Chapter 17: Chi-Square Tests
Chapter Outline
17.1 Parametric and Non-Parametric Statistical Tests
17.2 The Chi-Square Test for Goodness of Fit
The Null Hypothesis for the Goodness-of-Fit Test
The Data for the Goodness-of-Fit Test
Expected Frequencies
The Chi-Square Statistic
The Chi-Square Distribution and Degrees of Freedom
Locating the Critical Region for a Chi-Square Test
An Example of the Chi-Square Test for Goodness of Fit
In the Literature - Reporting the Results for Chi-Square
Goodness of Fit and the Single-Sample t Test
17.3 The Chi-Square Test for Independence
The Null Hypothesis for the Test for Independence
Observed and Expected Frequencies
The Chi-Square Statistic and Degrees of Freedom
An Example of the Chi-Square Test for Independence
17.4 Measuring Effect Size for the Chi-Square Test for Independence
The Phi-Coefficient and Cramér’s V
17.5 Assumptions and Restrictions for Chi-Square Tests
18.6 Special Applications of the Chi-Square Tests
Chi-Square and the Pearson Correlation
Chi-Square and the Independent-Measures t and ANOVA
The Median Test for Independent Samples
Learning Objectives and Chapter Summary
1. Students should recognize the research situations in which a chi-square test is appropriate.
Chi-square tests are intended for research questions concerning the proportion of the
population in different categories. For a chi-square test, there is not a numerical score for
each individual and you do not compute a sample mean or a sample variance. Instead,
each individual is simply classified into a category and you count the number of
individuals in each category. The resulting data are called observed frequencies.
Instructor Notes - Chapter 17 - page 249
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Which of the following accurately describes the chi-square test for independence? Select one: a. It is similar to a single-sample t test because it uses one sample to test a hypothesis about one population b. It is similar to a correlation because it uses one sample to evaluate the relationship between two variables_ c. It is similar to an independent-measures t test because it uses separate samples to evaluate the difference between separate populations_ d. It is similar to both a correlation because it can be used to evaluate a relationship between variables
Which of the following accurately describes the chi-square test for independence? It is similar to both a correlation and an independent-measures t test because it can be used to evaluate a relationship between variables Or a difference between populations_ It is similar to a single-sample t test because it uses one sample to test a hypothesis about one population. It is similar to a correlation because it uses one sample to evaluate the relationship between two variables_ It is similar to an independent-measures t test because it uses separate samples to evaluate the difference between separate populations_
20.Which of the following accurately describes the chi-square test for independence?a.It is similar to a single-sample t test because it uses one sample to test a hypothesisaboutone population.b.It is similar to a correlation because it uses one sample to evaluate the relationshipbetween two variables.c.It is similar to an independent-measures t test because it uses separate samples to evaluatethe difference between separate populations.d.It is similar to both a correlation and an independent-measures t test because it can be usedto evaluate a relationship between variables or a difference between populations.ANS:DPTS:1REF:p. 606TOP:17.2
21.A chi-square test for goodness of fit is used to examine the distribution of individuals across threecategories, and a chi-square test for independence is used to examine the distribution of individuals ina 2-2 matrix of categories.Which test has the larger value for df?PTS:1REF:p. 609TOP:17.3
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22.A chi-square test for goodness of fit is used to examine the distribution of individuals across fourcategories, and a chi-square test for independence is used to examine the distribution of individualsacrossthe six categories in a 2-3 matrix of categories.Which test has the larger value for df?PTS:1REF:p. 609TOP:17.3
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23.A chi-square test for independence is used to evaluate the relationship between two variables.If bothvariables are classified into two categories, then what is the df value for the chi-square statistic?PTS:1REF:p. 609TOP:17.3
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24.What is evaluated by the chi-square test for goodness of fit?