On the theory and practice of Essen-Möller's W value and Gürtler's paternity index (PI).

In cases of disputed parentage the biostatistical information is contained in the frequencies X and Y (as defined by Essen-M oller ); X denotes the hypothesis "paternity", Y the hypothesis "non-paternity". Essen-M oller proposed a probability of paternity which includes both values: W = X/(X + Y) (where X + Y becomes 1). G urtler recommends the ratio X/Y as a "Paternity Index" (= PI). Both W and PI are based on a neutral prior probability (= 0.5 in normal triplet cases) and contain the same information, though differing in form. It is this difference which can lead to different results in forensic practice. W% is the common form for expressing probabilities, and each range of W values has an appropriate, easily understood verbal predicate . By contrast, the PI value is more abstract and can be interpreted as providing fixed decision limits, a possibility increased by the lack of distinct subdivisions with verbal predicates . Tables and computer programs are available for calculating W values even in complex cases. If one chooses to use PI values instead of W they must be calculated by the following formula: (formula; see text) Calculations become complicated where more than two hypotheses are involved, as e.g. in cases involving several men ("multi-men cases"). The author cannot find any arguments for preferring PI to W. Accordingly, he recommends the use of the W value and not the Paternity Index in biostatistical evaluations of blood group findings in cases of disputed parentage.