Uncertainty Analysis in Forensic Science

Many decisions within forensic science are made in the face of uncertainties. As the world becomes increasingly complex, and along with it the complexity of crimes and their investigations, there is an escalating need by forensic scientists to provide more and better statistical information in order to more effectively fight criminals. One of the major tasks confronting the forensic science community is to carefully plan so that the quantity and quality of information obtained will meet the requirements to solve crime and convict criminals. However, any mathematical value that is calculated to estimate an actual value involves an uncertainty. Although uncertainty exists with regard to the quantity and quality of information, it can be minimized by using critical thinking, objectivity, and systematic measurement and examination of the facts.

Uncertainty with regards to mathematical statistics is the estimated amount or percentage by which an observed or calculated value may differ from the actual value. In other words, the uncertainty of a calculated result is a measure of the accurateness (or goodness) to the actual value. Without such a comparative measure, it would be impossible to judge the fitness (or goodness) of the value as a basis for making informed decisions relating to forensic science. For example, in the investigation of a drug bust, a forensic chemist might find from his chemical analysis of a white powder that 35.0 ± 1.0% of the contents of the tested powder is the narcotic drug cocaine. The plus-or-minus (±) one percent value (which is sometimes called a margin of error) is the uncertainty associated with the chemist's result; that is, the actual value could vary from 34.0–36.0% of cocaine, or one percent on either side of the value 35.

In this particular case, the chemist is wise to account for the fact that the equipment and instruments used to measure the concentration of cocaine in the tested powder are not perfectly accurate, so uncertainty arises in the measured value. Thus, uncertainty analysis in the field of forensic science, or in any other field for that matter, involves the procedures, methods, and tools of systematically accounting for every factor contributing to such uncertainties. It covers a wide range of topics that include probability and statistical variables, mathematical relationships and equations, and design and sensitivity of experiments.

The forensic purpose of uncertainty analysis is to evaluate the result of a particular measurement, in a particular laboratory, at a particular time; and as a consequence of knowing that such measurements are not totally accurate, to assign assumptions and approximations to those results. The most widely accepted and commonly used statistical approach to modeling uncertainty is probability theory, which is the branch of mathematics that deals with measuring or determining quantitatively the likelihood that an experiment or event will have a particular outcome.

A common probability measure used to calculate uncertainty is called the confidence interval, which is based on multiple runs of the same analysis. Thus, a confidence interval is a range around a measurement that shows how precise the measurement has been made. For instance, the forensic chemist who found out that 35.0 ± 1.0% of the tested substance is cocaine might also report that after repeated laboratory analysis of the substance there is a 95% certainty that the concentration of cocaine within the tested substance lies between 34.0 and 36.0 percent. The level of significance—in this case 95%—is a statistical term for defining how confident a measurement is contained within the confidence interval. In this case, the chemist is 95% confident that the actual concentration of cocaine (within the tested sample) lies between 34.0 and 36.0%. There are other confidence intervals based on different levels of significance, such as 90% or 99%. With a 95% confidence interval, the chemist has a 5% chance of being wrong (and a 95% change of being correct); with a 90% confidence interval, a 10% chance of being wrong; and with a 99% confidence interval, a 1% chance of being wrong.

Evaluation of uncertainty is becoming more important within forensic science. Forensic test laboratories are increasingly required to include uncertainty analyses in measurement results through quality management standards such as the ISO 9000 series (where ISO is the common short name for the International Organization for Standardization, the world's largest developer of standards). Several organizations, such as the National Conference of Standards Laboratories and the International Standards Organization are currently investigating ways to standardize and simplify the approach to uncertainty analysis within forensic science.