Less Conservative Distribution-free Confidence Intervals and Tests for the Median

抄録

The sign test is a best known statistical technique to make inferences about the population median, and has been applied in various research fields. A confidence interval is also easily obtained by inverting the test. In spite of their wide applicability the sign test and the confidence interval still have several problems. One notable difficulty is the conservativeness of confidence intervals in the sense that the actual confidence coefficients are greater than the nominal value. The inconsistency between testing and estimation in the presence of ties is another problem.
The aim of the present paper is to propose a modified procedure to reduce such difficulties. In constructing confidence intervals, the mid-P value is also taken into account in addition to the usual P-value. Consequently, our modified intervals have actual confidence coefficient closer to the nominal value than those obtained by the conventional method. A modification of usual sign test is also introduced, which is consistent with the interval estimation. Modified confidence intervals obtained by inverting the Wilcoxon signed rank test and the Wilcoxon-Mann-Whitney rank sum test are also discussed.