O.K., you know what to do: Google “spurious correlation health.” You are immediately led to the tale of certain Pacific Islanders who long believed that having lice made you healthy, because they observed that people with lice were, typically, healthier than those without. They were, of course, mixing up cause and effect: lice tend to infest the healthy, so they were a consequence, not a cause, of good health.
The application to Medicaid should be obvious. Sick people are likely to have low incomes; more generally, low-income Americans who qualify for Medicaid just tend in general to have poor health. So pointing to a correlation between Medicaid and poor health as evidence that Medicaid actually hurts its recipients is as foolish as claiming that lice make you healthy. It is, as I said, a lousy argument.
–Paul Krugman, NY Times