Supreme Court, New York CountyApr 19, 1993
157 Misc. 2d 783 (N.Y. Misc. 1993)
157 Misc. 2d 783598 N.Y.S.2d 911

April 19, 1993

Legal Aid Society (Robert Baum and Gary Greenberg of counsel), for defendant.

Robert Morgenthau, District Attorney of New York County (Paul Schechtman of counsel), for plaintiff.

This case is before the court on defendant's pretrial challenge to the procedures that the New York City Police Laboratory employs to determine whether a mixture contains 500 milligrams or more of cocaine. For the reasons set forth below, the court concludes that those procedures are sufficiently reliable to permit the Police Laboratory's test results to be received into evidence at defendant's trial.


On December 3, 1991, defendant Robert McLaurin was indicted in a two-count indictment. Count one charged defendant with possessing cocaine with intent to sell, in violation of Penal Law § 220.16 (1). Count two charged defendant with possessing 500 milligrams or more of cocaine, in violation of Penal Law § 220.06 (5). The charges arose from an incident that occurred six days earlier, when a police officer allegedly saw defendant discard a plastic bag which contained 72 vials of crack cocaine.

Section 220.06 (5), which was enacted in 1988, makes it a class D felony knowingly to possess "five hundred milligrams or more of cocaine." The statute contemplates a "pure weight" standard in which the amount of pure cocaine that a defendant possesses determines his culpability. Not every narcotics statute is drafted in this fashion. Penal Law § 220.09 (1), for example, makes it a class C felony to possess "one or more * * * substances of an aggregate weight of one-eighth ounce or more containing a narcotic drug." Such an "aggregate weight" standard does not require the laboratory to estimate the purity of a defendant's drugs. (See, People v Davis, 95 Misc.2d 1010, 1013 [Dutchess County 1978].)

Following his indictment, defendant moved to dismiss count two on the ground that "the Police Laboratory uses scientifically unsound * * * principles to determine the pure weight of narcotics submitted for testing." Defendant buttressed his motion with a report from Aaron Tenenbein, chairman of the Statistics and Operations Research Department at New York University, in which Dr. Tenenbein concluded that "the laboratory's use of a single sample to estimate the total weight of pure cocaine * * * is not statistically valid." On May 6, 1992, a Frye hearing was ordered to consider defendant's challenge to the Laboratory's procedures. (See, Frye v United States, 293 F 1013.)

The Frye hearing was granted by Justice Altman.


At the hearing, which stretched over three days, the court heard evidence on the New York City Police Laboratory's procedures, on statistical methodology, on scientific studies regarding the mixing of chemicals, and on test results obtained in the Monroe County Laboratory in upstate New York.

A. The New York City Police Laboratory's Procedures

The procedures employed by the New York City Police Laboratory to determine whether a mixture contains 500 milligrams or more of cocaine are not in dispute. First, the chemist empties the contents of the vials (or other containers) and determines an aggregate weight. The contents of the 72 vials allegedly recovered from defendant weighed 1943.94 milligrams. Second, the contents are ground into a fine powder using a mortar and pestle, and the powder is mixed by repeated tossing and stirring. In this way, the chemist seeks to create a "homogeneous mixture." Third, a sample of one or two grains (65 to 130 milligrams) is extracted by drawing small quantities from four or five places across the mixture. Fourth, this sample is tested by gas chromatography to determine its purity. In defendant's case, the sample tested 88.9% pure. Finally, the total "pure weight" of cocaine is determined by multiplying the aggregate weight and the estimated purity, i.e., .889 X 1943.94 = 1728 milligrams of cocaine. It is this figure that the Police Laboratory reports to the Grand Jury and the court.

As the parties agree, this methodology produces only an estimate of the weight of pure cocaine. There are two sources of potential error in this estimate. The first is sampling error, which arises from the fact that the sample that is tested may not be identical in purity to the entire mixture. The second is measurement error, which arises from the fact that scientific instruments do not yield perfect measurements. For these two reasons, the figure that the Police Laboratory reports — here, 1728 milligrams — is not an exact assay of the weight of pure cocaine in the mixture.

The Police Laboratory takes these two sources of potential error into account by allowing for a 10% margin of error before reporting its test results. A simple example explains its calculation: assume that the aggregate weight of a defendant's mixture is 1000 milligrams and that a sample extracted from it tests 54% pure. In such a case, the Police Laboratory would initially estimate that the defendant possessed 540 milligrams (1000 mg X .54) of cocaine. However, in recognition of the potential errors in the estimation procedure, the Laboratory subtracts 10% from this estimate, i.e., 540 — 54 = 486 milligrams. Because the resulting figure is less than 500 milligrams, the Laboratory would report that the defendant did not possess the requisite weight of pure cocaine.

