Thursday, April 16, 2009

Bigger scoops, I guess

Maybe someone can explain this to me. Several years ago, Kellogg's had a big ad campaign to show us that every box of Raisin Bran contained two scoops of raisins. [Note: I did some Googling, and apparently the slogan has been reintroduced to Canada.] While that isn't the big thrust of their marketing campaign, it's still featured on their box; we can see the words "Two Scoops!," and a smiling sun is holding a scoop of raisins in each hand.

Here's my question. The 20 ounce box features "Two Scoops!" The 25.5 ounce box features "Two Scoops!" I'm not going to make a trip to the store just for this meager blog post, but I would guess the 15 ounce box looks pretty much the same.

So, do the various sizes have different-sized scoops, or are we getting ripped off raisin-wise when we buy the large size?

Added note: There is a result from math, counter-intuitive to some, that in a container that holds two different sizes of bodies, if you agitate the container sufficiently, the smaller bodies fall to the bottom. Some people think the heavier ones drop to the bottom, but what actually occurs is that the small ones can easily move downward, so they congregate there.

I'm guessing some work went into raisin bran to get the size of the flakes right. If they're too big relative to the raisins, all the fruit would end up on the bottom. Generally, that doesn't happen.

Added added note: Before I published this, I decided to go out and see if anyone had looked into this before (nice Internet). Naturally, some people have. The two examples I found are both from students, which isn't too surprising.

The first just wanted to see what constituted a scoop, so he took a single box (475 g - cursed Canadians and their funny metric system - that's about 16-3/4 oz) and found that each scoop is about half a cup. No answer to my question here.

The second was far more methodical, taking two boxes each of the 15, 20, and 25.5 ounce sizes, and counting the number of raisins in each (of course, this work had more resources, involving a PhD and a JD). The two hypotheses tested were:

(A) Scoop size is independent of box size. In other words, the same scoops are used to add raisins to each box, regardless of box size, so that the number of raisins per box is constant.

(B) Scoop size is proportional to box size. In other words, larger scoops are used for the larger boxes so that the number of raisins per ounce of cereal remains constant.

The empirical data, which is limited in applicability by the small sample size (only two boxes of each size), failed to support either hypothesis. There was a lot of variability in the number of raisins, both within the sizes and across them. Raisins per ounce varied from 12.1 to 19.1.

My conclusion: Kellogg's may not be using a scoop at all!

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