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Microarray data often consist of a large number of genes and a
small number of replicates. We have examined testing the null hypothesis
of equality of mean for detecting differentially expressed genes. The
p-value for each gene is often estimated using permutation samples not
only for the target gene but also for other genes. This method has been
widely used and discussed. However, direct use of the permutation method
for the p-value estimation may not work well, because two types of genes
are mixed in the sample; some genes are differentially expressed,
whereas others are not. To overcome this difficulty, various methods for
appropriately generating null permutation samples have been proposed. In
this paper, we consider two classes of test statistics that are
naturally modified to null statistics. We then obtain the uniformly most
powerful (UMP) unbiased tests among these classes. If the underlying
distribution is symmetric, the UMP unbiased test statistic is similar to
that proposed by Pan (2003). Under another condition, the UMP unbiased
test statistic has a different formula with one more degree of freedom
and therefore is expected to give a more powerful test and a more
accurate p-value estimation from a modified null statistic. In
microarray data, because the number of replicates is often small,
differences in the degree of freedom will produce large effects on the
power of test and the variance of the p-value estimation. Some
simulation studies and real data analyses are illustrated to investigate
the performances of the methods.

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