For square contingency tables, Iki, Tahata and Tomizawa (2011) considered the measure to represent the degree of departure from the marginal homogeneity model. Using the first-order term in the Taylor series expansion, the estimated measure with the cell probabilities replaced by the corresponding sample proportions is an approximately unbiased estimator when the sample size is large. The present paper proposes the improved approximate unbiased estimator of the measure which is obtained by using the second-order term in the Taylor series expansion. Also, it shows that the improved estimator approaches to the true measure faster than the original estimator as the sample size becomes larger by the simulation studies.
An abundance of data from microarray studies are available in publicly-accessible databases. Most of these studies are conducted by university based research labs. It is not uncommon for such studies to run only three or four replicates for each experimental condition tested. With this low sample size and the high variability and multiple testing problems inherent to microarray technology, it is difficult to draw statistically significant conclusions from any one such study. Meta-analysis could improve this situation by combining evidence from related studies to increase statistical power. In this work we discussed several meta-analysis methods for small sample gene expression studies. We compared the performances of the traditional Fisher’s log-sum and Stouffer’s- Z meta-analysis methods, as well as three weighted variants of Stouffer’s method. Higher false discovery rates were observed for the traditional methods compared to the weighted methods.
Network data have become very popular with the growth of technologies and social applications such as Twitter and Facebook. However, few visualization tools have been created for exploring large-scale networks. We propose a simple and quick procedure to explore a network in this study. The algorithm changes the edge representation based on the complement of a simple graph and the partition method of vertex coloring. Furthermore, the colors provide additional information on top of the partitions. Our proposed method is demonstrated in some famous networks.
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