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Using Statistical Significance Tests

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Using Statistical Significance Tests

Overview: Suppose a group of U.S. election reformers argues that switching to a system based on proportional representation (PR) would significantly increase voter turnout. Skeptics claim that the reform wouldn't significantly affect turnout. The following table, which reports mean turnouts and accompanying standard errors for PR and non-PR countries, will help you determine which side—the reformers or the skeptics—is more correct.

Electoral System Mean Turnout Standard Error
Proportional 69.5 1.9
Non-PR 61.5 1.7

Table 7.1: Electoral Turnout by Election Type
(Source: Pollock, 2016)

Respond:

Part 1
State the null hypothesis for the relationship between the type of electoral system (PR/non-PR) and turnout.

Part 2
Calculate and write down the 95 percent confidence intervals for turnouts in PR and non-PR countries.

Based on a comparison of the 95 percent confidence intervals, should the null hypothesis be rejected or not?

Explain how you know.

Part 3
Calculate and write down the mean difference between PR and non-PR countries.

What is the standard error of the difference between the PR mean and the non-PR mean?

Does the mean difference pass the eyeball test of significance?

Explain how you know.

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Formulas, explanations and step-by-step calculations are shown for the example problems on statistical significance.

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Using Statistical Significance Tests

Overview: Suppose a group of U.S. election reformers argues that switching to a system based on proportional representation (PR) would significantly increase voter turnout. Skeptics claim that the reform wouldn't significantly affect turnout. The following table, which reports mean turnouts and accompanying standard errors for PR and non-PR countries, will help you determine which side—the reformers or the skeptics—is more correct.

Table 7.1: Electoral Turnout by Election Type
(Source: Pollock, 2016)

Respond:

Part 1
State the null hypothesis for the relationship between the type of electoral system (PR/non-PR) and turnout.

There is no relationship between the mean turnout in a PR system and the mean turnout in a non-PR system.
Ho: pPR = pnon-PR

Part 2
Calculate and write down the 95 percent confidence intervals for turnouts in PR and non-PR ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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