Combining wilcoxon tests with censored data: An application to well water contamination

A sampled data set can often be classified into several groups, say K , defined by covariates. While within each group it is usually reasonable to assume that the observations are homogeneous, group effects are frequently far from being negligible. Suppose it is of interest to compare two treatments non‐parametrically. A rank test is naturally called for within each group. However, the group effects, in location as well as in scale, prevent the rank test from being carried out with pooled data across the groups. A suitable way to compare treatments is to combine the K independent rank tests, one from each group. The key to such a combining procedure is a good weighting scheme which typically is a function of the sample sizes and sample dispersion. In order to use the combined statistic for testing, the weights need to be consistent so that inferences can be made based on the asymptotic null distribution of the combined test statistic. However, when there are censored observations, non‐parametric consistent estimators of dispersion parameters are usually nonexistent because of the lack of tail information. Zhang offered a method of accommodating the consistency problem through estimating the ratios of group dispersion parameters. The consistency of the weights are supported by the consistency of the quantile estimation based on Kaplan–Meier estimators. The purpose of this paper is twofold. First, of statistical interest, it is to illustrate the application of the general method proposed by Zhang with some well water contamination data. Second, of environmental interest, it is shown that application of fertilizer increases the level of nitrate contamination in water from shallow wells.