Not really. Imagine a company where 99% of hires had graduated from Stanford and 1% from Harvard, but only 1% of people promoted to management were Stanford gra

Not really. Imagine a company where 99% of hires had graduated from Stanford and 1% from Harvard, but only 1% of people promoted to management were Stanford grads. You wouldn't say "well, the percentage of Stanford graduates in the country is statistically insignificant so it makes sense for there to be very few Stanford grads in management".