Erring on the Margin of Error (Sampling‪)‬

1. Introduction As most teachers of probability and statistics know, one of the most difficult concepts to convey 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 public alike are exposed to this concept almost on a daily basis. In fact, when the authors recently accessed the Dow-Jones Interactive News Library (1) 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.