G18.9

CMV infection and coronary restenosis. Exercise 18.3 found that 43% of CMV+ experienced arterial restenosis within 6 months of atherectomy. In contrast, 8% of CMV- patients experienced a similar outcome. Table 18.8 contains observed counts.

1. Use a chi-square statistic to test the association for statistical significance.
2. Repeat the test with a z-statistic. Show the relation between the chi-square statistic and the z-statistic.

[Even though the book asks for the z test, the sample size requirements are not met for the z test. Just proceed anyway, noting the issue]

Hypotheses:

H0:

Ha: .

Assumptions:

We use Stata to compute the chi-squared test statistic and P-value: . tabi 21 28\2 24, chi2 expected

| Key | I I I frequency I I expected frequency | + + | col row I 1 2 | Total + + 1 | 21 28 | 49 | 15.0 34.0 | 49.0 + + 2 | 2 24 | 26 | 8.0 18.0 | 26.0 ___________ +______________________+__________ Total | 23 52 | 75 | 23.0 52.0 | 75.0 Pearson chi2(1} 9.8791 Pr = 0.002 Two-sample test of proportions *: Number of Ohs, = 49 y: Number of gha, = 26 Mean Std. Err. Z P> IZI [95$ Conf. Interval] . 42857 . 0706959 . 2900085 . 5671315 V . 07692 . 052258 -. 0255038 . 1793438 + diff I . 35165 . 0879137 . 1793424 . 5239576 under Ho: . 1118792 3.14 0 . 002 diff = prop (x) - prop (y) Z : 3. 1431 Ho: diff = 0 Ha: diff 0 Priz |21) = 0.0017 Er (2 > 2) = 0.0008