## Statistical Calculations

If the man tested cannot be excluded as the biological father of the child in question, then statistical calculations are performed to aid in understanding the strength of the match. The most commonly applied test in this regard is the paternity index.

The paternity index (PI) is the ratio of two conditional probabilities where the numerator assumes paternity and the denominator assumes a random man of similar ethnic background was the father. The numerator is the probability of observed genotypes, given the tested man is the father, while the denominator is the probability of the observed genotypes, given that a random man is the father. The paternity index then is a likelihood ratio of two probabilities conditional upon different competing hypotheses. This likelihood ratio reflects how many times more likely it is to see the evidence (e.g., a particular set of alleles) under the first hypothesis compared to the second hypothesis. When mating is random, the probability that the untested alternative father will transmit a specific allele to his child is equal to the allele frequency in his race (see Eisenberg 2003).

The PI is generally represented in the formula X/Y where X is the chance that the alleged father (AF) could transmit the obligate allele and Y is the chance that some other man of the same race could have transmitted the allele. Typically, X is assigned the value of 1 if the AF is homozygous for the allele of interest and 0.5 if the AF is heterozygous. A population database containing frequency distributions for the various alleles at the tested genetic markers, such as Appendix II, is used to calculate the potential of a randomly selected man passing the obligate allele to the child.

The PI is calculated for each locus and then individual PI values are multiplied together to obtain the combined paternity index (CPI) for the entire set of genetic loci examined. The generally accepted minimum standard for an inclusion of paternity is a PI of 100 or greater (Coleman and Swenson 2000). A PI of 100 correlates to the probability that the alleged father has a 99 to 1 better chance of being the father than a random man.

Another statistical test performed in paternity testing is the exclusion probability, which is the combined frequency of all genotypes that would be excluded if the pedigree relationships were true assuming Hardy-Weinberg equilibrium. Computer programs used for statistical calculations in parentage testing include DNA View (http://www.dna-view.com/dnaview.htm), Familias (http:// www.math.chalmers.se/~mostad/familias/), and EasyDNA (Fung 2003, Fung et al. 2004).