This thesis is divided into three sections all pertaining to microarray experimental design and analysis. Microarrays are a tool used in biological research which enables scientists to measure the relative level of expression many genes within an organism at the same time. Microarrays have also opened new research areas in statistics which are currently being investigated concerning different aspects of data normalization, experimental design, and analysis.

The first chapter entails a comparison of two commonly used experimental designs in two-dye microarray experiments. Both designs are applicable only to experiments containing treatments with two levels. One design is shown to be more powerful when constrained by the number of arrays. Also, mixed model analysis is often used for both designs. With small sample sizes, mixed model analysis is shown to give inaccurate results under certain conditions. Due to this problem, an alternative method of analysis is proposed for both experimental designs which eliminates this concern.

Two-dye microarray experiments require special consideration in design since they have multiple random effect in the model. This is because arrays are usually viewed as a random factor that should always be contained in a model for the data. Research has been done on comparing two-dye microarray experimental designs by requiring calculation of array differences. This is shown to inhibit the power of the analysis by removing inter-block information. There are also experimental designs that are viable options which can not be compared using this method. An alternative method of analysis is proposed which allows for multiple random effects in the model. Under certain conditions, this method is shown to choose designs that either would not be chosen, or cannot be considered, when using methods based on array differences.

The third chapter discusses new methods for analyzing microarray experiments by categories. Most commonly, microarray analysis is performed on a gene-by-gene basis with the goal of finding the genes whose expression differ the greatest between varieties of treatments. However, scientists often would like to know what aspect of cell life is affected most by differences in varieties. There could be cases where a group of genes pertaining to the same task are all have a mild change in expression which would not be found using gene-by-gene analysis. Two different resampling based methods are proposed for solving this problem. Both methods are compared and results are visualized on a directed acyclical graph.