Multiple Mean Comparison for Gene Expression Data via F -Type Tests under High Dimension with A Small Sample Size |Biomedgrid

Multiplicity of data is very common in medical studies when experimental subjects are treated under different treatments. When there are multiple measurements on each subject and the number of subjects is limited, the multiple comparison among different treatments is facing with the problem of high dimension with small sample sizes, or even the total sample size across all treatments is less than the number of measurements. Traditional methods such as the multivariate analysis of variance for multiple mean comparison is going to lose power or becoming inapplicable when the total sample size is approaching to the data dimension. In this paper we propose to use Läuter's F -type tests and Liang and Tang's generalized F -tests for high- dimensional multiple mean comparison. Both of these two types of tests are always applicable regardless of the sample size being greater or smaller than the data dimension. The practical application of these two types of tests is illustrated by some real datasets consisting of gene expression data of multiplicity. The box plots of projected data on the principal component directions are recommended as a supplementary tool for a double check of validation of the tests.