Statistical Evidence



In a medical fraud case, the attorney should almost always object to any statistical opinions rendered by experts.

1. Statistics is a Science

The California Supreme Court in Duran v. U.S. Bank National Association (2014) 59 Cal.4th 1, involved a trial court finding that a plaintiff class of 260 employees had been misclassified as exempt from the overtime laws. This factual conclusion was based on the representative testimony of 21 class members. Duran at 12, 16 The Supreme Court reversed. There were two grounds for the reversal. One is unrelated to this discussion. The second ground was that the court’s implementation of statistical sampling was flawed. (Duran at p. 25) 916.)

2. A Solid Scientific Foundation for “representative testimony” Is a Condition Precedent to Expert Testimony

The Duran decision established that a party can use “representative testimony” to raise inferences only if there is a sufficiently representative sample for the inferences to be justified. (Duran, at p. 38) It is not sufficient for an expert to “say” that in his opinion it is representative.

There has to be a real foundation. The court in Duran said that “[s]everal considerations determine whether a sample is sufficiently representative to fairly support inferences about the underlying population. … One such consideration is sample size. (Duran at p. 42) 325 P.3d 916.) “It is impossible to determine an appropriate sample size without first learning about the variability in the population.” (Ibid.) “One way to assess population variability is through the use of surveys.” (Ibid.) “With input from the parties’ experts, the court must determine that a chosen sample size is statistically appropriate and capable of producing valid results within a reasonable margin of error.” (Ibid.)

A second consideration is that the margin of error must not be intolerably large. (Duran at p. 46) “Statisticians typically calculate margin of error using a 95 percent confidence interval, which is the interval of values above and below the estimate within which one can be 95 percent certain of capturing the ‘true’ result.” (Ibid.)  If a statistical opinion is not as strong as the proof of guilt “beyond a reasonable doubt”, then how much weight does the opinion get?  Since statistics (unlike reasonable doubt) rely on numbers, a reliability number is the only way to evaluate the value of the opinion (assuming that the data itself is reliable, accurate and sufficient in number to rely upon).

3. Judicial Discretion to Admit Evidence Cannot Ignore Science

“Trial courts have broad discretion in many areas. But they cannot exercise that discretion in ways contrary to the internal rules of a scientific specialty, such as statistics, and then rely on that specialty’s established reliability as if the rules had been followed.” (Duran at p. 45)

Sampling is a methodology based on inferential statistics and probability theory. “The essence of the science of inferential statistics is that one may confidently draw inferences about the whole from a representative sample of the whole.” (In re Chevron U.S.A., Inc. (5th Cir.1997) 109 F.3d 1016, 1019–1020.)
Duran v. U.S. Bank Nat. Assn. (2014) 59 Cal.4th 1, 38


If an expert thinks that he is a statistics expert, discovery on this qualification needs to be provided. There must then be a hearing per People v. Kelly (1976) 17 Cal.3d 24 to determine his expertise, the science he relies upon (is it established as reliable) and whether the expert  properly followed the scientific rules for his purported statistical analysis.


Mathematical probability statistics were held to be an improper subject of expert testimony in People v. Collins (1968) 68 Cal.2d 319. Collins dealt with testimony from the prosecution’s purported expert witness, a mathematician, offered to demonstrate the statistical probability of guilt based on an inaccurate eyewitness identification. The appellate court found the expert’s deductions were not based on statistical data derived from scientific research, but rather on statistical theory unsupported by any evidence whatsoever.
The court found two defects in the use of statistical probability data.

As we shall explain, the prosecution’s introduction and use of mathematical probability statistics injected two fundamental prejudicial errors into the case: (1) The testimony itself lacked an adequate foundation both in evidence and in statistical theory; and (2) the testimony and the manner in which the prosecution used it distracted the jury from its proper and requisite function of weighing the evidence on the issue of guilt, encouraged the jurors to rely upon an engaging but logically irrelevant expert demonstration, foreclosed the possibility of an effective defense by an attorney apparently unschooled in mathematical refinements, and placed the jurors and defense counsel at a disadvantage in sifting relevant fact from inapplicable theory.
(People v. Collins (1968) 68 Cal.2d 319, 327, Emphasis added)

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