Arnold Loewy, professor of criminal law at Texas Tech University, wrote an editorial about the Casey Anthony case that has statistical undertones. Prof. Loewy discusses the fact that there are two kinds of errors that can occur in a court trial: an innocent person can be sent to jail or a guilty person can be acquitted. He points out the words of William Blackstone, "It is better that ten guilty persons escape than that one innocent suffer." Therefore, Loewy argues, it is best that the burden of proof in a criminal trial is set so high.
Statisticians call these errors "false positives" and "false negatives." All people encounter these issues regularly, a fact that is discussed at length by Kaiser Fung in his excellent book, Numbers Rule Your World. Have you ever set off an alarm while going through airport security because you forgot to remove your keys or dump your bottled water? If so, you know that the airport security system is set to a high sensitivity, which results in many false positives. The alarm sounds often, but in most cases the embarrassed person is not a terrorist.
In contrast, the sports pages are filled with stories about athletes who passed drug tests for years, only to eventually admit that, yes, they were using performance enhancing drugs. A drug tests that fails to expose a guilty athlete is a false negative. The drug tests are designed to catch blatant offenders, without besmirching the reputations of honest athletes.
Every test (be it a screening test, a drug test, or a legal trial) weighs evidence and delivers a verdict based on the evidence. The people who design the tests set the sensitivity of the test in a manner that is deemed appropriate for that test. For a criminal trial, the sensitivity is the proportion of truly guilty people who are correctly identified (convicted); the specificity is the proportion of truly innocent people who are identified (acquitted).
Some people are upset at the Casey Anthony verdict and say that the courts set the burden of proof too high. What they might not realize is that there is a trade-off between the sensitivity of a test and its specificity. It is a mathematical fact that if you lower the burden of proof so that more people are convicted on less evidence, you will simultaneously increase the number of truly innocent people who are convicted.
The converse is also true—a fact that Lord Blackstone and Prof. Loewy clearly understand. For criminal trials, the "due process clause" of the Fifth Amendment requires that criminal defendants cannot be convicted unless the evidence is "beyond a reasonable doubt." A criminal trial is designed to acquit the innocent.
It would be wonderful to develop an airport security system and a criminal trial system that have 100% sensitivity (detect all guilty people) and 100% specificity (acquit all innocent people), but in practice that is impossible. Instead, we as a society set a threshold, and then we must accept the trade-offs.