Scientific thinking at breakfast

I recently read the following on a pack of Kellogg's Fruit 'n Fibre:

FACT: Families who eat cereal for breakfast each day are less likely to be overweight than those who don't.

I get the impression from their website that Kellogg's is more responsible than many companies in making appropriately backed-up claims, so the following is not meant as an attack on them.

However, the scientist in me couldn't help digging into what exactly they're claiming here.

The study that backs up their claim (I assume there was one) was probably designed around a chi-square analysis - they counted the families that fall into four groups - A, B, C, and D - as in the table below:

The "FACT" quoted above amounts to the following:And a bit of simple algebra gives us the following (mathematically-equivalent) espression:This second expression could be read as follows:

FACT: Families that are overweight are less likely to eat cereal for breakfast each day than those who aren't.

So we have the same data, the same facts, but two subtly different statements. One suggests that eating breakfast helps prevent people from being overweight (perhaps even reverses it). The other suggests that being overweight leads people to avoid eating cereal for breakfast.

I could discuss the linguistic distinction between entailment and implicature; I could go on about the role of statistics and the need for precise language.

But remember, this was just a cereal box.

Mainly, this was simply a diverting exercise in taking something you might see every day, and using reason and some straightforward math to dig down into what's really being said.

Humanism, and the empirical skepticism I practiced above, are not just things I bring out when confronted by outrageous pseudoscience or millennial zealots. They are part of how I see the world, day to day. They colour how I react to everything, from ads on cereal boxes to stubbing my toe to deciding what to get Deena for Valentine's Day.