Chi-Square Tests and Nonparametric Tests

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Chapter 12

• Chi-Square Tests and Nonparametric Tests

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12.1 Chi2 Test for Difference Between 2
Proportions (Independent Samples)

• techniques rely on the cross-classification or
  cross-tabulation table structure.
• Sometimes called contingency tables.

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The Chi2 Test

• As with all hypothesis tests, the same steps are
  used
• Develop hypotheses
• Develop rejection region / decision rule
• Examine sample / test statistic
• Make decisions and conclusions.

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Mechanics

• H0 pi1 pi2
• Point estimate?
• Test statistic
• If H0 is true, then the test statistic should be
  small because observed and expected frequencies
  are close.
• If H0 is false, then the test statistic will be
  large.
• Assume that expected frequencies greater than 5.

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12.2 Chi-Square Test for Differences Among More
than Two Proportions

• Each column of the contingency table contains the
  data from one of the populations.
• Stay with 2 rows one for success and one for
  failure.
• Few modifications from 12-2 are required.
• Post hoc testing is available.

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Post hoc testing

• Marascuilo Procedure compare all pairs of groups.
• It is a critical range test.
• Compute the difference in sample proportions for
  success for all pairs.
• Compute the critical range Formula 12.6.

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12.3 Chi-Square Test of Independence

• More than 2 populations.
• Hypotheses slightly different
• H0 two categorical variables are independent.
• H1 two categorical variables are dependent.
• What are independence and dependence?
• How many values may each variable assume?
• Test Statistic and Decision Rule are same as that
  of Test of Equal Proportions (12-3).

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Difference between 12.2 and 12.3

• Test of Equal Proportions has 1 factor or
  variable of interest with 2 or more levels. For
  each group or level, there are successes and
  failures.
• Test of Independence has 2 factors or variables
  of interest, each of which has two or more
  levels. Draw a sample and assess the values of
  both variables.