Margin of Error

Dear students,

Earlier this month, an Associated Press story concerning the presidential race appeared in our local newspaper. The last sentence of this article caught my eye because it seemed related to our course content.

The newspaper article reports the results of a telephone survey of 1,000 adults. Several questions were asked of the male and female participants, with these being some of the findings: (1) "Women are slightly less likely than men to be interested in the presidential campaign," (2) women are "more likely to be dissatisfied with politics," (3) women are "more likely than men to believe the election will make a difference in their lives," and (4) "more women than men feel that this election is an important one."

The final sentence of the newspaper article said this: ''Because some questions were asked only of some of the respondents, the margin of error ranged from plus or minus 3 percentage points to 6 percentage points."

In studies like this one, the "margin of error" is nothing more than a confidence interval that's been dressed up (or maybe I should say "dressed DOWN") for popular consumption. That's because the margin of error is the amount that gets added to and subtracted from the sample statistic (in this case, a percentage) so as to form the upper and lower "ends" of the confidence interval.

The article's final sentence said that the margin of error on different questions ranged from 3 to 6 percentage points BECAUSE SOME QUESTIONS WERE ASKED ONLY OF SOME RESPONDENTS. Hopefully you can see the connection between (1) what was said in this newspaper article about the margin of error and (2) the question on our midterm exam last month that asked you to specify whether the width of a confidence interval would increase or decrease if the sample size goes up.

The main point I'd like you to know is simply this: Assuming other things are held constant, there's an inverse relationship between n, on the one hand, and either the size of the margin of error or the width of the confidence interval, on the other. Simply stated, larger sample sizes function to make margins of error smaller and confidence intervals narrower.

(Don't forget, however, that the population parameter being estimated can and sometimes will lie "beyond the margin of error" or "outside the CI." That will happen, of course, about 5 times out of 100 whenever margin-of-error or CI statements are created by using a 95% "strategy.")

Sky Huck

Copyright © 2012

Schuyler W. Huck
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