Measures of Association for contingency tables 4 Figure

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 • =(E 1 -E 2)/(E 1), where E 1 is the number of errors you would make guessing the dependent variable if you did not know the independent variable, and E 2 the number of errors you would make guessing the dependent variable if you knew the categories of the independent variable. • To find E 1, subtract the largest row marginal total from N • To find E 2, 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 ch 8 sk 2] • 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. 309 -312 determining the nature of the pairs

Other measures of Association for nominal variables (cont) • • • Avoiding common pitfalls (p. 314) THURS 6/20: Hw/ Skills 6, 7 p. 315 -16 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) 5