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Assignment 1:
Provide some examples of surveys (perhaps some from your own experience) where non-response is possible. How serious is the issue of non-response in each of your examples? How might one increase the response rate? What might one do to estimate the non-response bias?
The sampling plan below was used in a statistical audit. The columns of the table list the strata indices, strata sizes, sample sizes and a description of the strata.
| 1 | 25 | 25 | > $ 40,000.00 |
| 2 | 250 | 50 | 15,000.00 – 40,000.00 |
| 3 | 450 | 38 | 5,001.00 – 14,999.00 |
| 4 | 800 | 32 | 1,000.00 – 5,000.00 |
| 5 | 2,000 | 30 | <1,000.00 |
| Totals | 3,525 | 175 |
The means and standard deviations of erroneously paid dollars by strata were ($10,045, $623), ($8,756, $401), ($4,265, $211), ($809, $75) and ($53, $45), respectively.
- Calculate an estimate of the average error per case in the sampling frame (population) and a 90% confidence interval for the same.
- Calculate an estimate of the total dollars in error in the sampling frame (population) and a 90% confidence interval for the same.
Assignment 2:
Based on your calculations in the assignment 1, what restitution amount is the judge likely to set? Why?
An expert for the audited party argued that all 25 cases in strata 1 were included in the sample. This is extremely unlikely if random sampling was used. Furthermore, the sample sizes in the other strata are disproportionate to the strata sizes, so this sample cannot be representative and the estimates based on this sample should be disregarded. What do you think?
The following references may provide some context:
- Heiner, K. W., Fried, A., and Wagner, N., (1984), “Successfully Using Statistics to Determine Damages in Fiscal Audits”, Jurimetrics, 24, No. 3, Spring.
- Karl W. Heiner, Owen Whitby, (1980) Maximizing Restitution for Erroneous Medical Payments When Auditing Samples. Interfaces 10(4):46-54. (You will find this article in attachment)
- Heiner, K. W., (1995), “Computerized Interactive Stratification in Statistical Audits:, Mathematics with Vision, Computational Mechanics Publications, Southampton, UK, pp. 199-206.
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