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The purposes of this research were to develop confidence intervals for the difference of binomial proportion with the adjusted delta method, and to compare efficiency of confidence interval between the Newcombe Hybrid Score method and the adjusted Newcombe Hybrid Score method. Research methodology was simulation data in r by the situations with sample sizes, parameters of the difference of binomial proportions, and nominal level 224 conditions (28 x 4 x 2). Then to compare the efficiency, data were analyzed about coverage probability and average width of confidence interval for each method. As a result, confidence intervals for the difference of binomial proportions with the adjusted Newcombe Hybrid Score method were lower limit and upper limit when . For comparison the efficiency for both confidence intervals, it was found that the adjusted Newcombe Hybrid Score method had a greater efficiency than the Newcombe Hybrid Score method with the following conditions: (1) both equal sample case, sample sizes were more than 25 and the parameter of the difference of binomial proportions did not exceed 0.4, and (2) unequal sample case, the first sample with more than 15, the second one with more than 50 with the parameter of the difference of binomial proportions did not exceed 0.4. Therefore, confidence intervals for each methods are appropriate depending on sample size and difference of binomial proportion.
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