In this paper,Scheffé and Simplified Scheffé simultaneous confidence intervals are firstconstructed for mean difference of several multivariate normal distributions.Then the authors theoreticallyprove that w...In this paper,Scheffé and Simplified Scheffé simultaneous confidence intervals are firstconstructed for mean difference of several multivariate normal distributions.Then the authors theoreticallyprove that when there are only two populations,Bonferroni bounds and Simplified Scheffébounds are the same and they are shorter than Scheffé bounds for p10.In the case for 3k10and 2p10,there exists n(p,k)such that Bonferroni method is better than Simplified Schefféprocedure for nn(p,k),otherwise Simplified Scheffé procedure is better.Finally,the authors findout that neither of Scheffé critical values nor Simplified Scheffé critical values are always larger thananother through numerical calculation.展开更多
Comparing two samples about corresponding parameters of their respective populations is an old and classical statistical problem. In this paper, we present a simple yet effective tool to compare two samples through th...Comparing two samples about corresponding parameters of their respective populations is an old and classical statistical problem. In this paper, we present a simple yet effective tool to compare two samples through their medians. We calculate the confidence of the statement “the median of the first population is strictly smaller (larger) than the median of the second.” We analyze two real data sets and empirically demonstrate the quality of the confidence for such a statement. This confidence in the order of the medians is to be seen as a pre-analysis tool that can provide useful insights for comparing two or more populations. The method is entirely based on their exact distribution with no need for asymptotic considerations. We also provide the Quor statistical software, an R package that implements the ideas discussed in this work.展开更多
基金supported by the Natural Science Foundation of China under Grant No.70671043
文摘In this paper,Scheffé and Simplified Scheffé simultaneous confidence intervals are firstconstructed for mean difference of several multivariate normal distributions.Then the authors theoreticallyprove that when there are only two populations,Bonferroni bounds and Simplified Scheffébounds are the same and they are shorter than Scheffé bounds for p10.In the case for 3k10and 2p10,there exists n(p,k)such that Bonferroni method is better than Simplified Schefféprocedure for nn(p,k),otherwise Simplified Scheffé procedure is better.Finally,the authors findout that neither of Scheffé critical values nor Simplified Scheffé critical values are always larger thananother through numerical calculation.
文摘Comparing two samples about corresponding parameters of their respective populations is an old and classical statistical problem. In this paper, we present a simple yet effective tool to compare two samples through their medians. We calculate the confidence of the statement “the median of the first population is strictly smaller (larger) than the median of the second.” We analyze two real data sets and empirically demonstrate the quality of the confidence for such a statement. This confidence in the order of the medians is to be seen as a pre-analysis tool that can provide useful insights for comparing two or more populations. The method is entirely based on their exact distribution with no need for asymptotic considerations. We also provide the Quor statistical software, an R package that implements the ideas discussed in this work.
