Erring on the Margin of Error

Abstract

term of is often erroneously explained in news articles reporting the results of public-opinion polls. We present here a number of representative examples of such misinterpretations drawn from the popular news media as well as from a number of authoritative Web sites (including that of the Gallup Organization) that explain the margin of error incorrectly. We suggest that encouraging students to search for, recognize, and correct misinterpretations of the margin of error can be a useful way of enhancing their understanding of sampling error, and we describe a number of classroom exercises that can help in this regard. to students is that of sampling error. Yet with the proliferation of the reporting of the results of public- opinion polls in the news media, students and the general alike are exposed to this concept almost on a daily basis. In fact, when the authors recently accessed the Dow-Jones Interactive News Library' and typed in the words public opinion poll, we registered nearly 60,000 hits in major newspapers and newswires for the period 1990 to the present. Often accompanying the discussion of the poll results is a statement describing the accuracy of the poll's estimates, which ordinarily reads something like, The margin of error is 3 percentage points with a 95% level of confidence.2 Because to many readers the meaning of this statement is fuzzy, the article sometimes attempts to clarify what the margin of error indicates about the poll's accuracy. However, from our experience, the attempted explanation is often completely in error-sometimes outrageously so. In this article, we first briefly explain the correct way of interpreting the margin of error, which currently seems to be the fashionable way to explain in the media what statisticians routinely call sampling error. margin of error concept is also gradually making its way into the professional economics literature (see Borenstein and Rose 1994; Brezis 1995) and into business/economics statistics textbooks as well (e.g., Anderson, Sweeney, and Williams 2002; Bowerman and O'Connell 2003). Next, we present some typical misinterpretations of the margin of error drawn from the news media that will prove interesting to both teachers and students and useful as classroom examples.