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### Statistical Approaches

There are generally three statistical approaches used in forensic DNA interpretation:^{05}

- Full Bayesian
- Frequentist logical (or likelihood ratio)
- Logical (or likelihood ratio)

The scientific community's knowledge of population genetics provides the framework for each of these methods. Each approach requires the use of allele frequencies, which are calculated from various databases. This module will focus on the frequentist and logical approaches, the most widely used statistical approaches in the United States.

### Frequentist Approach

The frequentist approach uses probabilities or genotype frequencies to address statistical questions. Coincidence probability, or random match probability (RMP), and the probability of exclusion are each frequentist approaches that are applied by the forensic science community.

Probability theory was first introduced in seventeenth century France when two mathematicians, Blaise Pascal and Pierre de Fermat, debated over problems from games of chance.^{10} The idea was that a person who understands decision making in the face of uncertainty has an advantage over someone that does not.^{01}

Assuming that all outcomes are equally probable, then the probability of event A is the number of ways event A can happen divided by the total number of possible outcomes.^{11}

For example, what is the probability of drawing an ace from a shuffled deck of 52 playing cards? S=4 aces in the deck N=52 cards in the deck S/N = 4/52 = 1/13 |

The frequentist approach requires a basic understanding of some factors about probability:

0 < Probability of an event A < 1 |

- The probability can be any single value between 0 and 1 inclusive.
^{02}If an event is impossible, then the probability value is 0; if the event is certain to occur it has a probability of 1. All other events that could potentially occur have probabilities that lie somewhere between 0 and 1. It is common practice to multiply the probability of an event by 100 to obtain a percentage of probability.

Probability of an event A or B = Probability (A) + Probability (B) |

- If two events, A and B, are mutually exclusive, then the probability that one or the other of them (A or B) is true is equal to the sum of the probabilities of A and B.
^{02}

Probability of an event A and B = Probability (A) x Probability (B) |

- The probability that two independent events, A and B, will both take place is calculated by multiplying the probability of the events A and B.
^{01}This is the product rule.

The term odds is often used incorrectly; odds are not the same thing as probability. The odds on an event occurring is the ratio of two competing probabilities- the probability that the event will occur and the probability that it will not occur. If the probability of the event is p, the probability that it will not occur is 1 – p. The odds are therefore p/(1-p).^{01,03}

### Additional Online Courses

- What Every First Responding Officer Should Know About DNA Evidence
- Collecting DNA Evidence at Property Crime Scenes
- DNA – A Prosecutor’s Practice Notebook
- Crime Scene and DNA Basics
- Laboratory Safety Programs
- DNA Amplification
- Population Genetics and Statistics
- Non-STR DNA Markers: SNPs, Y-STRs, LCN and mtDNA
- Firearms Examiner Training
- Forensic DNA Education for Law Enforcement Decisionmakers

- What Every Investigator and Evidence Technician Should Know About DNA Evidence
- Principles of Forensic DNA for Officers of the Court
- Law 101: Legal Guide for the Forensic Expert
- Laboratory Orientation and Testing of Body Fluids and Tissues
- DNA Extraction and Quantitation
- STR Data Analysis and Interpretation
- Communication Skills, Report Writing, and Courtroom Testimony
- Español for Law Enforcement
- Amplified DNA Product Separation for Forensic Analysts