The Drug Enforcement Administration’s Handling of Cash Seizures
Audit Report 07-06
January 2007
Office of the Inspector General
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. | |
M_{i} | The number of secondary units in the i^{th} sampled primary unit. | |
m_{i} | The number of secondary units sampled from the i^{th} primary unit M_{i}. | |
R_{ij} | The number of tertiary units in the j^{th} sampled secondary unit from the i^{th} sampled primary unit. | |
r_{ij} | The number of tertiary units (test items) sampled from the j^{th} sampled secondary unit within i^{th} sampled primary unit R_{ij}. | |
y_{ijk} | Random variable and its value corresponding to k^{th} sampled tertiary unit from the j^{th} secondary unit sampled from the i^{th} primary unit. | |
y_{ijk} | { | 1 If k^{th} sampled item selected from the j^{th} secondary unit selected from the i^{th} primary unit found to have the characteristic.
0 Otherwise |
Thus | y _{ijk} ∈ {0,1} | |
Estimate of the total number of items in the population with the characteristic. | ||
_{i} | Estimate of the total number of items in the i^{th} primary unit with the characteristic. | |
_{ij} | Estimate of the total number of items in the j^{th} secondary unit selected from the i^{th} primary unit with the characteristic. | |
_{i} | The probability of including the i^{th} primary unit in the sample. | |
The percentage of each characteristic was computed after subtracting the number of non-applicable items from the total as denominator.
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