The whole is not always the same as its parts

You are going to buy a new home.  The house is 2000 square feet on a 3/4 acre lot.  You hire Rich (the termite inspector) to check it out before you buy. After all, no one wants to buy a house with termites. 

  • Good news!  The house passed.  No termites.  Thus, you buy the house.
  • Bad news!  A month after the sale closes you discover - termites.  

What?  How could this happen?

 
You go back and look a little deeper in the method of inspection Rich relied upon.  You find out his methodology was to only check "one square inch" of the floor in the house.  When he did not find anything wrong within the "one inch" he assumed everything else was also termite free.
 

How do you feel now?
 
A part of something does not always represent the whole. Determining how many termites are in "one square inch" of a house does not really answer the question whether you have a termite problem.
 
The termite inspector committed what logicians call the all things are equal fallacy.  This occurs when when it is assumed, without justification, that conditions have remained the same at different times and places.
 
The same danger is present when attempting a forensic measurement.  For example, in a typical DUI case where a blood sample is taken, the lab will test less than a M&M size sample of blood.  However, in Arizona the legal definition of an alcohol concentration is grams per 100 micro-liters. Translation, the legal definition of an alcohol concentration requires multiplying the results of the "one inch" by about 1000 (assuming the M&M is about 100 micro-liters).
 
The danger is assuming the rest of 1000 micro-liters (or 100 milliliters) has a proportional amount of ethanol in it.  Small errors multiplied by 1000 can easily mislead you to believe that a person's alcohol concentration is above a legal limit when it is not.
 
Like the termite inspection, it is up to the crime laboratory to prove their justification for assuming using such a tiny amount below the legal definition of an alcohol concentration answers the question - is the person above the legal limit?  After all, no one wants termites...or people being wrongfully convicted.
 
 
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