It is important to recognize that not all approaches are universally accepted and discussion/debate still exists regarding the application of some statistics to forensic DNA typing results (e.g., Bayesian approaches, see Chapter 21).

Models are used in statistics to help interpret data. Yet there are usually assumptions involved so these models are simplified versions of true genetic processes and are attempts to model the real world. The examples provided in this text will be those approaches that are most widely used today largely due to the acceptance of the National Research Council's report on The Evaluation of Forensic DNA Evidence, which was published in 1996 and is commonly referred to as the NRCII. Both the NRCII report (1996) and the DNA Advisory Board (DAB) recommendations on statistics (DAB 2000, see Appendix V) recognize that rarely is there only one statistical approach to interpret and explain evidence. In fact the DAB recommendations state, 'The choice of approach is affected by the philosophy and experience of the user, the legal system, the practicality of the approach, the question(s) posed, available data, and/or assumptions' (DAB 2000). The DAB further states that simplistic and less rigorous approaches can be employed, as long as false inferences are not conveyed (DAB 2000).

With the caveat in mind that multiple approaches may exist in the literature, we will attempt to build a foundation for the reader in the next few sections on probability, basic statistics, and population genetics.

In the case of a rape or murder, there may be no witnesses available to assist in verification of who was the actual perpetrator of the crime. Therefore, DNA evidence developed as part of a criminal investigation of necessity has to be made in the face of uncertainty. While a crime scene sample may match the DNA profile of a suspect, the result is typically cast in the language of probabilities rather than certainty. Probability statements are designed to attach numerical values to issues of uncertainty.

Probability is the number of times an event happens divided by the number of opportunities for it to happen (i.e., the number of trials). The concepts of probabilities can be difficult to grasp because we are often in the mindset of thinking simply that something either happened or it did not. Probability is usually viewed on a continuum between zero and one. At the lower extreme of zero, it is not possible for the event to occur (or to have occurred). In other words, there is a certainty of non-occurrence. At the upper end, where the probability is equal to one, the event being measured or calculated did in fact occur. Quite often in scientific determinations, the probability of an event occurring is understood to never be completely zero or completely one. Thus, decisions in science, as in life, often need to be made in the face of uncertainty.

If a weather bureau predicts a 60% chance of rain, then this probability was arrived at because experience has shown that under similar meteorological conditions it has rained six out of ten times. If one of two events is equally possible, such as heads or tails when flipping a coin, then the probability is considered 50% or 0.5 for either one of the events. Probabilities are mathematically described with symbols, such as P. The probability that an event can occur is given by the notation or formula: P(H | E) or Pr(H | E) = ... This notation is shorthand for stating 'the probability of event H occurring given evidence E is equal to ...'. Every probability is conditional on knowing something or on something else occurring.

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