Chapter 10 - Part III

Chapter 10 - Part III - Association in (r x c) tables : In...

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Association in (r x c) tables : In the last lecture we learnt how the difference of and the ratio of can be used to measure the strength of association in contingency tables. Basically, these measures compare the (or probabilities) for a particular response over the categories of the explanatory variables. These measures can be generalized to tables which have more than 2 rows and/or columns. For such tables, these measures compare the proportions for a particular response categories for various pairs of the categories of the explanatory variables. Eg : A general social survey, conducted in 1991 probed the relationship between job satisfaction and income for a sample of Americans . Here was the response variable having categories : Dissatisfied, Moderately satisfied, Very satisfied. On the other hand, is the explanatory variable having categories : < $ 5000, $ 5000 - 25,000, > 25,000
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We have the following contingency table : Income Job satisfaction Total Dissatisfied Moderately satisfied Very satisfied < 5000 6 (0.273) 13 (0.591) 3 (0.136) 22 5000 – 25,000 9 (0.155) 37(0.638) 12(0.207) 58 > 25,000 3(0.125) 13(0.542) 8 (0.333) 24 Total 18 63 23 104 The values in the brackets refer to the conditional proportions for each cell. Let us first consider the “very satisfied” response category. The difference between the proportions in this category for the “< 5000” and “> 25,000” categories of income is Thus, individuals with income tend to be satisfied with their jobs than those with income. Now consider the “moderately satisfied” category of job satisfaction. The difference between the proportions in this category for the “5000 – 25,000” and “> 25,000” categories of income is . Thus, individuals with income above $ 25,000 tend to have a general satisfaction with their jobs
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than those with income between $ 5000 and $ 25,000 (this is interesting!!) Now, let us look at the relative risk values for the different categories. Suppose we consider the “dissatisfied” category. The relative risk of this outcome comparing the “ < 5000” and “ > 25,000” categories of income is . Thus, the estimated proportion of subjects who are dissatisfied with their jobs is more than for those with income “< 5000” than those with incomes “ > 25,000”. None of the difference of proportions values were very high – this implies that maybe associated with BUT the association is NOT very strong. As mentioned in the last lecture, a large value of the statistic (hence a small ) doesnot necessarily implies association between two variables – it only means that the two variables are associated, nothing more. Infact, for a given of association (between two variables), larger Chi – square values occur for larger – this means that even if two variables are associated, the resulting Chi
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square statistic may be if the sample sizes are Eg : Let us go back to the “roles of women” dataset. The following three hypothetical tables relate the
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This note was uploaded on 04/18/2008 for the course EXP 3116 taught by Professor Fasig during the Spring '08 term at University of Florida.

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Chapter 10 - Part III - Association in (r x c) tables : In...

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