The Drug Enforcement Administrationís Handling of Cash Seizures

Audit Report 07-06
January 2007
Office of the Inspector General


Appendix II
Statistical Sample Design

The universe of items for sample selection consisted of 2,609 non‑adopted cash seizures between April 5, 2005, and November 3, 2005, by 152 DEA offices located in 20 DEA Field Divisions (excludes the Atlanta Field Division) throughout the country. A multistage clustered statistical sample was designed to provide effective and efficient coverage of the dispersed universe of sample items. The sample consisted of seven primary units (Field Divisions) from 20 with probability proportional to size at a sample fraction of 35 percent; 29 out of 152 secondary units (DEA offices) in the universe at a sample fraction of 19 percent; and 547 out of 2,609 tertiary units (cash seizures) within the seven primary units and 29 secondary units. The random sample of tertiary units yielded a sample fraction 21 percent of the universe. The details of the sample test and the testing process is presented in the body of the audit report.

Sample Test Results

The results of eight attribute tests were considered for computation of the point estimate projections. For each of the attribute tests, four types of test outcomes (characteristics) were considered: (1) test did not pass (NO), (2) the test result could not be determined (CND), (3) test passed (YES), and (4) the sampled item was not applicable to the objective of the test (NA). The estimated projections and percentages for each of these four test outcomes were computed.

To arrive at these results, the mathematical model notations, and formulae used to compute unbiased estimates of total values and the percentages is as follows.

N The number of primary units in the universe.
n The number of primary units sampled.
Mi The number of secondary units in the ith sampled primary unit.
mi The number of secondary units sampled from the ith primary unit Mi.
Rij The number of tertiary units in the jth sampled secondary unit from the ith sampled primary unit.
rij The number of tertiary units (test items) sampled from the jth sampled secondary unit within ith sampled primary unit Rij.
yijk Random variable and its value corresponding to kth sampled tertiary unit from the jth secondary unit sampled from the ith primary unit.
yijk { 1 If kth sampled item selected from the jth secondary unit selected from the ith primary unit found to have the characteristic.

0 Otherwise

Thus y ijk ∈ {0,1}
Y with a circumflex accent Estimate of the total number of items in the population with the characteristic.
Y with a circumflex accenti Estimate of the total number of items in the ith primary unit with the characteristic.
Y with a circumflex accentij Estimate of the total number of items in the jth secondary unit selected from the ith primary unit with the characteristic.
product symboli The probability of including the ith primary unit in the sample.

formulas

The percentage of each characteristic was computed after subtracting the number of non-applicable items from the total as denominator.



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