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Injuries, Illnesses, and Fatalities
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Fact Sheet | Effects of Rounding on Published Estimates | November 2019
Effects of Rounding on Published Estimates
Incidence rates and counts by industry and case type published by the Survey of Occupational Injuries and Illnesses (SOII) are rounded to one decimal point. However, the estimates are calculated using unrounded data. This can produce a situation where the sum of published estimates does not add to the total or where a published estimate changes over time even when the components of the total do not change.
Single-Year Example
Table 1 shows three measures, labeled Component 1, Component 2, and Total, which is the sum of the Components. All measures are unrounded during estimation but rounded to one decimal place for publication. In this example, the rounded Total (7.8) does not equal the sum of the rounded Components (7.9, from the sum of 4.2 and 3.7).
| Measure | Unrounded | Rounded |
|---|---|---|
Component 1 | 4.15 | 4.2 |
Component 2 | 3.66 | 3.7 |
Total | 7.81 | 7.8 |
Multi-Year Example
Table 2 shows the same measures as Table 1 and illustrates how summed values can vary over multiple years even as their rounded components remain unchanged. The Total of 7.8 for Rounded (Year 1), differs from the Total of 8.0 for Rounded (Year 2), despite no change in the rounded form of Components 1 and 2 at 4.2 and 3.7, respectively. In addition, neither combination of the rounded components sums to the expected value of 7.9.
| Measure | Unrounded (Year 1) | Rounded (Year 1) | Unrounded (Year 2) | Rounded (Year 2) |
|---|---|---|---|---|
Component 1 | 4.15 | 4.2 | 4.24 | 4.2 |
Component 2 | 3.66 | 3.7 | 3.73 | 3.7 |
Total | 7.81 | 7.8 | 7.97 | 8.0 |
Last Modified Date: June 17, 2020