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Microarray is a widely used high-throughput biotechnology. It measures the expression levels of thousand of genes at the same time. The methods to test individual genes have been well developed. Nowadays, multiple independent microarray datasets may be available for studying one relevant research question. A major question in data analysis is to find the concordance or relationships between two a priori unrelated classifications of biological separate items. This is difficult because the datasets may be in different tissues, different platforms or different species. To answer this affinity question, various methods have different sensitivities. The unsupervised clustering and supervised classification methods have been used as well as the recent more general transcriptional signatures score calculation and gene set tests. Gene set tests relate independent datasets with high sensitivity. They test genes by prior-defined sets. There are at least two types of null hypotheses of gene set tests. They are competitive null hypotheses and self-contained null hypotheses. Competitive tests test gene sets relative to other genes which are not in the set. Self-contained tests test whether at least some of the genes in the set are significantly differentially expressed, and not relative to other genes. Most available competitive methods unrealistically assume independence of genes in array data. Most available self-contained tests are limited by sample sizes and experimental designs. In the first half of this thesis, statistical methods of both types are developed that have good power and hold the correct false positive rate. To properly test a competitive hypothesis, while accommodating gene-wise correlations, a correlation adjusted Mean Rank based test, called CAMERA, is proposed. To test a self-contained hypothesis in small complex-designed microarray datasets, ROAST is developed based on rotation, a Monte-Carlo simulation technology for multivariate regression models, to get