# Miller Light versus Bud Light (in the wild)

After losing both ends of a slow pitch softball double header this past Sunday, I showed up at my friend’s (Mike) house to watch football. Dejected, I brought over the remnants of a 12 pack of Miller Light from the previous weekend. The following exchange then took place:

Mike: “Ugh. Miller Light”

Me: “It all the same. Miller Light, Bud Light, Coors Light….”

Mike: “No way. It’s easy to tell the difference.”

Me: “Oh yeah. Prove it.”

This led to a trip to the the store for red plastic cups and pizza. I brought Miller Light, and he had Bud Light in his fridge. So it was the Bud Light versus Miller Light challenge.

So we set it up. A modern day frat house version of Fisher’s lady tasting tea experiment. 8 cups. 4 Bud Light. 4 Miller Light.

Now, Mike claimed that not only could he tell that there was a difference, he could tell which beer was which without any point of reference (besides his entire life experience). This meant he claimed to be able to drink the first cup and name which beer it was without contrasting it against any other cup. Quite the claim.

Out of 8 cups, Mike figured if he got 6 correct that should prove that he can tell the difference. However, correctly identifying 6 of 8 yields a one sided p-value of 0.243. Good, but hardly statistical proof. Usually a p-value of <.05 is required. So, Mike had to go 8 for 8 to prove it to me. (A p-value of 0.0143).

Well, after some dramatics and going back and changing a guess, our hero Michael did go 8 for 8. A true connoisseur of light beer. Congratulations. (Or condolences, depending on your view).

As for me, I can't tell the difference and went 2 for 8 cause it's all the same.

Cheers.

Posted on September 15, 2009, in Uncategorized. Bookmark the permalink. 2 Comments.

Nice post. Quick question… I get how 8 from 8 is p=0.0143 (i.e. 1/70) but how did you get p=0.129 for 6 out of 8 correct guesses?

I’m not sure where I got that number, but if you look at the nature of what we were testing, I suppose that offers some clues.

It should be p=.243=17/70 (16/70+1/70). I fixed it in the post. Thanks for the comment.

Actual

BL ML

BL 3 1 4

ML 1 3 4

4 4 8

Pr(getting 8 correct)=(4 choose 4)*(4 choose 0)/(8 choose 4)=1/70

Pr(getting 6 correct)=(4 choose 3)*(4 choose 1)/(8 choose 4)=16/70

So the p-value of observing something more extreme than 6 out of 8 in a one sided test is 17/70=.243.

http://en.wikipedia.org/wiki/Fisher's_exact_test