Association Between Variables Measured at Nominal Level Chisquare

Association Between Variables Measured at Nominal Level Chi-square Based Measures of Association ¡ Proportional Reduction in Error (Pre) ¡ A Pre Measure for Nominal-level Variables: Lambda ¡ The Computation of Lambda ¡ The Limitations of Lambda ¡

¡ Cramer's V A chi square-based measure of association. appropriate for nominally measured variables that have been organized into a bivariate table of any number of rows and columns. ¡ proportional reduction in error (PRE) The logic that underlies the definition and computation of lambda.

¡ lambda A measure of association appropriate for nominally measured values that have been organized into a bivariate table. ¡ Phi A chi square-based measure of association.

¡ E 1 For lambda, the number of errors of prediction made when predicting which category of the dependent variable cases will fall into while ignoring the independent variable. ¡ E 2 For lambda, the number of errors of prediction made when predicting which category of the dependent variable cases will fall into while taking account of the independent variable.

Measures of Association Chi-Square Based ¡ Phi ¡ Cramer's V Proportional Reduction in Error (PRE) ¡ Lambda

Chi Square-based Measures of Association Phi - easy to compute. ¡ Cramer’s V - used for larger tables. ¡ Limitation Absence of a direct or meaningful interpretation for values between the extremes of 0. 00 and 1. 00. ¡

Steps in PRE Measures of Association 1. 2. 3. Attempt to predict the category into which each case will fall on Y while ignoring X. Predict the category of each case on Y while taking X into account. The stronger the association between the variables the greater the reduction in errors.

PRE Measure for Nominal Values: Lambda The improvement for predicting the dependent variable with knowledge of the independent. as compared to ¡ Predicting the dependent without knowledge of the independent. ¡

Limitations of Lambda Asymmetric - the value of the statistic will vary, depending on which variable is taken as independent. ¡ Misleading when one of the row totals is much larger than the others. ¡