Is there any empirical evidence of the claim that ivy league and similar grads are objectively better analytical writers than the mean college grad, and if so,

Is there any empirical evidence of the claim that ivy league and similar grads are objectively better analytical writers than the mean college grad, and if so, how much better? How is that quantified? The only conclusion you can always make about someone who graduated from a prestigious college is that many people will find this impressive. That's not to say this has no value, clearly it does.