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• Sample ID - Since multiple measurements (on the multiple genes within the functional group) come from the same sample, sample ID is added to the model, otherwise the ANOVA assumption of sample independence is violated
• Gene ID - Since not all genes in a functional group express at the same level, gene ID is added to the model to account for gene-to-gene differences
• Factor * Gene ID (optional) - Interaction of gene ID with the factor can be added to detect changes within the expression of a GO category with respect to different levels of the factor, referred to in this document as the disruption of the categories expression pattern or simply disruption

Suppose there is an experiment to find genes differentially expressed in two tissues: Two different tissues are taken from each patient and a paired sample t-test, or 2-way ANOVA can be used to analyze the data. The GO ANOVA dialog allows you to specify the ANOVA model, which includes the two factors: tissue and participant ID. The analysis is performed at the gene level, but the result is displayed at the level of the functional group by averaging of the member genes’ results. The equation of the model that can be specified is:

y = µ + T + P + ε

• y: expression of a functional group
• µ: average expression of the functional group
• T: tissue-to-tissue effect 
• P: participant-to-participant effect (a random effect)
• ε: error term

When the tissue is interacted with the gene ID then the ANOVA model becomes more complicated as demonstrated in the model below. The functional group result is not explicitly derived by averaging the member genes as the new model includes terms for both gene and group level results:

y = µ + T + P + G + T *G + S(T * P) + ε

• y: expression of a functional group
• µ: average expression of the functional group
• T: tissue-to-tissue effect
• P: patient-to-patient effect (this is a random effect)
• G: gene-to-gene effect (differential expression of genes within the function group independent of tissue type)
• T*G: Tissue-Gene interaction (differential patterning of gene expression in different tissue types)
• S (T*P): sample-to-sample effect (this is a random effect, and nested in tissue and patient)
• ε: error term