Chapter Fifteen

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Chapter Fifteen

• Chi-Square and Other Nonparametric Procedures

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Nonparametric Statistics

• used when
• dependent scores form skewed or otherwise
  nonnormal distributions,
• population variance is not homogeneous,
• scores are measured using ordinal or nominal
  scales.

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One-Way Chi SquareThe Goodness of Fit Test
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One-Way Chi Square

• used when data consist of the frequencies with
  which participants belong to the different
  categories of one variable

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Statistical Hypotheses

• H0 all frequencies in the population are equal
• Ha all frequencies in the population are not
  equal

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Assumptions of the One-Way Chi Square

1. Participants are categorized along one variable
   having two or more categories counting the
   frequency in each category
2. Each participant can be in only one category
3. Category membership is independent
4. The computations include the responses of all
   participants in the study
5. The fe in any category should be at least 5

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Computing One-Way

• Where fo are the observed frequencies and fe are
  the expected frequencies
• df k - 1 where k is the number of categories

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The Two-Way Chi SquareThe Test of Independence
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Two-Way Chi Squarethe Test of Independence

• used when you count the frequency of category
  membership along two variables

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Computing Two-Way

• Where fo are the observed frequencies and fe are
  the expected frequencies
• df (number of rows - 1)(number of columns - 1)

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Nonparametric Statistics
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The Mann-Whitney U test

• Used to test two independent samples of ranks
  when the n in each condition is equal to or less
  than 20

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Rank Sums Test

• Used to test two independent samples of ranks and
  either n is greater than 20

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Other Nonparametric Tests

• Wilcoxon T test is used to test two related
  samples of ranked data
• Kruskal-Wallis H test is used to study one factor
  involving at least three conditions where each is
  tested using independent samples and at least
  five participants in each sample
• Friedman test is used to study one factor
  involving at least three conditions where the
  samples in each are related (either matching or
  repeated measures)