[gleb]

It's not about being disjoint, you need to known total numbers to make a useful conclusion. It's not really that the title is wrong, it's just misleading. In the same way as the following is misleading:

Gentiles far more likely than Jews to win Nobel prize

If the numbers from that PDF are right your conclusion is actually 3x stronger - i.e. a Masters of Engineering is an order of magnitude more likely to lead to a CEO position than an MBA.

If wonder if that's really true, I find that level of difference odd. Wouldn't be surprised if numbers go the other way if look at only top schools. I.e. MBA is useful, but only MBA from a top-20 school, which is a generally accepted wisdom. I bet at the end it just correlates to IQ and maybe gender.

[Synthetase]

I don't have the number in the database off the top of my head but I can say with certainty that the number of business graduates exceeds engineering graduates.

I'd be uncomfortable mixing our numbers with national numbers since our data is skewed toward smaller start-ups. Our data and analysis wasn't perfect but it does reflect the fundamental truth that engineers are more likely to lead companies.

I do think we could have clearer in that regard and that is my oversight.

[jforman]

The conclusion ended up the same, but in the future you should consider normalizing against the size of the population you're drawing from.

In this case, rather than "business undergrad CEOs vs. eng undergrad CEOs" you should have "business undergrad CEOs per 1000 business undergrads vs. eng undergrad CEOs per 1000 eng undergrads".

Or the more wonky form of P(CEO | biz undergrad) vs. P(CEO | eng undergrad) ("probability of being a CEO given a business/eng undergrad degree...").