No doubt some of you are working today with the Census Bureau's just-released income and poverty rates. Naturally, I'm looking at Colorado's numbers in comparison to the other states.
The state-by-state estimates of median income and of poverty rates are accompanied by measurements of standard error. Does anyone know the confidence level associated with these standard errors? The appendices dealing with how to work with standard error seem to indicate that the confidence interval, at least for U.S.-level estimates, is 90 percent. Does that same confidence interval hold for the state-level estimates?
A specific example: Colorado's three-year average median income is $44,349. The standard error is $1,075.
Would I, then, be correct in saying something like this: "The Census Bureau is 90 percent certain that Colorado's median annual income ranged between $43,274 and $45,424." ?
A corollary question: Which of the median income (or poverty rate) measures is best to use? The three-year averages? The most recent 2-year rolling average? – Jeff Thomas, The Gazette, Colorado Springs, Colo.
The state-level data also is reported at the 90% c.l. [confidence level] This is noted in Table D in the footnote for the percent change column (those percent changes that are statistically significant). The Census release uses the three-year average for income (see the bulleted item on Alaska's income). This gives them a dartboard that's a bit larger. – Neill Borowski, The Philadelphia Inquirer, Philadelphia, Penn.
The Census Bureau usually reports error margins at one standard error, which means the confidence level is 68 percent. I don't have the report to which you refer, so I can't evaluate the indication that it is 90 percent. But for 90 percent confidence, according to sampling theory, you need an error band that is 1.65 standard errors wide. – Philip Meyer, University of North Carolina, Chapel Hill, N.C.
This is a common mistake in interpreting confidence intervals. We cannot be certain that the true mean (or whatever parameter) falls within the confidence interval. The correct way to interpret a confidence interval is to say: "In repeated sampling, our range (confidence interval) would encompass the true mean 90% of the time." Thus, if we were to sample from a population 100 more times and determine the mean and respective intervals for each of those samples, then 90 of the intervals would contain the true population mean. – Mary A. Davis, Center for Environmental Studies, Virginia Commonwealth University, Richmond, Va.