# Common Errors in Statistics and How to Avoid Them - Good P.I

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The expert testifying that the probability of defendants paternity was 96.5% knew absolutely nothing about the facts of the case other than those revealed by blood and tissues tests of defendant, the victim, and the child.. .10

In calculating a final probability of paternity percentage, the expert relied in part on this 99% probability of exclusion. She also relied on an assumption of a 50% prior probability that defendant was the father. This assumption [was] not based on her knowledge of any evidence whatsoever in this case ... [she stated] everything is equal... he may or may not be the father of the child.11

Was the experts opinion valid even if the jury disagreed with the assumption of .5 [50%]? If the jury concluded that the prior probability is .4 or .6, for example, the testimony gave them no idea of the consequences, no knowledge of what the impact (of such a change in the prior probability) would be on the formula that led to the ultimate opinion of the probability of paternity.12

. . . [T]he experts testimony should be required to include an explanation to the jury of what the probability of paternity would be for a varying range of such prior probabilities, running for example, from .1 to .9.13

8 See, for example, Davis v. State, 476 N.E.2d 127 (Ind. App. 1985) and Griffith v. State of Texas, 976 S.W.2d 241 (1998).

9 130 N.J. 484 (1993)

10 Id. 489.

11 Id. 492.

12 Id. 498.

13 Id. 499.

CHAPTER 6 LIMITATIONS OF SOME MISCELLANEOUS STATISTICAL PROCEDURES 81

In other words, Bayes Theorem might prove applicable if regardless of the form of the a priori distribution, one came to more or less the same conclusion.

Courts in California,14 Illinois, Massachusetts,15 Utah,16 and Virginia17 also have challenged the use of the 50-50 assumption. In State v. Jackson,18 the expert did include a range of prior probabilities in her testimony, but the court ruled the trial judge had erred in allowing the expert to testify as to the conclusions of Bayes Theorem in stating a conclusion, that the defendant was probably the father of the victims child.

In Cole v. Cole,19 a civil action, the Court rejected the admission of an experts testimony of a high probability of paternity derived via Bayes formula because there was strong evidence the defendant was sterile as a result of a vasectomy.

The source of much controversy is the statistical formula generally used to calculate the provability of paternity: the Bayes Theorem.. .. Briefly, the Bayes Theorem shows how new statistical information alters a previously established probability. ... When a laboratory uses the Bayes Theorem to calculate a probability of paternity it must first calculate a prior probability of paternity.

. .. This prior probability usually has no connection to the case at hand. Sometimes it reflects the previous success of the laboratory at excluding false fathers. Traditionally, laboratories use the figure 50% which may or may not be appropriate in a given case.

Critics suggest that this prior probability should take into account the circumstances of the particular case. For example if the woman has accused three men of fathering her child or if there are reasons to doubt her credibility, or if there is evidence that the husband is infertile, as in the present case, then the prior probability should be reduced to less than 50%.20

The question remains as to what value to assign the prior probability. And whether absent sufficient knowledge to pin down the prior probability with any accuracy we can make use of Bayes

Theorem at all. At trial, an expert called by the prosecution in

14 State v. Jackson, 320 NC 452, 358 S.E.2d 679 (1987).

15 Commonwealth v. Beausoleil, 397 Mass. 206 (1986).

16 Kofford v. Flora 744 P.2d 1343, 1351-2 (1987).

17 Bridgeman v. Commonwealth, 3 Va. App 523 (1986).

18 320 N.C. 452 (1987).

19 74 N.C. App. 247, affd. 314 N.C. 660 (1985).

20 Id. 328.

82 PART II HYPOTHESIS TESTING AND ESTIMATION

Plemel v. Walter21 used Bayes Theorem to derive the probability of paternity.

If the paternity index or its equivalents are presented as the probability of paternity, this amounts to an unstated assumption of a prior probability of 50 percent. ... the paternity index will equal the probability of paternity only when the other evidence in this case establishes prior odds of paternity of exactly one"22

... the expert is unqualified to state that any single figure is the accuseds probability of paternity. As noted above, such a statement requires an estimation of the strength of other evidence presented in the case (i.e., an estimation of the prior the probability of paternity), an estimation that the expert is no better position to make than the trier of fact.23

Studies in Poland and New York City have suggested that this assumption [a 50 percent prior probability] favors the putative father because in an estimated 60 to 70 percent of paternity cases the mothers accusation of paternity is correct. Of course, the purpose of paternity litigation is to determine whether the mothers accusation is correct and for that reason it would be both unfair and improper to apply the assumption in any particular case.2

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