2. Measures of association - Lambda The U.S. Census Bureau collects information about households and family living quarters, including data on the number of family households with children under the age of 18, the type and race of the family, and the presence of parents in the household. The following table shows the presence of parents in the household by the race of the family. (Fictitious data, based on actual data from 2012 U.S. Census. Data values are x 1,000.) Race (X) Parent Presence (Y) Black White Asian Totals Both parents present 4,622 40,425 2,825 47,872 At least one parent absent 6,650 15,721 475 22,846 TOTALS 11,272 56,146 3,300 70,718 Suppose you are interested in the possible association between family type and race. You decide to use the measure lambda to assess the strength of the relationship. Recall that you calculate lambda by finding two quantities: the number of prediction errors made by ignoring the independent variable (E1 ) and the number of prediction errors made while taking the independent variable into account (E2). The following steps will walk you through the calculation of lambda for this table: Step 1: Find Ej by subtracting the largest row subtotal from the total number of cases (N). E, = Step 2: For each column, subtract the largest cell frequency in the column from the column total. Complete the following table with the correct values: Column Largest cell frequency Column total - largest cell frequency Step 3: Add up the values you found for the final row of the table in Step 2. The result is Ez = Step 4: Subtract Ez from El . El - Ez = Step 5: Divide the quantity you found in Step 4 by E1. The result is lambda = This result indicates a relationship between parent household presence and race. According to the proportional reduction in error or PRE, interpretation, taking race into account would improve predictions of parent household presence by