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It has been observed that means are related to variances in microarray experiments; usually genes with high expression level show high variances, while genes with low expression level display small variances (Figure 1).
Microarray experiments usually involve a large number of genes, with variance components varying greatly across the genes.
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First, the samples prepared for microarray experiments are usually a mixture of cells from different tissues and, possibly, at different points of a cell cycle or developmental stage.
Ordinarily, given a random sample, we assume that we can generalize the results and conclusions drawn from the sample to the population; however, the sample size for microarray experiments is usually small.
Despite the effectiveness of the technology, microarray experiments are usually done with very few replicates due to budgetary constrains, which often results in high false positive (Type I error) and false negative rates (Type II error).
Circadian microarray experiments are usually designed to collect data every 4 h over a course of 48 h, generating expression profiles with 12 or 13time-pointstime-pointsnd Ueda, 2007).
Microarrays are well suited for this task as they are a high-throughput method for determining the expression of tens of thousands of genes in parallel [ 6]. Results of microarray experiments are usually validated by applying low-throughput methods for measuring gene expression, e.g. qPCR or Northern blots [ 7], or confirmed with protein assays like Western blots.
Furthermore, comparing to the large number of genes (variables) measured by microarray experiments, sample sizes are usually too small to give enough statistical power.
Coexpression data, derived from microarray experiments for example, are usually carried out to discover disease-related genes based on the assumption that the coregulated genes from expression data are considered functionally related.
In fact, the limitation of resources and high cost of the microarray experiments make the sample sizes usually much smaller relative to the number of considered genes, which results in the decrease of the statistical power (SP), high false positive rate (FPR), and the enlargement of sample's error [10].
In microarray experiments, the end-stage analysis usually consists of simple two-sample test statistics such as the t-statistic or the Wilcoxon Rank Sum test statistic to test for differential expression.
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