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Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 16: Research with Categorical Data. Objectives. Goodness-of-Fit test χ 2 test of Independence χ 2 test of Homogeneity Reporting χ 2 Assumptions of χ 2 Follow-up tests for χ 2 McNemar Test. Background.
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Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 16: Research with Categorical Data
Objectives • Goodness-of-Fit test • χ2 test of Independence • χ2 test of Homogeneity • Reporting χ2 • Assumptions of χ2 • Follow-up tests for χ2 • McNemar Test
Background • Sometimes we want to know how people fit into categories • Typically involves nominal and ordinal scales • Person only fits one classification • The DV in this type of research is a frequency or count
Goodness-of-Fit Test • Do frequencies of different categories match (fit) what would be hypothesized in a broader population? • χ2 will be large if nonrandom difference between Oi and Ei • If χ2 < critical value, distributions match
Goodness-of-Fit Test • χ2 is nondirectional (like F) • Assumptions: • Categories are mutually exclusive • Conditions are exhaustive • Observations are independent • N is large enough
χ2 Test of Independence • Are two categorical variables independent of each other? • If so, Oij for one variable should have nothing to do with Eij for other variable and the difference between them will be 0.
Interpreting χ2 Test of Independence • Primary purpose is to identify independence • If Ho retained, then we cannot assume the two variables are related (independence) • If Ho rejected, the two variables are somehow related, but not necessarily cause-and-effect
χ2 Test of Homogeneity • Can be used to test cause-effect relationships • Categories indicate level of change and χ2 statistic tests whether pattern of Oi deviates from chance levels • If significant χ2, can assume c-e relation
Reporting χ2 Results • Typical standard is to include the statistic, df, sample size, and significance levels at a minimum: χ2 (df, N = n)= #, p < α χ2(6, N = 240)= 23.46, p < .05
Follow-up Tests to χ2 • Cramér’s coefficient phi (Φ) • Indicates degree of association between two variables analyzed with χ2 • Values between 0 and 1 • Does not assume linear relationship between the variables
Post-Hoc Tests to χ2 • Standardized residual, e • Converts differences between Oi and Ei to a statistic • Shows relative difference between frequencies • Highlights which cells represent statistically significant differences and which show chance findings
Follow-up Tests to χ2 • McNemar Test • For comparing correlated samples in a 2 x 2 table • Table 16.9 illustrates special form of χ2 test • Ho: differences between groups are due to chance • Example presented in text and Table 16.10 provides an application
What is Next? • **instructor to provide details