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Analysis of variance (ANOVA) is a very powerful technique for identifying differentially expressed genes in a multi-factor experiment such as this one. In this data set, ANOVA will be used to generate a list of genes that are significantly different between Down syndrome and normal samples with an absolute difference bigger than 1.3 fold.

The ANOVA model should include Type because it is the primary factor of interest. From the exploratory analysis using the PCA plot, we observed that tissue is a large source of variation; therefore, Tissue should be included in the model. In the experiment, multiple samples were taken from the same subject, so Subject must be included in the model. If Subject were excluded from the model, the ANOVA assumption that samples within groups are independent will be violated. Additionally, the PCA scatter plot showed that the Downs syndrome and normal samples separated within tissue type, so the Type*Tissue interaction should be included in the model.

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You can specify which factors are random and which are fixed when you import your data or after importing by right-clicking on the column corresponding to a categorical variable, selecting Properties, and checking Random effectEffect. By doing that, the ANOVA will automatically know which factors to treat as random and which factors to treat as fixed.

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