Sam Specious, Private Eye: Case #2 Analysis…..
Once again, much thanks to Mike D for participating in my attempt at bringing critical thinking to the masses. Mike came close to what I had in mind regarding the detective’s mistake but didn’t quite hit the mark perfectly. Naturally there may be more than one way to approach this case, but, after all, this is my post so I get to call the shots. Regardless, Mike has won a beer on me at the next meeting of the GHSS.
My take on this case is that the detective and Dr. Van Helsing committed a common mistake made when facing a complex medical complaint, that of ordering a large battery of tests just to see what comes up abnormal. This ”shotgun” or “rule-out” approach, especially when used without first establishing what the possible diagnoses might be and what the prior probability of each of those is, often leads to wasting time chasing red herrings. To understand why this is so, one must first know how normal lab values are typically derived.
The normal ranges of most laboratory tests are derived from taking the results of a large number of healthy volunteers. After determining the mean, usually a result is declared abnormal only if it falls outside of two standard deviations of that value. So, by definition, what is considered a normal test will only include 95% of healthy people, leaving 5% of folks to face the potential stigma of a false positive test such as increased anxiety, the unnecessary expense of further testing, and a potentially delayed accurate diagnosis.
Complicating the situation is the fact that with each additional test ordered, the likelihood that at least one of them will be falsely abnormal increases. For instance, when twenty different test results are obtained there is only a 36% chance that they will all be normal. So it is easy to see how, in the case of Vincent the vampire, his abnormal iron and magnesium resulsts might be spurious. This case is far from solved.
There are two logical fallacies that I believe may also apply to this case. One is that correlation, assuming these lab values did represent true deficiency, does not always equal causation. These deficiencies may be unrelated to Vincent’s condition or they may also be merely a symptom of whatever the true cause is. Thus simply replacing them with supplements might not do the trick. Additionally, this could be seen as a version of the Texas sharpshooter’s fallacy. In this instance, Sam and Van Helsing simply fired a number of shots into the side of a barn and then drew bullseyes around iron and magnesium after the fact.
Keep an eye out for the next installment: Sam Specious, Private Eye: The Case of Red-Faced Flyboy.