Ch12PPT - Chapter 12: Measures of Association for Nominal...

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Chapter 12 – 1 Chapter 12: Measures of Association for Nominal and Ordinal Variables Proportional Reduction of Error (PRE) Degree of Association For Nominal Variables Lambda For Ordinal Variables Gamma Using Gamma for Dichotomous Variables
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Chapter 12 – 2 Measures of Association Measure of association —a single summarizing number that reflects the strength of a relationship, indicates the usefulness of predicting the dependent variable from the independent variable, and often shows the direction of the relationship.
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Chapter 12 – 3 Take your best guess? The most common race/ethnicity for U.S. residents (e.g., the mode )! Now, if we know that this person lives in San Diego, California , would you change your guess? With quantitative analyses we are generally trying to predict or take our best guess at value of the dependent variable. One way to assess the relationship between two variables is to consider the degree to which the extra information of the independent variable makes your guess better . If you know nothing else about a person except that he or she lives in United States and I asked you to guess his or her race/ethnicity, what would you guess?
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Chapter 12 – 4 Proportional Reduction of Error (PRE) PRE —the concept that underlies the definition and interpretation of several measures of association. PRE measures are derived by comparing the errors made in predicting the dependent variable while ignoring the independent variable with errors made when making predictions that use information about the independent variable .
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Chapter 12 – 5 Proportional Reduction of Error (PRE) 1 2 1 E E E PRE - = where: E1 = errors of prediction made when the independent variable is ignored E2 = errors of prediction made when the prediction is based on the independent variable
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Chapter 12 – 6 Two PRE Measures: Appropriate for… Lambda NOMINAL variables Gamma ORDINAL & DICHOTOMOUS NOMINAL variables λ γ
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Chapter 12 – 7 Lambda Lambda —An asymmetrical measure of association suitable for use with nominal variables and may range from 0.0 ( meaning the extra information provided by the independent variable does not help prediction ) to 1.0 ( meaning use of independent variable results in no prediction errors ). It provides us with an indication of the strength of an association between the independent and dependent variables. A lower value represents a weaker association, while a higher value is indicative of a stronger association
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Chapter 12 – 8 Lambda 1 E 2 E 1 E Lambda - = where: E1= N total - N mode of dependent variable - = categories all for category for e mod category ) N N ( 2 E λ
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Example 1: 2000 Vote By Abortion Attitudes Vote Yes No Row Total Gore 46 39 85 Bush 41 73 114 Total 87 112 199 Abortion Attitudes (for any reason) 2000 Presidential Vote by Abortion Attitudes Source: General Social Survey, 2002 Step One
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Ch12PPT - Chapter 12: Measures of Association for Nominal...

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