# M&M’s Revisited (for the Last Time!)

If you haven’t been here before, then you don’t know that we’ve already talked about M&M’s twice (here and here) and you don’t know that we’ve talked a little bit about the colors of M&M’s in the bags.

Well, today I want to keep talking about the different colors of M&M’s in the bags.  Except today I want to talk about the percent of M&M’s that are red, orange, yellow, green, blue, brown.  Before we continue our M&M discussion, do you have a guess?   That is, what percent of the M&M’s manufactured are red, orange, yellow, green, blue, brown?

Hmmm . . . Let’s pretend that we don’t know (maybe you really don’t!).  I think a pretty educated guess would be that 16.67% of the M&M’s are red, 16.67% of them are orange, 16.67% yellow, etc., etc.  Can you live with that guess?

I’m going to use the data I collected in my last M&M post, except instead of individual bags I’m going to look at my entire sample of M&M’s.

Here’s the percentage breakdown of M&M’s:

Let’s make a nice table, based on what I would expect to get, given my educated guess of 16.67% of each color and what I actually got:

So, I wonder if the distribution of colors I got in my sample would be likely, if the colors of M&M’s really were distributed evenly at the manufacturer?

Luckily for us there’s a statistical test we can use to answer that exact question.  And, luckily for us its a pretty straightforward test to understand!  It’s called the Chi-Square Goodness of Fit Test.  The Chi-Square Goodness of Fit test compares the observed values (in our case my M&M colors) to the expected values (if our initial assumption was true).  In our case we would subtract the expected value from the observed value and square the difference.  Then, we would divide by the expected value.  We’d do this for each color of M&M and add up the results.  Don’t worry, I’ll do it (actually, I did it with the help of this website). . .

Based on the Chi-Square Goodness of Fit Test it’s fairly reasonable to assume that I could have gotten this distribution of M&M colors given the fact that M&M Mars makes 16.67% of each color of M&M’s.

So, here’s my next question?  Do they?

(So here’s the thing, about 5 years ago the M&M Mars website used to answer this exact question, but in 2008 they stopped.  This person wrote to M&M’s and posted the response)

Use the distribution for Milk Chocolate M&Ms detailed by M&M Mars and run another Chi Square Goodness of Fit Test with my data (or your own, if you collected any).  How does this compare to the 16.67% guess?