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Immigration and Naturalization Service's Deferred Inspections at Airports
APPENDIX III
Statistical Sampling Model The statistical sampling universe for our model was defined as INS deferred inspections (sampling units) at nine air ports of entry (POE) [redacted]. The deferrals issued at these airports represented 70 percent of all deferrals granted during the period covered by our audit. The defined universe contained 7,443 deferred inspections (sampling units), and our sample test results were projected only to our defined universe. Our model did not contain the deferred inspections at foreign airports or smaller domestic airports (representing 30 percent of deferred inspections), and we did not project specific results to those airports. Nevertheless, in our judgment, the policy recommendations contained in this report are appropriately addressed to the deferred inspection process taken as a whole because: (1) our coverage was substantial, and (2) even in the unlikely event that no errors existed in small or foreign airports, the statistically computed error rate would still be significant. Because the number of deferred inspections varied widely from POE to POE, we used a stratified random sampling method to provide effective coverage of the units and to obtain precise estimates of the characteristics tested. Each unit was tested for multiple characteristics, which we term as discrete variables involving nominal measures. Thus each unit was tested for multiple variables. Statistical analysis was conducted on the test results of twelve variables. Two of these twelve variables were nested in another variable. Statistical estimates of the totals and the 95 percent confidence intervals were computed on all variables, except the nested variables.^{11} On the nested variables, the estimated number of items was computed using the formula (C) below. We present both lower and upper 95 percent confidence limits on the expected total number by using the formulas (A) and (B) given below. From the universe of 7,443 units we tested a random sample of 725 units (a sampling fraction of 9.74 percent). The randomly sampled units were spread across all nine air POEs, which were considered for the sampling universe. The sample test results were projected to the universe of 7,443 deferred inspections. The table below provides the details of the test results and projections for the random variables tested. Following the table are the mathematical model notations, and formulas used to compute the estimates of expected values and variances. Test Results and Projections for the Random Variables Tested
Mathematical Model Notations and Formulas Used to Compute the Estimates of Expected Values and Variances The mathematical model notations, and formulas used to compute the unbiased estimates of expected values, totals, and the variances are as follows:
To compute the variance of the estimate the formulas used are as follows.
The 95% lower confidence limit on the estimate is given by (A) and 95% upper confidence limit on the estimate is given by (B) To estimate rates in nested environment, we used the following formulas. Let k_{2} type for a variable j_{2} is nested in the k_{1} type of the variable j_{1}. Then the estimated number of occurrences of the type k_{2} for the variable i_{2} is given by the following formula. (C) Footnotes
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