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My team manages a survey that has been reporting for many years as "relative sample error" a range of figures which are in fact the Xs in "+/- X percent" of an estimate where X is chosen to make up a 95 percent confidence interval. So in fact they are about 1.96 times the relative standard error. The users - who are not statisticians - appreciate these numbers because they can easily turn them into a confidence interval (which would take them one more step than they wanted if we quoted actual standard errors).

My question is, what is the correct way to describe these figures?

  • "Relative standard error" is certainly wrong;
  • "1.96 * RSE" is clumsy and not quite correct (because they might be created with a bootstrap method which does not calculate the confidence interval that way)
  • "Relative half confidence interval" is probably correct but not very plain English
  • "95 percent confidence interval, expressed as plus or minus percentage of the estimate" is correct but verbose

Putting aside any questions about how these are calculated, any views on good terminology?

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I've never heard a specific term for exactly that thing, but my closest guesses would be "relative margin of error" or "margin of error of X percent". –  G. Jay Kerns Jan 16 '12 at 2:40

2 Answers 2

up vote 4 down vote accepted

"Margin of Error" is fairly common and relatable term. Margin of error is commonly expressed as the radius of the confidence interval, Wikipedia entry. You could include a footnote or reference to details on your 95% confidence intervals.

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The California Supreme Court described this statistic as the "relative margin of error" when it wrote in Duran v. U.S. Bank Nat. Ass’n, 325 P.3d 916, 172 Cal.Rptr.3d 371, 382 n.13 (Cal. 2014), that "The relative margin of error is the percentage of deviation possible around the point estimate at a specific confidence interval. Here, the point estimate was 11.87 hours, and deviation around this estimate ranged from 6.73 to 17.01 (i.e., plus or minus 5.14 hours) at a 95 percent confidence interval. The relative margin of error is calculated by dividing the absolute margin of error by the point estimate. In this case: 5.14/11.87 = 43.30 percent."

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Thanks; and based on the answer by @tharen and comment by G Jay Kerns, "relative margin of error" is the terminology we now use. –  Peter Ellis Jul 6 at 21:24

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