Estimating the Difference Between Two Proportions

  • Richard L. Scheaffer
  • Ann Watkins
  • Mrudulla Gnanadesikan
  • Jeffrey A. Witmer
Part of the Textbooks in mathematical sciences book series (TIMS)


A Gallup Poll of 1,200 people that stated 60% of the public favor stricter gun control lows also stated that a similar poll five years earlier produced a sample percentage of 65% in favor of stricter gun control. Has the true percentage of people favoring stricter laws actually decreased? In the current poll, the percentage of women favoring stricter laws was 71%, while the percentage of men favoring stricter laws was 48%. Are these significantly different? In the same poll, 42% of those responding agreed that handguns should be banned except for police and other authorized persons, while 50% said they should not be banned, and 8% had no opinion. How can we make a fair comparison between percentages taken in two different polls? How can we make a fair comparison between two different percentages calculated from the same poll? These are the two most common types of comparisons made between sample proportions, and we will study their properties in this activity.


Sample Proportion True Proportion Authorized Person Poll Fault News Magazine 
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    Stephen Ansolabehere and Thomas R. Belin (1993), “Poll faulting,” Chance, 6 (Winter): 22–27.Google Scholar
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    A. J. Scott and G. A. F. Seber (1983), “Differences of proportions from the same survey,” The American Statistician, 37:319–320.Google Scholar
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    C. J. Wild and G. A. F. Seber (1993), “Comparing two proportions from the same survey,” The American Statistician, 47: 178–181.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Richard L. Scheaffer
    • 1
  • Ann Watkins
    • 2
  • Mrudulla Gnanadesikan
    • 3
  • Jeffrey A. Witmer
    • 4
  1. 1.University of FloridaUSA
  2. 2.California State UniversityNorthridgeUSA
  3. 3.Fairleigh Dickinson UniversityUSA
  4. 4.Oberlin CollegeUSA

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