Wednesday, September 26, 2012

The Reese's Rainbow: Validating a Child's Delusional Compulsions

I think it's only fair to say that everyone has a few weird compulsions that are fairly benign.  One of mine is the way I eat certain types of candy.  Today we're going to talk about Reese's Pieces.

Ever since I was a child - certainly as long as I can remember - I've eaten Reese's Pieces in the same way.  Pour out a handful, then from that handful eat them in sets of three comprised of one of each color.  One orange, one yellow, and one brown.  When one color runs out, do the same for pairs of the remaining two colors.  When reduced to one color eat those in pairs or just all at once, depending on how many are left.

Odd, to be certain.  Disruptive or detrimental?  Hardly.

The result, however, is that as long as I can remember I have been accidentally carrying out sampling studies on Reese's Candy.  Over time I realized that I'd been subconsciously internalizing some of the patterns.  In particular, I had become pretty confident that orange was always going to be the color left over at the end.  Brown and yellow seemed comparable, though my inclination was that yellow was the rarer piece, so to speak.

Well, it's a testable hypothesis.  So, let's test it.

I picked up a few bags of Reese's Pieces on sale a few days ago, and sat down to count through them.  These were the big bags, and for the record I guess the big bags have somewhere around 600 individual pieces in them.

The first bag had 565 pieces, 303 of them orange.  The second bag had a few more, with 629, and only 281 of them orange.  Both bags seemed to fit with my initial suspicion, though I was wary of making any claims given not only the variability of color but also the variability of bag size.

With that in mind I picked up a few more of the smaller boxes of Reese's Pieces and set to counting them.  They're quite a bit smaller, with only around a quarter of the pieces as the larger bags.  Each box again had orange showing up as the clear favorite.  The graph below highlights the relative proportions in each set (1 and 2 are the larger bags, 3-5 are boxes):

The trend seems to be there - orange is the most common color in each of the different samples.  A test of the proportions confirms that this is in fact significant, even with the small sample.  The mean proportion of orange pieces in packages of Reese's Pieces is significantly higher than the proportion of either yellow or brown.  

That wraps up the first part, and it does seem that what I suspected from childhood is true - orange seems to be over-represented in bags of Reese's Pieces.  This statistically significant effect is large enough and consistent enough that I'm confident in saying that with only 5 samples.  I'm betting that the orange machine at the Reese's plant is dialed in somewhere at or just below 50% - the mean would suggest 48.96%, close enough to 50% that a larger investigation might reveal that they picked an easy half as something to shoot for. 

What is more difficult is parsing out the difference between yellow and brown.  While the suspicion from my years of sampling (that yellow is rarer than brown) seems to be somewhat reflected in the trend so far, there simply aren't enough data points yet to be very confident in what appears to be at best a small effect.  There are even situations (like the first box) where yellow showed up at a higher percentage. 

This is where you come in, reader.  I already have a whole lot of Reese's Pieces queued up to be eaten slowly, hopefully over the next few months or more.  I don't need to keep adding to that pile.  What I'm asking is for all of you to go out and pick up a bag, or a box, or a larger bag, and do some counts.  Teach a statistics class?  Have them do it. 

Post the numbers in a comment and we can revisit this at some point and run the numbers on a larger sample.  I'll even sweeten the deal (har har) if you post numbers and mail you a (unopened) bag of Reese's Pieces for your trouble if I 1) know who you are, and 2) know where you live.  Consider it a buy one get one free.  Obviously, don't just post your address on here, but we can figure it out.  Terms and conditions apply, promotion may be canceled at any time without warning.        

If there's a message in here anywhere, perhaps its that science should be all around us.  Observe your world, form hypotheses, then test them.  Teach the lesson to kids - if it involves activities like counting then eating a bunch of candy they'll probably listen. 


  1. I'm surprised they don't publish their population proportions. I did a demonstration in class where I gave out fun size M & M packages fully expecting that across all the samples (bags) the proportions would be approximately equal across colors. However, our values weren't even close to being equal (across about 140 bags with an average of 18 pieces in them). I dug around on the internet and found out that M & Ms population proportions vary quite considerably. For instance, blue is the most prevalent at about (24%). I think yellow was the least prevalent with somewhere around 14 percent, but I don't remember the exact numbers.

  2. Interesting - maybe I'll do something on M&M bags once I get through all these Reese's.

    The image at the top of this post is one of the bags just poured out on my scanner, so while I haven't counted what's in the image it was drawn at random from a bag which had the above proportions. What strikes me is just how...correct the proportion appears - if given a quick glance I'd probably be willing to bet that it was an even split.

    I am confident that someone at Hershey sat down and did the marketing focus groups (at some point in history) to figure out how to put together these bags of Reese's Pieces so that they look as balanced as they do. It's possible that someone did the same for M&M's?

  3. I bet certain colors are cheaper to produce.

  4. Wikipedia says the population proportions are 50% orange, 25% yellow, and 25% brown. Surprised there aren't fewer browns. Who likes brown? You could do a chi-square test to compare your achieved proportions to these population proportions, as Ed did with the M & Ms.

  5. my bag was 40% orange, 33% Yellow and 26% brown.

  6. "The colors of the candy coating were designed to coordinate with the color of the Reese's package. The goal color distribution is 50% orange, 25% brown, and 25% yellow." -Wikipedia

  7. I tend to find that brown has occurred the least in my portions I always place my candy in order from greatest to least (weird habit) and brown is always the least.

  8. Has anyone found themselves preferring the taste of one color? My preferred method of eating them is individually, allowing the piece, never pieces, to almost dissolve on my tongue. I gotta say that I firmly believe the yellow has a smoother flavor than the other two. When I try to prove this in a blind taste test however I never guess correctly on which was yellow. I guess the visual plays a role with my palate.

    1. That's a good question. I'll admit that I do this with M&Ms, and oddly agree with you that yellow is always the one that I save for last because it has a smoother flavor (I'm honestly not kidding). I've never found a difference in reeses, but maybe it's because I've just had fewer of them throughout my life?

  9. My best friend in high school and I had a scam we would pull on people that had them convinced we could taste the difference between the colors of M&Ms and/or Reese's Pieces. One of us would be blindfolded and taste a candy and then correctly identify the color. The trick was that the accomplice how handed them the candy would have code words in their question. "Okay, how about this one?" = Orange, "What's this one?" = Yellow, "What color is this?" =Brown. We had several of our friend fervently tasting them to see if they were missing some subtle differences that we were able to taste. :-)