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> people defended by public defenders are significantly more likely to go to jail than people with a private lawyer

It has long been acknowledged that poverty is correlated with both criminal activity and conviction. Just mentioning this does not make it a causal relationship.

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And how has it been acknowledged? Through the courts? If so then see above...

Sure, so we'd expect the class of people who would hire a lawyer to be disproportionately represented in jail. This statistic though is about people who are being defended at trial (or in the judicial system) and the rate at which they go to prison. In other words, even if there were a million people defended by public defender and only a thousand by private lawyers, comparing the likelihood for each class to go to prison is still informative.

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