Presentation on theme: "Association Between Two Variables Measured at the Nominal Level"— Presentation transcript:
1Association Between Two Variables Measured at the Nominal Level Chapter 13Association Between Two Variables Measured at the Nominal Level
2Nominal Level Measures of Association It is always useful to compute column percentages for bivariate tables.But, it is also useful to have a summary measure – a single number – to indicate the strength of the relationship. That’s what we’ll learn about in this chapter.
3Nominal Level Measures of Association For nominal level variables, there are two commonly used measures of association:Phi or Cramer’s VLambda
4Nominal Measures: PhiPhi is used for 2x2 tables.The formula for Phi:
5Nominal Measures: Cramer’s V Cramer’s V is used for tables larger than 2x2.Formula for Cramer’s V:
6SPSS: Phi and Kramer’s V SPSS has both instructions combined into oneYou need to know which one appliesPhi if it’s a 2 x 2 tableKramer’s V for any other cross tabulation
7Strength of Phi or Kramer’s V ValueStrengthBetween 0.0 and 0.10WeakBetween 0.10 and 0.30ModerateGreater than 0.30Strong
8Let’s ask SPSS to calculate a few chi square based measures Class and happinessAger3 and grassAger3 and attendAttend and grassAttend and happy
9Nominal Measures: Lambda Like Phi and Kramer’s V, Lambda is used to measure the strength of the relationship between nominal variables in bivariate tables.Unlike Phi, Lambda is a PRE(proportional reduction of error) measure and its value has a more direct interpretation.While Phi is only an index of strength, the value of Lambda tells us the improvement in predicting Y while taking X into account.
11Lambda as PRE measureE1 = errors made in predicting the dependent variable without knowing the independent variable = N – largest row totalE2 = For each column, subtract the largest cell frequency from the col. total and add those valuesThis will become more clear when we look at an example
12Association and Bivariate Tables To compute λ, we must first find E1 and E2:E1 = N – largest row total = 44 – 22 = 22E2 = For each column, subtract the largest cell frequency from the col. total = (27 – 17) + (17 – 12) = = 15Lambda = (E1-E2)/E1 = (22-15)/22 = 7/22 = .32Low Author.HighAuthor.TotalsLow Efficiency101222High Efficiency1752744
13Nominal Measures: Lambda Lambda is a PRE measure.A Lambda of .32 means that knowing authoritarianism (X) increases our ability to predict efficiency (Y) by 32%.
14The Limitations of Lambda Lambda gives an indication of the strength of the relationship only.It does not give information about pattern.To analyze the pattern of the relationship, use the column %s in the bivariate table.When the mode is the same in each column of the independent variable, lambda will be zero even if a relationship exists. Thus we request both lambda and Kramer’s V/Phi.
15Calculate lambda for this example. Low Author.HighAuthor.TotalsLow Efficiency2 (7%)8 (47%)10(23%)High Efficiency25 (93%)9 (53%)34(77%)27(100%)17(100%)44(100%)