Reporting Significant Digits and Rounding of Estimates

Do you have any recommended practices for rounding and significant digits you could share?

For regional planning, we often have report 1-year ACS values that have a fair amount of uncertainty. Here's an example of this type of reporting: see table 1 Population by Race and Ethnicity 1-year estimates

For example for the Puget Sound Region 2019 1 year data- we have an estimate of 40,512 +/- 7,084 American Indian or Alaskan Native alone population. Analysts chose, in this case, to report the numbers to the 100s in the report to express for regular people the uncertainty in the estimate.

We've noticed that Census Bureau reports estimates to the nearest integer, with no rounding. While we understand technically that the estimate and the margin of error expressing the uncertainty in the data may be the most precise- we are concerned about our audience understanding the information.

Also if we are not reporting margins of error, how should we round?

Most of our audiences to do not understand standard error, sampling, and weighting. Nearly every time we report a number with error, we have to go into a fairly lengthy description of what it means, and we're pretty sure they still don't understand it.

Thank you!!!

  • This isn't really a solution, but to help users interpret MOEs, our ACS Profiles application uses visual cues. 

    Bold numbers (for example the one marked by a red circle) indicate the "best" numbers with the lowest relative MOEs, < 15%. Regular type (blue circle) shows numbers with moderate RMOE (15% - 35%). "Dimmed" or gray numbers (green circle) have RMOEs greater than 35%. Also, if a user hovers their mouse cursor over any number, it shows both the RMOE and the range covered by the MOE (yellow highlight).

    It's not ideal, and certainly not very accessible, but it's useful for at-a-glance recognition of the reliability of the individual numbers. It also very graphically shows that MOEs are greater ("worse") for smaller populations and smaller areas. (The screen shot omits the column heads. The data are from the nation, Missouri, and Boone County, MO.)

    As for rounding, we don't do it for counts. For percentages, one digit after the decimal point is all I ever use. 0.1% = 0.001 or 1/1000, which is close enough for us.

  • As a statistician, I always include digits after the decimal (usually 1) to indicate that the number in the report comes from an estimate (e.g. from a statistical model).  Since the ACS is a survey all the numbers have decimals.  A mean has decimals (technically a mean is based on a statistical model.) Most of the work that I have done has been working closely with other statisticians (they need no explanation), with physicians, or other researchers. I usually have the opportunity to explain. For research papers I include a footnote explaining the issue. If you must round to avoid questions, then use standard rules, nearest integer, for 0.5 go up or down. Different people use different rules for 0.5.

    Hope this helps.