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.
 
 

Measuring and Counting

 MEASURING

Measuring is the assignment of a number, and all the uncertainties of that of that number, to something.  The purpose of assigning a number is to give meaning to the object measured.

  • Uncertainty: A bag placed upon a scale shows its weight to be 41 pounds.  If the bag must be less than 50 pounds, then the number produced by the scale indicates it meets this requirement.  However, you must know how far from its true value might the 41 pound number be off by?  Uncertainty is the amount of doubt (e.g. the amount of possible variation) you should expect that number might be off.
  • Fit for Purpose: Assume there are two scales.  The same bag weighing 41 pounds is place on both scales.  However, it was determined that Scale A produces numbers that can be off by as much as 30 pounds.  It was also determined that the number produced by Scale B merely off by as much as 3 pounds.  Knowing the amount of uncertainty contained in the number helps distinguish counting from measuring.  Knowing the uncertainty allows you determine if the measurement is fit for the purpose of determine if the object exceeds 50 pounds.

Measuring relies upon estimation.  The choice of data, the methodologies employed, and level of quality measures used tells you how confident you can be in the estimation.  Once you have a reliable estimation of how close a number may be (or not be) to the true value, you can make informed decision as to what purposes the number can be used - and not used.  

 

COUNTING

Counting is not the same as measuring.  However, the two are often confused.  Counting is usually a technique within a measuring process (methodology).  Counting can result in an exact number.  However, measurement will never claim to represent a true value. Measurements are merely estimations.

Counting an exact amount of something is often not possible or practical.  The thing you are intending to measure (the measurand), the matrix it is found in, or the level of accuracy required may make counting impossible.   Thus a system is needed to provide a reliable estimation which you can rely upon.  

Some things to take into account when making an estimation:

  • Distinguishing: Some molecules are so similar to others that it is often impossible continuously distinguish them from each other.  Thus, they cannot be easily counted.
  • Location: Some substances are contained in places we cannot practically enter to count them.  The best way to know how much alcohol is affecting a person's brain at a particular time would be to take a sample of brain tissue.  However, society has not yet determined such a procedure falls outside the protections of a person's 4th Amendment rights.
  • Gas Chromatographs: The results of a gas chromatograph are often used to determine whether a person's alcohol concentration is above a legal limit in DUI cases.  However, the machine does not measure a person's blood alcohol concentration.  If properly used, the machine merely counts the number ethanol molecules in a gas portion of a headspace vial.  Thus, it indirectly counts a microscopic amount ethanol from a tiny sample.  

A measurement based upon a machine's indirect count of a substance results from combining it with algorithms, numerous assumptions, and historical data regarding the past performance of the machine (and software) used in the process.  This is known as an uncertainty calculation.

In this manner, measuring requires much more than counting.  Measuring requires more than merely assigning a number to an object.  More importantly, one can assign a number to an object but not create a measurement.  When this occurs it is not a measurement.  It is a misrepresentation.

 

Counting is what you do to get a number.  Measuring is what you do if you want to know the truth about the number.

You have a bandwidth problem

An analyst from a crime lab testifies that a defendant, who is charged with DUI, has a blood alcohol concentration of .120.  Despite the legal requirements that the state must prove the test is trustworthy, most jurors have made a blink judgement the that test is correct.  As is often the case, the appearance of science is a powerful tool of persuasion.  This is true  even when the opinion is based upon junk science.
 
Here, despite the claims of the analyst and unbeknownst to the jury, the test result was done using unreliable equipment relying on defective software.  Your challenge: undo the jury's initial judgments, demonstrate the analyst is too biased and lacking the qualifications to understand the severity of the equipment's defects, and show the result can't be trusted.  This is no small task.
 
This task will take time.  It requires a thorough understanding of the many underlying scientific disciplines involved.  Adequately educating the jury will require information from several different sources.  Each piece of evidence will present a different evidentiary challenge.  In short, beyond the inherent difficulties of such cases, you also have a bandwidth problem.
 
Bandwidth is the amount of data that can be transmitted in a fixed amount of time.  DUI trials have time and evidentiary limitations.  There are not intended to be semester long science classes.  There are practical realities inhibiting you from properly educating a jury with the knowledge they need to debunk these unsound claims.  If left unaddressed, a court may not even recognize this bandwidth dilemma.
 
Consider the problem in the following terms.  A presentation that does not reach the audience persuades no one.  If Netflix creates next years best new drama, but there is not enough bandwidth to stream it, then what was the point of creating it.  No one pays a subscription fee to see a "buffering" message.  Quality is meaningless without bandwidth.
 
Being right is does not convince a jury without an adequate opportunity to present it to a jury.   In these cases, you don't have a right or wrong problem - you have a bandwidth problem.  Accordingly, neglecting the bandwidth argument can be fatal.  If you don't sufficiently address this issue, then no one may hear how right you are.

The anatomy of a gas chromatograph

 

The results produced by a gas chromatograph are usually the difference between innocence and guilt in a DUI case.  The prosecution’s purported blood alcohol concentration (BAC) is typically the “end-all be-all” of their case. Let’s take a look at how this machine creates such a critical measurement.

