Robust Permutation Tests for Matched-Pairs Designs
提出一种分支定界算法，无需枚举整个参考分布即可计算配对设计中的置换P值，并研究了基于截尾均值的置换检验，发现适度截尾均值可显著减小P值和置信区间宽度。
A branch-and-bound algorithm is described for finding the permutation (randomization) P value in matched-pairs designs without enumeration of the entire reference distribution. It is not restricted to test statistics that are linear in functions of the observations, and permutation tests based on trimmed means are investigated. We apply the algorithm to six examples, demonstrating that the use of a moderately trimmed, instead of an untrimmed, mean can sometimes lead to substantially smaller P values and shorter confidence intervals. Confidence intervals are obtained by trial-and-error inversion of the P value. Permutation tests arise in randomization inference, though they can be applied to nonrandomized studies. Under the randomization model, permutation tests are exact, giving the correct probability of a Type I error, without distributional assumptions. The observed test statistic is compared with the reference set of test statistics that would occur under all possible randomizations. Thus inference is based on the known randomization distribution. This robustness of validity, however, does not necessarily carry over to robustness of efficiency. The mean pair difference, the test statistic often suggested for permutation analysis of matched-pairs designs, is well known to lack robustness to outliers and long-tailed distributions. With a trimmed mean, however, robustness of efficiency also appears possible. Trimming two observations from each tail performs well, relative to no trimming, in the six examples studied. This stretegy reduces a one-sided P value of .380 (no trimming) to .028 in a 14-pair example comparing fault rates on telephone equipment. The width of the 95% confidence interval is similarly reduced, by 42%. In the largest example, a cloud-seeding experiment with 37 pairs, the width of the 95% confidence interval for the effect of seeding is reduced by 24%. Thus gains in efficiency large enough to be of practical interest appear possible.