In a recent FRED Blog post, we discussed how confidence intervals show the level of certainty about the accuracy of an estimate. In short: Wider confidence intervals signal more uncertainty.
Also, larger survey sample sizes increase the statistical accuracy of the data collected and allow data users to confidently compare apples to apples. Today’s post offers a bite-size example.
Our FRED graph above shows US Census estimates for median household income in three US counties:
- Pitkin, CO (solid blue line), home to the town of Aspen.
- New York, NY (dashed red line), the borough of Manhattan in New York City.
- Teton, WY (solid green line), home to the town of Jackson in the Jackson Hole valley.
Between 1989 and 2023, estimated median household income was frequently very similar for all three locations listed above: the coastal urban center and the two mountainous rural areas. But the number of residents was vastly different.
Population size influences the number of households sampled to collect income data: The more populous the county, the more households are sampled. So the estimated data are relatively more precise in more populous counties (e.g., New York County) than in less populous counties (e.g., Pitkin and Teton counties).
FRED also has data that capture the confidence intervals reported along with the estimated income data. The relative confidence interval for New York, NY, data can be as much as five times smaller than those for the Pitkin, CO, and Teton, WY, data, as seen in the graph below. That means far less uncertainty about the accuracy of the reported figures.
So, clearly, it’s best to be cautious when you try to make fair apples-to-apples data comparisons, including data from the Big Apple itself.
How these graphs were created: Search FRED for and select “Estimate of Median Household Income for Pitkin County, CO.” Click on the “Edit Graph” button and select the “Add Line” tab to search for “Estimate of Median Household Income for New York County, NY.” Don’t forget to click on “Add data series.” Repeat the last two steps to add the third series: “Estimate of Median Household Income for Teton County, WY.” Lastly, use the “Format” tab to customize the line styles. For the second graph, follow the same general procedure, except that each line is now composed of three series: Search first for “90% Confidence Interval Upper Bound…,” then “90% Confidence Interval Lower Bound…,” and finally the above mentioned estimate. Then apply the formula (a-b)/c on each line.
Suggested by Diego Mendez-Carbajo.
