Analyze the data in Table 4.12, p. 127, using the methods for 2x2xK tables in Ch
ID: 3206849 • Letter: A
Question
Analyze the data in Table 4.12, p. 127, using the methods for 2x2xK tables in Chapter
2 to test the hypothesis that merit pay is independent of race, controlling for the
potential differences due to district.
(a) Report the conditional odds ratios and their 95% condence intervals.
(b) Report the marginal odds ratio and determine whether Simpson's paradox is
present.
(c) Perform the Breslow-Day and Cochran-Mantel-Haenszel tests. Write down their
null and alternative hypotheses and interpret the results.
**iF YOU WANT THE DATA IN SAS CODE I CAN PROVIDE IT, JUST COMMENT
Table 4.12. Data for Problem 4.15 on Merit Pay and Race Blacks, Merit Pay Whites, Merit Pay No Yes Yes District No 47 NC 12 45 10 NE NW SE 16 10 54 59 SW 12 Source: J. Gastwirth, Statistical Reasoning in Lawand Public Policy, Vol. 1, 1988, p. 268.Explanation / Answer
Common odds ratio 2.16578
MHC statistic DF P-Value
6.97974 1 0.0082437
Binary Logistic Regression: Yes, Grand Total versus Race, District
Link Function: Logit
Response Information
Variable Value Count
Yes Success 324
Failure 78
Grand Total Total 402
Logistic Regression Table
Odds 95% CI
Predictor Coef SE Coef Z P Ratio Lower Upper
Constant 0.749472 0.295814 2.53 0.011
Race
White 0.791285 0.285318 2.77 0.006 2.21 1.26 3.86
District
NE 0.258368 0.420667 0.61 0.539 1.29 0.57 2.95
NW 0.138364 0.405170 0.34 0.733 1.15 0.52 2.54
SE 0.120871 0.372868 0.32 0.746 1.13 0.54 2.34
SW 0.0044501 0.384864 0.01 0.991 1.00 0.47 2.14
Log-Likelihood = -193.493
Test that all slopes are zero: G = 8.594, DF = 5, P-Value = 0.126
Goodness-of-Fit Tests
Method Chi-Square DF P
Pearson 2.13966 4 0.710
Deviance 2.07098 4 0.723
Hosmer-Lemeshow 0.83725 5 0.975
Table of Observed and Expected Frequencies:
(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)
Group
Value 1 2 3 4 5 6 7 Total
Success
Obs 31 31 47 59 54 57 45 324
Exp 29.9 32.1 48.6 58.5 53.8 55.6 45.5
Failure
Obs 13 14 12 12 10 9 8 78
Exp 14.1 12.9 10.4 12.5 10.2 10.4 7.5
Total 44 45 59 71 64 66 53 402
Measures of Association:
(Between the Response Variable and Predicted Probabilities)
Pairs Number Percent Summary Measures
Concordant 12791 50.6 Somers' D 0.19
Discordant 7959 31.5 Goodman-Kruskal Gamma 0.23
Ties 4522 17.9 Kendall's Tau-a 0.06
Total 25272 100.0