B. Dr. Tenenbein's Testimony

The thrust of defendant's challenge is (i) that to determine the precision of the estimate which the Police Laboratory reports to the court, it is necessary to calculate a standard deviation, and (ii) that a standard deviation cannot be calculated unless the Police Laboratory extracts at least two samples of cocaine and estimates their purity. In his testimony, Dr. Tenenbein provided an example that is instructive. Assume in defendant's case that five samples had been taken and that the percentage of pure cocaine in each were as follows: 88.9%, 70%, 50%, 30% and 10%. In this example, the mean purity is 49.78%, a number that is far lower than the 88.9% which the Police Laboratory would report if only one sample were tested.

The standard deviation is a measurement of the dispersion in a distribution. By calculating the standard deviation, a statistician can determine the probability that the true purity of cocaine falls within a certain range of values. On assumptions that seem reasonable in this context, a statistician multiplies the standard deviation by two to obtain a so-called "95 percent confidence interval", i.e., an interval in which the true value can be said to fall with 95% certainty. An example is helpful: if a statistician estimates that 57% of the voters favor Clinton for President and that the standard deviation for sampling error is 1.5%, it is common to report that Clinton is leading with 57 ± 3% of the vote. That means the statistician is 95% confident that Clinton's true share is between 54 and 60%.

This mean figure is still only an estimate of the true purity. However, because multiple samples were taken, it is possible to determine the precision of this estimate. This is done by estimating the standard deviation and deriving 95% confidence intervals. (See, n 3, supra.) Thus, in the example, a statistician would report with 95% confidence that the true purity of the mixture was between 24.2 and 75.3%. Because the Police Laboratory tests only one sample, Dr. Tenenbein found it impossible to determine the reliability of its estimate, and therefore concluded that its procedures were scientifically invalid.

C. Dr. Cavanagh's Testimony

In response to this claim, the People offered the testimony of Christopher Cavanagh, an associate professor in the Economics Department of Columbia University, where he teaches statistical methods. Dr. Cavanagh readily acknowledged that the figure reported by the Police Laboratory was only an estimate of the pure weight of cocaine and that the precision of the estimate could be determined by taking multiple samples. He testified, however, that multiple samples were not required. Critical to his alternative approach was the assumption that the Police Laboratory's mixing procedures created a sample for testing that could be treated as one approximating a random sample of the particles in the mixture.

A random sample has a precise statistical meaning: it is one in which each of the powder particles in the mixture has the same probability of being in the sample as any other and in which the fact that a particular particle is in the sample does not alter the probability that any other particle is in the sample.

Dr. Cavanagh gave this example to explain his approach. Assume that there are only two kinds of particles of equal size and weight that a cocaine dealer can mix — one is 100% pure cocaine; the other is a noncocaine adulterant. Assume further that a drug dealer mixes 100,000 particles of pure cocaine and 100,000 particles of adulterant so that his mixture is 50% pure. Next assume that the drugs are seized and given to a chemist to analyze for purity, that the chemist extracts 400 particles at random, and that 192 of those particles are found to be pure cocaine and 208 are adulterant. Based upon this sample, the chemist would estimate that the defendant's substance was 48% (192/400) pure cocaine.

Dr. Cavanagh testified that the precision of this estimate can be calculated if it is assumed that the 400 particles are a random sample of the particles in the mixture. (This assumption permits a statistician to treat the particles that the chemist has drawn not as one sample but as a sample of size 400.) Using standard statistical procedures, Dr. Cavanagh calculated that the purity of the cocaine was 48% ± 5%, i.e., that the true value of the purity was between 43 and 53% with 95% certainty.

This estimate is determined from the statistical fact that the standard deviation for the average of a random sample is equal to the standard deviation of a single component of that random sample divided by the square root of the number of components in the average. In the example, the standard deviation of a single particle is 50%. (That is because the particle is either 100% or 0% pure.) Since the sample contains 400 particles, the standard deviation for sampling error is .5/ 400 = 2.5%. Two standard deviations is twice that amount: ± 5%.

Dr. Cavanagh used this same approach to analyze the New York City Police Laboratory's procedures. Making several conservative assumptions, e.g., that measurement error was unlikely to be greater than 3% and that the test sample contained at least 150 particles, he concluded that the Police Laboratory's methodology of taking one sample and allowing for a 10% margin of error gave a scientifically valid estimate of the total weight of cocaine in defendant's case.

