How could this happen? You go back and look into the method John used for the inspection. You discover his methodology was to only check “one square inch” of the entire house. After John didn’t find anything within that square inch, he assumed the rest of the house was also termite-free.

Representativeness
The problem in John’s termite inspection process has a name. It’s called representativeness. A sample is a portion (or subset) of something larger. A sample is representative when it accurately reflects the characteristics of a larger group. Think of it this way: is the sample capable of answering your questions about the larger group it was taken from?

The Fallacy of Composition: a logical fallacy where you assume that something is true of the whole, from the mere fact that it is true of only a part, of the whole.

If your slice of cake can’t reveal how much sugar is in the rest of the cake, then it’s not a representative sample.

Determining how many termites are in “one square inch” of a house does not reveal whether you have a termite problem in the rest of the house. John committed what they call in a logic class the fallacy of composition. The basic (and expensive) lesson of the termite inspector’s flawed process is: a part of something, does not always represent the whole.

Forensic Representativeness?
A rational thought: “Surely when it comes to forensic science, which creates evidence used to determine guilt or innocence, crime labs don’t have issues with using representative samples?” While rational, this belief is incorrect.

Whether a sample, used to make a measurement, is representative of what it claims is perhaps the most overlooked issue in forensic science. Take the results of blood alcohol tests in a DUI or vehicular crimes case. When a police crime lab says they tested a blood sample, and the result is .180 (e.g. Extreme DUI in Arizona), what does that really mean?

Representative of What?
To start you have to define a few terms. Law and science sometimes give unique meaning to things. In Arizona, it is illegal to have an “alcohol concentration” of .08 or greater. The term “alcohol concentration” is actually defined by law.

When police rely on a blood sample (opposed to breath), the law defines an alcohol concentration as the number of grams per 100 milli-litters.

Grams are a unit of Mass

Liters are a unit of Volume

Before your brains shuts off, because I just injected math like stuff into this – hold on. I will keep it simple.

Just know that any smaller portion of a blood sample tested by the lab must be representative of this legal requirement (grams per 100 milli-litters). What does this look like?

The lab does not test 100 milli-litters of blood. Not even close. Most labs test 100 (or 250) micro-liters of blood. This is a small fraction of the statutory definition. Like around 1000 times less.

Visually, picture one M&M candy. The lab will test a blood sample around half that size. Compare that to what 100 milli-litters looks like in the picture below.

Now, there is nothing inherently wrong with testing a smaller portion of a sample and then exponentially estimating the result. AS LONG AS THE LAB PROVES THE TINY FACTION OF THE SAMPLE TESTED – WAS REPRESENTATIVE OF THE REST OF THE SAMPLE.

If evidence for representativeness is not presented, the data cannot be characterized as effective for project decision-making (Crumbling, 2001).

In most impaired driving cases, this issue never even addressed, but it must. An alcohol concentration can an easily become artificially increased when a portion of the is not handled in a specific manner to ensure its integrity. Simply failing to allow a sample to come to room temperature, before testing it, can make a result falsely appear over the legal limit

John the termite inspector owed it to you, to ensure the sample he tested was representative before he told the house termite-free. Crime labs have no less of a duty. After all, no one wants termites…or inflated blood alcohol contraction.