Two ledgers, one borrowed percentage

The Ninety-Six Percent That Wasn't an Error Rate

The famous figure is true and routinely misdescribed. In the FBI's 2015 review, 257 of 268 trial transcripts contained at least one scientifically erroneous statement about microscopic hair comparison. That is not a 96% laboratory false-match rate. A separate casework study found that mitochondrial DNA excluded 9 of 80 hairs that microscopy had associated. Put the denominators back, and two different failures come into view: what an examiner saw, and what an examiner told a jury it meant.

Tap the claim that travelled. Then inspect what it counted.

The label is still folded shut.

The further result

What if the testimony was the only problem?

It was not the only signal in the record. Houck and Budowle reviewed 170 FBI hair examinations that received both microscopy and mtDNA analysis between 1996 and 2000. Among the 80 that microscopy associated, mtDNA excluded 9. That cross-check concerns the underlying comparisons, not what an examiner later said in court.

Operate the two unknown outcomes inside the 80

Table 2 reports one mtDNA result as inconclusive and one as insufficient in the microscopy-association row. Choose a transparent treatment. Each answer remains a description of this selected series only.

...%

...

...

WRONG ROW

Why the control stops at two. The paper reports 6 insufficient and 3 inconclusive mtDNA outcomes across all 170 examinations. Only 1 of each lies inside the 80 microscopy associations. Moving all nine into this denominator would silently import results from other microscopy categories.

The pinned source table

All 170 examinations, without moving a cell

The highlighted cell is the 9 in the second ledger. Row and column totals are recomputed in the browser from this transcription of Table 2.

Microscopy result mtDNA association mtDNA inconclusive mtDNA exclusion mtDNA insufficient Row total

“Association” in the mtDNA column means the sequences were concordant. It does not identify one person: maternal relatives share mtDNA, and unrelated people can share a haplotype.

What neither ledger can answer

Selected records do not become populations by division

The transcript audit

The 2015 release described an ongoing review. The 268 cases were trials with inculpatory FBI examiner testimony found and reviewed under the project’s scope. They were not a random sample of every hair comparison, every examiner, or every jurisdiction. One case could contain several statements and several hairs, but counted once here.

The casework series

The 170 examinations were hairs submitted to the FBI for both methods from 1996 through 2000. The paper notes that few hairs excluded by microscopy in ordinary casework were sent for mtDNA. Selection happened before the table, so a Wilson interval describes binomial uncertainty conditional on these observations, not the selection process.

What exclusion says

An mtDNA exclusion contradicts common source for the compared samples, assuming valid testing and samples. A non-exclusion does not identify one donor. The paper itself says the 9 exclusions should not be construed as a false-positive rate for microscopy or a false-exclusion rate for mtDNA.

What the review did not decide

The 257 cases contained scientifically erroneous statements. That count does not establish 257 wrongful convictions, legal materiality in each case, innocence, or how often the microscopic associations themselves were incorrect.

A live institutional disagreement

“Valid when limited” is not the same claim as “validated”

The FBI review page says microscopic comparison remains valid when used with appropriate limits and mtDNA. PCAST’s 2016 review of the studies cited by DOJ concluded that those studies did not provide a scientific basis for calling the process valid and reliable. This page does not settle that broader dispute. It exposes the two selected datasets that both positions must account for.

The instrument has teeth

The check

The page computes its displayed percentages and Wilson intervals from the source counts. The checks below take separate arithmetic routes, compare against source anchors chosen before calculation, and feed both checkers known-wrong data that must be rejected.

Running checks...

    Uncertainties and free choices, named

    • The 95% Wilson intervals use z = 1.959963984540054 and treat each selected ledger as binomial. They do not correct selection bias or make either series representative.
    • The bounds control offers three declared treatments of the two unresolved mtDNA outcomes within the 80. No option converts the result into a population rate.
    • The browser uses a hand transcription of Houck and Budowle Table 2. The offline verifier pins the same 4 by 4 cells independently and checks every margin.
    • The FBI’s 96% is its rounded presentation of 257 / 268 = ...%. The page displays 95.90% to preserve the arithmetic.
    • No causal claim about convictions is computed. No claim about a universal operational false-positive rate is made.

    Sources and apparatus

    Follow the two ledgers home

    1. FBI, April 20, 2015FBI Testimony on Microscopic Hair Analysis Contained Errors in at Least 90 Percent of Cases in Ongoing Review. Source for 257 of 268, the review scope, and the unit of trial cases with erroneous statements.
    2. Houck and Budowle, 2002Correlation of Microscopic and Mitochondrial DNA Hair Comparisons, Journal of Forensic Sciences 47(5), 964 to 967. Source for the 170-examination cross-tabulation and 9 exclusions among 80 microscopic associations.
    3. FBI and DOJ reviewFBI/DOJ Microscopic Hair Comparison Analysis Review. Source for review criteria, the FBI’s institutional position, and the role of mtDNA after 1996.
    4. PCAST, 2016Forensic Science in Criminal Courts: Ensuring Scientific Validity of Feature-Comparison Methods, section 5.7. Source for the contrary assessment of the foundational studies cited by DOJ.