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Unformatted text preview: Describing Association for Describing Association for Discrete Variables Discrete Variables Discrete variables can have one of two different qualities: 1. ordered categories 2. nonordered categories 1. Ordered categories e.g., “High,” “Medium,” and “Low” 2. Nonordered categories e.g., “Yes” and “No” Relationships between two variables may be either: 1. symmetrical or 2. Asymmetrical Symmetrical means that we are only interested in describing the extent to which two variables “hang around together.” [ nondirectional ] Symbolically, X ←→ Y Asymmetrical means that we want a measure of association that yields a different description of X’s influence on Y from Y’s influence on X. [ directional ] Symbolically, X → Y Y → X Ordered Categories Asymmetrical Relationship No Yes Yule’s Q Cramer’s V Gamma ( G ) Lambda ( λ ) Somers’ d yx No Yes For symmetrical relationships between two nonordered variables , there are two choices: 1. Yule’s Q (for 2x2 tables) 2. Cramer’s V (for larger tables) Respondents in the 1997 General Social Survey (GSS 1997) were asked: Were they strong supporters of any political party (yes or no)?; and, Did they vote in the 1996 presidential election (yes or no)? Party Identification Not Strong Strong Total Voting Voted a b a + b Not Voted c d c + d Total a + c b + d a+b+c+d ( 29 ( 29 ( 29 ( 29 bc ad bc ad Q s Yule + = ' Party Identification Not Strong Strong Total Voting Voted 615 339 954 Not Voted 318 59 377 Total 933 398 1,331 ( 29 ( 29 ( 29 ( 29 bc ad bc ad Q + = Q = [( 615 )( 59 ) ( 339 )( 318 ) ] / [( 615 )( 59 )+( 339 )( 318 )] = [(36,285)  (107,802)] / [(36,285) + (107,802)] = (71,517) / (144,087) =  0.496 What does this mean? Yule’s Q varies from 0.00 (statistical independence; no association) to + 1.00 (perfect direct association) and – 1.00 (perfect inverse association) Use the following rule of thumb: 0.00 to 0.24 " No relationship " 0.25 to 0.49 " Weak relationship " 0.50 to 0.74 " Moderate relationship " 0.75 to 1.00 " Strong relationship " Yule’s Q = “ 0.496 ". . . represents a moderate inverse association between party identification strength and voting turnout." Party Identification Strong Not Strong Total Voting Voted 954 954 Not Voted 377 377 Total 954 377 1,331 What would be the value of Yule's Q ? Q = [(954)(377)(0)(0)] / [((954)(377)+(0)(0)] = [(359,658)(0)] / [(359,658)+(0)] = (359,658) / (359,658) = 1.000 Party Identification Not Strong Strong Total Voting Voted 477 477 954 Not Voted 188 189 377 Total 665 666 1,331 In this case, Yule's Q would be: Q = [( 477 )( 189 )  ( 477 )( 188 )] / [( 477 )( 189 ) + ( 477 )( 188 )] = [(90,153)  (89,676)] / [(90,153) + (89,676)] = (477) / (179,829) = 0.003 Obviously Yule's Q can only be calculated for 2 x 2 tables. For larger tables (e.g., 3 x 4 tables having three rows and four columns), most statistical programs such as SAS report the Cramer's V statistic. Cramer's V has properties similar to Yule's...
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This note was uploaded on 02/04/2008 for the course PPD 404 taught by Professor Velez during the Fall '07 term at USC.
 Fall '07
 Velez

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