The precise calculations that Dr. Cavanagh made are not easily followed without a knowledge of statistics that this court, for one, does not possess. A brief summary may be useful for the cognoscenti: from his conversations with the chief chemist at the Police Laboratory, Dr. Cavanagh estimated that the standard deviation of the measurement error was not greater than 3%. This estimate was not seriously challenged at the hearing which focused principally upon sampling error. Dr. Cavanagh then estimated an upper bound for the standard deviation of the sampling error at 4.1%. In doing so, he assumed that the test sample contained at least 150 particles (this conservative figure was chosen to allow for imperfect mixing and clumping), that it was a random sample of the mixture, and that the maximum standard deviation of any one particle was 50%. (.5/ 150 = 4.1%.) On the further assumption that measurement and sampling errors are independent of each other and not additive, Dr. Cavanagh calculated the upper bound of the standard deviation of both errors at approximately 5%. Two standard deviations would then be approximately 10% — a number in line with the "margin of error" allowed for by the Police Laboratory.

D. Dr. Krueger's Testimony

Much of the testimony at the hearing focused on whether Dr. Cavanagh was correct in assuming that the Police Laboratory's mixing procedure produced a test sample that could be treated as one approximating a random sample of the particles in the mixture.

In addition to Dr. Tenenbein (who found no basis for such an assumption), defendant called James E. Krueger, a chemist with broad experience in chemical quality assurance in private industry. Dr. Krueger testified that scientific studies showed that extracting a random sample of particles from a mixture is quite difficult. Nor is the problem solved simply by mixing the substance for a longer time period. It is possible to "over mix," as well as "under mix," and a chemist cannot ascertain by observation whether he has mixed too much or too little. These studies, Dr. Krueger concluded, militate strongly in favor of taking multiple samples to estimate the purity of a mixture.

E. Monroe County Statistics

To lend support to Dr. Cavanagh's approach, the People offered data from the Monroe County Department of Public Safety Laboratory. In Monroe County, the chemists prepare samples for analysis in a manner quite similar to that employed in the New York City Police Laboratory: the cocaine-containing exhibits (e.g., vials) are combined and the resulting mixture is "homogenized," using a mortar and pestle to grind it into a fine powder. However, unlike in New York City, two samples of 15 to 20 milligrams are removed, and each is tested for purity.

Monroe County averages the two estimates and then reports that average to the court. It allows for a 5% margin of error, i.e., if the average pure weight is 524 milligrams, it is reported as less than 500 milligrams.

The Monroe County data show a remarkable degree of uniformity between the two test results. In 137 randomly chosen cases, the purity of the second sample was almost always within a percentage point or two of that of the first. For example, in one typical case, the purity of the first sample was 80.1% and the purity of the second sample was 79.0%. The greatest variation was slightly more than six percentage points — sample one was 22.95% pure; and sample two was 29.0% pure. And where the purity of the samples was high (e.g., 75% or more) the variation between the two estimates was invariably quite small.

For example, the pairs of estimates in 15 high-purity cases were as follows: 78.4% and 76.4%; 79.87% and 78.45%; 80.1% and 80.0%; 95.36% and 94.64%; 83.9% and 84.7%; 87.5% and 84.7%; 79.6% and 80.8%; 81.5% and 81.47%; 84.4% and 83.4%; 81.6% and 79.6%; 84.2% and 86.2%; 81.9% and 82.4%; 98.12% and 98.05%; 86.9% and 85.7%; and 75.3% and 74.9%.

F. Retesting Defendant's Drugs

The People also presented evidence regarding additional tests performed on the drugs allegedly seized from defendant. As noted, when the drugs were first tested, their purity was estimated at 88.9%. It was this single estimate that was presented to the Grand Jury. For the Frye hearing, the drugs were reanalyzed: the cocaine-containing powder was remixed using the Police Laboratory's standard procedures; five samples were then extracted from the mixture; and a gas chromatography analysis was performed on each sample. The five new tests showed purities of 90.3, 89.9, 89.9, 90.6, and 89.9% cocaine.


The issue before the court is the reliability of the procedures that the New York City Police Laboratory employs to determine whether a substance contains 500 milligrams or more of cocaine. If those procedures pose an appreciable risk of exposing an innocent person to criminal liability, then defendant's challenge clearly has merit.

