I got a powerful reminder a few months ago of a lesson I learned in grad school: numbers don’t speak for themselves. We must interpret them alertly if we are to learn from them.
The numbers I came across are these:

[Medicare] spends roughly $3 on administration for each $100 of medical services it buys for its beneficiaries, compared to as much as $17 by private insurers.”]
That’s from an article in Reason.
By chance, I had come across a reference to these numbers two days earlier, in an article in Econ Journal Watch:

There is a similar story with Medicare and indeed publicly run health care programs like the ones in Canada or the system of socialized medicine in the UK. The administrative costs in these public systems are far lower than in the private systems in the United States (emphasis added).

Now, what are these numbers “saying”? Do they provide evidence that government-provided health insurance works better than privately-provided health insurance, or the other way around?
By themselves, they do neither. Again, we must interpret them. Numbers virtually never give us proof of one position or another, but depending on the thoughtfulness with which we interpret them, they can form part of a more or less persuasive argument.
The author of the article in Econ Journal Watch argues that Medicare’s lower administrative costs show the superiority of government-provided health insurance. He says “It is entirely reasonable to support these programs on the grounds that they are more efficient than their private sector counterparts.”

The author of the article in Reason argues the opposite, based on the same numbers. “Medicare,” he says,

has unleashed a torrent of unnecessary care, accidental death, and inattention to the personal needs of the patient… Bizarrely, Medicare’s very incompetence only confirms its advocates’ belief in its superior efficiency… [Its] supposedly superior ratio [of administrative costs to treatments purchased] is only the mathematical result of Medicare’s unwillingness to do any meaningful administration and its simultaneous willingness to pay for any treatment whatsoever, no matter how useless or destructive.

That puts the numbers in a completely different light, doesn’t it? Much of what one author accepts as $100 worth of “care,” the other author asserts is valueless, or even harmful, expenditure. What one accepts as lean administration the other considers insufficient cost control.
Which of these positions is more persuasive? Let us leave that aside for now. My point is that we always have to judge the soundness of arguments within which numbers are used, deciding which understanding of those numbers is the more persuasive. The numbers don’t speak for themselves.
Howard Baetjer Jr. is a Lecturer in the Department of Economics at Towson University, where he teaches courses in microeconomics, comparative economic systems, and money and banking. He is also a frequent faculty member at IHS Summer Seminars and has starred in Learn Liberty videos on the dangers of government safety regulations and the FDA.