Measures of Association for contingency tables 4 Figure 8.2 : lambda – association; +-1: strong; near 0: weak Positive association: as value of the independent variable rises (falls), the dependent variable rises (falls) Negative association: as value of the independent variable falls (rises), the dependent variable rises (falls)

Measures of Association for nominal variables 4 lambda – a measure of association for use with nominal variables, i.e. it is used whenever both of the variables in a pair are nominal, or when one is nominal and one is ordinal Lambda is a measure of association which reflects the proportional reduction in error when values of the independent variable are used to predict values of the dependent variable. A value of 1 means that the independent variable perfectly predicts the dependent variable, while a value of 0 means that the independent variable is no help in predicting the dependent variable

Lambda 3 =(E1-E2)/(E1), where E1 is the number of errors you would make guessing the dependent variable if you did not know the independent variable, and E2 the number of errors you would make guessing the dependent variable if you knew the categories of the independent variable. To find E1, subtract the largest row marginal total from N To find E2, add up the highest frequencies of each category of the independent variable and subtract the sum from N

Lambda (cont.) 4 will always result in a positive number with value between 0 and 1. If negative, something wrong Calculation: subtract the single highest row marginal frequency for each category of the independent variable and subtract each result from N. Skills 2, p. 300 (using their table, p. 329, don’t peek) [excel ch8sk2] Gen ex 2, p. 338

Lambda (cont.) 4 by SPSS ( p. 301) Reading the table: Symmetric value of : neither variable is treated as independent—they are “associated”, without a cause and effect relationship Asymmetric value of : treats one as independent in relation to the other

Other measures of Association for nominal variables 3 Goodman and Kruskal’s tau - index of strength of association Phi and Cramer’s V - Only used with contingency tables of four or fewer cells (each variable has only two categories) P 306, Skills 3

Other measures of Association for nominal variables (cont) 3 Gamma – a measure like that has a “proportional reduction in error” interpretation Comparing the responses to questions by individual respondents Concordant pairs: when performing bivariate analysis of ordinal variables, a relationship in which the values of the independent and dependent variables are higher in one case than in another, comparison case.

Other measures of Association for nominal variables (cont) 2 Discordant pairs: when performing bivariate analysis of ordinal variables, a relationship in which the values of the independent variable is higher in one case than in another, comparison case, while the value of the dependent variable is lower.  =(C-D)/(C+D)), where C is the number of concordant pairs and D the number of discordant pairs

Other measures of Association for nominal variables (cont) 6 Tied pairs: when performing bivariate analysis of ordinal variables, a relationship in which the values of the independent or dependent variable in one case is identical to one of the corresponding values in another, comparison case. Tied pairs do not factor in the computation of  Skills 4, p. 308 Computation of  :  =(C-D)/(C+D)) C=2,D=2   =0  weak association P determining the nature of the pairs

Other measures of Association for nominal variables (cont) 5 Avoiding common pitfalls (p. 314) THURS 6/20: Hw/ Skills 6, 7 p p. 337/ 1,3,5 Hand in /p. 337/ #2, p. 341/#11 (do not do the portion of 11 that deals with control variables)