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Question 1: Contingency tables allow us to examine data from two categorical variables (at the nominal or ordinal levels of measurement) and in some cases provide us with useful descriptive statistics to examine the intersections of those data. However, we are also interested in relationships, and a number of measures of association are available to us aid in our understanding of relationships. With that in mind, discuss the calculation of the chi-square test statistic, and note (generally) what the results of a chi-square test tell us about the relationship.
Next, provide a brief explanation of the concept of proportional reduction in error (PRE), and outline what we can learn from the test statistic for PRE tests like gamma, Kendall's tau-b, and tau-c. Finally, provide an interpretation of the values of the chi-square and PRE measures of association and significance levels in Table 1.1 below. (Note: In your interpretation, you can assume we're using the same variable names from earlier group projects: patient perception of general health and satisfaction with health care services ... you're also free to create your own plausible relationship for the purposes of the discussion. Bonus points for humor.).
Table 1.1. Calculated Measures of Association
Test
Value
Significance
Chi-square
42.45
0.000
gamma
0.502
Kendall's tau-b
0.323
Kendall's tau-c
0.249
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