.)
How would one actually test the rule of threes? We would need to define the rule carefully. I have below a well defined rule, with parameters you can set, and from that you could do data collection (this could be a project for a student though you would surely prove there is no such rule).
- Decide on a definite time frame: T days. The deaths only count if they are within T days.
- Define celebrity. This may be the hardest part. I'll start with they must have a Wikipedia page of length W and they must have over H hits on Google. This may be hard to discern for people with common names or alternative spellings. You might also look into Friends on Facebook and Followers on Twitter. A big problem with all of this is that if you want to do a study of old data, before there was Google, Wikipedia, Facebook, and Twitter, you will need other criteria (ask your grandparents what it was like in those days).
- Decide whether or not to have a cutoff on age. You may decide that when Katherine Hepburn, Bob Hope, and Strom Thurmond died less than a month apart, at the ages of 96, 100, 100 this doesn't qualify. Hence you may say that the celebrities who die must be younger than Y years.
I doubt anybody will ever do the experiment--- those that believe its true (are there really such people?) have no interest in defining it carefully or testing it. And people who don't believe would not bother, partially because so few people believe it that its not worth debunking. But I wonder if a well thought out experiment might reveal something interesting. Also contrast the data to all deaths and see if there is a difference. For example, you might find that more celebs die in August then would be expected based on when all people die. Or that celebs live longer. Or shorter. Actually with enough p-hacking I am sure you could find something. But would you find something meaningful?
Astrology is in the same category- people who believe (there ARE such people!) could do well defined experiments but have no interest in doing so. I doubt they would find anything of interest if they did. Here there are enough people who believe it in to be worth debunking, but would a well designed science experiment convince them that astrology does not have predictive powers? Has such been done?
I once DID do such an experiment to disprove a wild theory. In 2003 a cab driver once told me (1) there is no Gold in Fort Know, and Ian Fleming was trying to tell us this in the book Goldfinger, (2) Reagan was shot since he was going to tell, (3) a small cohort of billionaires runs the world. I challenged him-- if that is the case then how come in 1992 Bill Clinton beat George Bush, who was surely the billionaires pick. He responded that Bill Clinton was a Rhodes Scholar and hence he is in-the-club. I challenged him- OKAY, predict who will get the Democratic Nomination in 2004. This was a well defined experiment (though only one data point) He would give me a prediction and I could test it. He smiled and said Wesley Clark was a Rhode Scholar. Oh well.