Table 6.
Minimum Detectable Impacts for Analysis Samples
| Arkansas | Florida | New Jersey | ||||
|---|---|---|---|---|---|---|
| Sample Size | Detectable Difference* | Sample Size | Detectable Difference* | Sample Size | Detectable Difference* | |
| Minimum detectable impacts on consumers service use | ||||||
| Nonelderly | 473 | 12.9 | 811 | 9.8 | 682 | 10.8 |
| Elderly | 1,266 | 7.9 | 736 | 10.3 | 783 | 10.0 |
| Children | — | — | 859 | 9.6 | — | — |
| Adverse events | ||||||
| Nonelderly | 460 | 13.1 | 809 | 9.8 | 668 | 10.8 |
| Elderly | 1,143 | 8.3 | 707 | 10.5 | 742 | 10.3 |
| Children | — | — | 857 | 9.6 | — | — |
| Satisfaction with paid care | ||||||
| Nonelderly | 322 | 15.8 | 404 | 13.9 | 474 | 12.9 |
| Elderly | 719 | 10.5 | 452 | 13.2 | 503 | 12.5 |
| Children | — | — | 562 | 11.8 | — | — |
| Minimum detectable impacts on caregivers: | ||||||
| All adults | 1,433 | 7.4 | 1,193 | 8.1 | 1,042 | 8.7 |
| Children | — | — | 829 | 9.7 | — | — |
| Minimum detectable impacts on costs:+ | ||||||
| Year 1 results | ||||||
| Nonelderly | 556 | 16.4 | 913 | 11.9 | 817 | 20.2 |
| Elderly | 1,452 | 6.9 | 904 | 12.0 | 938 | 12.3 |
| All adults | 2,008 | 7.2 | 1,817 | 7.7 | 1,755 | 13.4 |
| Children | — | — | 1,002 | 15.7 | — | — |
| Year 2 results | ||||||
| Nonelderly | 383 | 19.1 | 833 | 14.1 | 671 | 23.1 |
| Elderly | 928 | 8.0 | 591 | 25.3 | 776 | 20.1 |
| All adults | 1,311 | 8.1 | 1,424 | 12.5 | 1,447 | 15.3 |
| Children | — | — | 1,002 | 15.7 | — | — |
| Half width of 95% confidence intervals for paid workers | ||||||
| Adults | ||||||
| Hired by consumer | 391 | ± 5.0 | 298 | ± 5.7 | 382 | ± 5.0 |
| Agency worker | 281 | ± 5.8 | 255 | ± 6.1 | 308 | ± 5.6 |
| Children | ||||||
| Hired by consumer | — | — | — | — | 222 | ± 6.6 |
| Agency worker | — | — | — | — | 164 | ± 7.7 |
Calculations assume 80 percent power for two-tailed tests at the .05 significance level (for survey-based impacts) and the .10 level (for cost impacts). Outcome variables (other than costs) are assumed to be binary, and have a mean of .5. Minimum detectable effect calculations for costs are based on actual standard errors of the estimates of program impacts on total Medicaid costs for the year after enrollment.
Detectable differences are expressed as percentage points for impacts on binary outcomes for consumers and caregivers, and as a percent of the control group mean for impacts on costs. Confidence intervals are also in terms of percentage points for a binary variable with mean of .50.
The anomalous result of larger detectable differences in costs when estimated on all adults than when estimated on just the elderly, despite the larger sample, is due to the use of actual standard errors from the regressions for each sample in these calculations. The large difference in means between the elderly and onelderly subgroups in both Arkansas and New Jersey leads to a much larger variance for the all adults group, offsetting the larger sample size.