Big Pictures Thoughts

  • If done properly, gas chromatography is a reliable way to measure the amount of blood in an alcohol sample.  However, automobiles are also reliable, but there are still thousands of car wrecks every day.  There is no presumption of reliability simply because a gas chromatograph was used.
  • The measurement process has both human components and machine components.  All steps in the process must be done correctly for the measurement to be trusted.
  • The goal of is to produce a measurement, which is both accurate and reliable.

General Principles

  • Gas chromatography is an indirect measurement.  The machine does not test liquid portion of a blood sample.  In headspace gas chromatography, the machine converts substances to a gas, and then it must separate the different types of molecules in the sample.  After separation, a microscopic amount of the gas is measured by software.
  • The machine must demonstrate it is able to separate different types of molecules before it can measure them.  If it cannot properly separate different categories of molecules, then its measurements may be artificially higher.
  • Gas chromatography is done in manner like a production line.  Multiple samples (usually over 100 vials) are being processed in a “batch.”  It is essential to safeguard against the wrong information being assigned to the wrong sample.

Vocabulary

  • Gas chromatograph - a machine that separates molecules, and then measures, the amount of the various components in a sample.
  • Gas Chromatography - the scientific process performed by a gas chromatograph.
  • Chromatogram – the graphical representation of the data produced by the gas chromatograph.  This is where you will find the final measurement.  A chromatogram is the machine’s conclusion.

The Human Part

The measurement process starts long before the gas chromatograph is actually turned on.  The blood must be collected, identified, stored and transferred properly before the sample is put into the gas chromatograph.  Even the best machines cannot account for, or identify, that a sample has been corrupted.  The principle of garbage in garbage out must be kept in mind.  That is, incorrect (or poor quality) input will always produce wrong output.  

Human are also responsible for teaching the machine a specific alcohol concentration.  The machine does not come out of the box knowing any specific alcohol concentration.  Typically a lab will purchase approximately four (4) different alcohol concentrations from a vendor.  For example, .01, .10, .20, .40 are often used to calibrate the machine. 

These samples are put into the machine and the analyst programs the machine’s software to use these values.  If the analyst tells the machine a sample is a .40 but it is really a .30, the machine cannot tell the difference.  Ensuring a calibrator is what it purports to be is known as traceability.

The Machine Part

The machine starts its analysis after a small portion (less than the size of the a single M&M) of each blood sample is put into a headspace vial. The headspace vials (usually over 100) containing the samples are loaded into a part of the machine called the autosampler.  

The samples are then heated (in a headspace tube) forcing molecules in the liquid portion of the sample to rise.  After the molecules are vaporized, a needle punctures the top of the headspace vial and extracts a microscopic portion of the gas above the liquid.

These vaporized molecules are pushed through long thin columns by a carrier gas (hydrogen or helium).  These thin columns have a chemical coating inside them designed to interact with the molecules passing through them.  The carrier gas moves at a constant pressure.  This results in different molecules in the gas to group together (e.g. ethanol with ethanol, methanol with methanol).  Each molecule group, such as ethanol, has a unique rate of speed.  This accounts for the separation of the each substance in the columns.

After each molecule group is pushed out of the column, they will be pushed to a detector.  The time when is substance exits the column is called the time it elutes.  The detector’s software has been programmed to identify different substances by the time they elute from the column.  The Flame Ionization Detector, as the name implies, then burns each molecule group and then measures how much is burned.

The software gathers the “raw data” and then processes it.  The “process data” is graphically represented in something called a chromatogram.    The measurement is found here.

The above summary just scratches the surface of the measurement process using a gas chromatograph.  If you are going to rely upon the measurement produced by this technique, then every step in process (both the human and machine) must be shown to have been done correctly.

A reported result versus a complete result

 

In DUI cases, a machine called a gas chromatograph is often used to measure an alcohol concentration in a blood sample.   The measurement, which the machine prints at the end of the process, is called a reported result.  We are finally at the point in Arizona, where courts are starting to recognize that merely providing a reported result is not sufficient evidence.  The law is coming to the same realization that science did many years ago: a reported result from a machine is an incomplete measurement.

A complete measurement includes more than just a reported result.  As a matter of fact, simply providing a reported result is often misleading.  A reported result is only complete when accompanied by a “statement of its uncertainty.” See NIST Technical Note 1297, 1994 Edition.  No measurement is perfect.  The result of any measurement is only an estimation of its value.  A “statement of uncertainty” is the range of doubt that exists regarding a measurement.

A complete test result, must also include:

  • a “Range of Uncertainty” and;
  • “Confidence Interval.” 

To illustrate, let’s assume that a blood test result was .100.  Let’s also assume, based on a review of the machine’s prior performance, a “range of uncertainty” was determined to be ± 5%, with a “confidence interval” of 100%.  This means, the reported result could be as low as a .095 and as high as a .105.  Moreover, this also means, if the same blood sample were repeatedly tested on this equipment, the result would only be outside of the ± 5% range 1 out of a million times.  If this statistic were true, this would certainty be a reported result that you could trust.

On the other hand, what if for the same reported result of .100 the range was ± 30%, with a confidence interval of 50%?  Here, this means the reported result could be as low as .070 or as high as .130.   Furthermore, if you continued to test this sample on the same equipment, 300,000 times of out of a million, the reported result would be outside the range stated above.

When comparing the two complete test results, you can see that providing a mere reported result does not tell us the whole story.    Merely telling us the reported result can actually tell us a very misleading story.  Science will not accept incomplete measurements.  Why should the law?