The model developed by Dr. Cavanagh, when coupled with the data from the Monroe County Laboratory, satisfy the court that it is scientifically acceptable to test only one sample and to estimate the pure weight of cocaine from that sample, provided the Police Laboratory properly allows for a 10% margin of error. For the court, it is especially telling that if only one sample had been tested in Monroe County and if a 10% margin of error had been allowed for, a second sample would have afforded no additional protection to any defendant. That is to say, in no instance did the second sample produce an estimate more favorable to a defendant than the first estimate less 10%. If there were a statistically significant chance that the difference in purity between the two samples was more than 10%, the court would have expected to see at least one such instance in the 137 cases.

The proper way to allow for the 10% margin of error is discussed below at 791.

Thus, the Monroe County data lends considerable support to the assumption that standard mortar-and-pestle mixing produces a mixture in which the particles are distributed in a way that approximates a random distribution. And while one case is not definitive, the retests of the drugs allegedly seized from defendant indicate that the ability to mix well is not limited to chemists who practice outside New York City. Accordingly, Dr. Cavanagh's model seems a reasonable one, and the Police Laboratory should not be required to take two samples if it properly allows for a 10% margin of error after taking only one.

Moreover, on the particular facts of defendant's case, the conclusion that the Police Laboratory's procedures are sound seems inescapable. Defendant, after all, is alleged to have possessed 1943.94 milligrams of a cocaine-containing substance with an estimated purity of 88.9%. Only if the true purity were less than 25.8% would the mixture have a pure weight of less than 500 milligrams of cocaine. (1943.94 X .258 = 500 milligrams.) It strains credulity to believe that the Police Laboratory's standard mixing procedures could have produced a sample so biased that it would have overestimated the true purity to such an extent.

It is important to emphasize, however, that while the Police Laboratory's procedures are generally sound and assuredly so in defendant's case, there are circumstances where caution is warranted. The problem is that the Police Laboratory does not properly apply the 10% margin of error. Dr. Cavanagh presented a hypothetical that makes the point: assume a mixture which has an aggregate weight of 5000 milligrams and an estimated purity of 12%. The estimated weight of pure cocaine would then be 600 milligrams. Because this estimate is more than 10% greater than 500 milligrams, the Police Laboratory would report that the defendant possessed 500 milligrams or more of cocaine.

This calculation applies the 10% margin of error to the estimated pure weight of cocaine. Dr. Cavanagh testified, however, that the 10% margin of error should be applied to the estimate of the percentage of purity. It is that percentage which is subject to potential error. The difference in approaches is not academic. If Dr. Cavanagh's approach were employed, the estimated total weight of pure cocaine in the example would be only 100 milligrams (5000 milligrams X [12% — 10%] = 100 milligrams), and the defendant would not be guilty of the felony offense.

The difference between the Police Laboratory's calculus and Dr. Cavanagh's can be shown mathematically as follows:
Police Laboratory: (weight of mixture) X (estimated purity) X .9
Dr. Cavanagh: (weight of mixture) X (estimated purity — .1)
In defendant's case, the two calculations are quite close — (i) (1943.94 X .889) X .9 = 1554.6 milligrams, and (ii) (1943.94) X (.889 — .10) = 1533.7 milligrams — and each is far in excess of 500 milligrams.

In short, if the Police Laboratory continues to test only one sample, it must apply the 10% margin of error to the estimated purity before calculating the pure weight of cocaine. Its current approach of applying the margin of error to the estimated pure weight of cocaine is statistically invalid and should be discontinued. In this case, however, where the pure weight of cocaine is far in excess of 500 milligrams under either approach, dismissal of the section 220.06 (5) charge is clearly unwarranted.

As the chart below demonstrates, the lower the estimated purity, the more likely it is that the Cavanagh approach will prove favorable to a defendant. The chart shows the minimum aggregate weight that is needed at various levels of estimated purity for a chemist to report that a defendant possessed more than 500 milligrams of cocaine.


Defendant's motion to dismiss count two of the indictment is denied, and the New York City Police Laboratory's test results are found to be sufficiently reliable to be received into evidence at defendant's trial.

--------------------------------------------------------------- | Estimated Purity | Police Laboratory | Cavanagh | |-------------------|----------------------|--------------------| | .9 | 617 mg | 625 mg | |-------------------|----------------------|--------------------| | .8 | 694 mg | 714 mg | |-------------------|----------------------|--------------------| | .7 | 793 mg | 833 mg | |-------------------|----------------------|--------------------| | .6 | 926 mg | 1000 mg | |-------------------|----------------------|--------------------| | .5 | 1111 mg | 1250 mg | ---------------------------------------------------------------