McDaniel v. Brown: Whose Error?

The DNA analyst who miscomputed the siblingship probability and accepted the prosecutor's transposition of her random match probability in McDaniel v. Brown (discussed in the previous posting) now leads the Washoe County Sheriff’s Office Forensic Science Division. After the Ninth Circuit's ruling, she explained to a television news reporter that "the prosecutor ... led her through a complicated mathematical journey aimed at reducing Brown's guilt to a percentage." The mathematical journey, as recorded in the trial transcript (left panel), follows. Annotations are in the right panel.

Q [by the prosecutor]: Now, for my benefit, we're looking at a one in 3 million statistic, is there another way to show that statistic? In other words, what -- let's say 100 percent -- what is the likelihood that the DNA found in the panties is the same as the DNA found in the defendant's blood? A: Paternity testing uses percentages. Q: Okay. A: Not the way forensics likes to look at it. We prefer the one in 3 million.

The probability of paternity in parentage testing is a posterior probability computed via Bayes' rule with hypothetical prior odds of 1. It is no more (or less) a percentage than is any other fractional quantity.

Q: I understand that, but for just another way to look at it, what would that percentage be? A: It would be 99.99967 percent. That's what -- MR. SMITH: May I go to the blackboard, Judge? THE COURT: Well, we'll pull it out for you and you want her to write on it? MR. SMITH: No, I'd like to write on it. THE COURT: Well, I don't think you're a witness. I'm not going to let you write on it now. MR. SMITH: All right. THE COURT: If you want her to write on it, she can write on it. By MR. SMITH (continuing): Q: Okay. If -- Ms. Romero, if you'd write it down, please. A: Okay. THE COURT: Is there a -- could you make the decimal a little bigger for us older -- By MR. SMITH (continuing): Q: So, okay. So, if you would do, also, put 100 percent on top of that, if you would, please, with the corresponding number of zeros after the decimal point. And if you would please, then, subtract the lower number from the higher number. A: I don't think this is right. Just a minute. Q: All right. So, if you put a little line under the 99 there and a minus -- subtraction indication. All right. All right. Thank you. If you'd just take -- resume the stand.

Q: So, the -- would it be fair to say, based on that that the chances that the DNA found in the panties -- the semen in the panties -- and the blood sample, the likelihood that it is not Troy Brown would be .000033? A: I'd prefer to refer to it as the one in 3 million. Q: All right. But from a mathematical standpoint, would that be inaccurate? A: Repeat the question, please. Q: Would it be fair, then, to say that with that mathematical calculation there, that the likelihood that the DNA extracted from the semen in the panties and the DNA extracted from the blood that the likelihood that it's not Troy Brown, that it's not a match is .000033?

MR. LOCKIE: Your Honor, I'm going to object on relevance. The witness is testifying that it's not scientifically valid in her opinion. So it's not relevant. THE COURT: Well, I don't know that -- MR. LOCKIE: That's just a subtraction problem. THE COURT: Let's go back. I don't think that's what she said. I don't think that's what she said. Let's go back a step and find out. I don't think that's what she said.

According to the TV news reporter, "Romero found herself agreeing with the district attorney's math, but not in how he was applying it. She says the judge stepped in to clarify the matter, but it was the exchange between her and the prosecutor that was pulled out of the transcript and became the basis for Brown's appeal."

By MR. SMITH (continuing): Q: Now, I understand that — and what I'm trying to do is make this into a percentage where I can understand it. And so I recognize that as far as your testing, you would prefer to have it as a one in 3 million, but just as another way of looking at it, would it be inaccurate to state it that way? A: It's not inaccurate, no. Q: All right. Then in response to my question, would the likelihood that the semen from the DNA found in the panties and the blood from Troy Brown, that it's not the same, would it be -- the chances that they are not a match would be .000033? A: Yes. That's the way the math comes out. Q: All right.

THE COURT: Let's make sure. It's the same thing -- it's the same math just expressed differently. Is that correct? THE WITNESS: Yes. Exactly, your Honor.

Is this how the judge clarified the matter -- by having the witness unequivocally confirm that a DNA type that occurs with a frequency of one in three million in the general population is mathematically the same as a probability of innocence of .00003?