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• To invoke the ANOVA dialog, select Detect Differentially Expressed Genes in the Analysis section of the Gene Expression workflow
• In the Experimental Factor(s) panel, select Type, Tissue and Subject by pressing <Ctrl> and left clicking each factor
• Use the Add Factor > button to move the selections to the ANOVA Factor(s) panel
• To specify the interaction, select Type and Tissue by pressing <Ctrl> and left clicking each factor. Select the Add Interaction > button to add the Type * Tissue interaction to the ANOVA Factor(s) panel (Figure 1). Do NOT select OK or Apply. We will be adding contrasts to this ANOVA in an upcoming section of the tutorial. 
  
  

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SubtitleText Configuring ANOVA factors and interactions AnchorName ANOVA Configuration

Random vs. Fixed Effects – Mixed Model ANOVA

Most factors in ANOVA are fixed effects, whose levels in a data set represent all the levels of interest. In this study, Type and Tissue are fixed effects. If the levels of a factor in a data set only represent a random sample of all the levels of interest (for example, Subject), the factor is a random effect. The ten subjects in this study represent only a random sample of the global population about which inferences are being made. Random effects are colored red on the spreadsheet and in the ANOVA dialog. When the ANOVA model includes both random and fixed factors, it is a mixed-model ANOVA.

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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 effect. By doing that, the ANOVA will automatically know which factors to treat as random and which factors to treat as fixed.

Nested/Nesting Relationships

The subject factor in the ANOVA model is listed as “8. Subject (6. Type)” this means that Subject is nested in Type. PGS can automatically detect this sort of hierarchical design and will adjust the ANOVA calculation accordingly.

Linear Contrasts 

By default, an ANOVA only outputs a p-value for each factor/interaction. To get the fold change and ratio between Down syndrome and normal samples, a contrast must be set-up.

• Select Contrasts… to invoke the Configure dialog
• Choose 6.Type from the Select Factor/Interaction drop-down list. The levels in this factor are listed on the Candidate Level(s) panel on the left side of the dialog
• Left click to select Down Syndrome from the Candidate Level(s) panel and move it to the Group 1 panel (renamed Down Syndrome) by selecting Add Contrast Level > in the top half of the dialog. Label 1 will be changed to the subgroup name automatically, but you can also manually specify the label name 
• Select Normal from the Candidate Level(s) panel and move it to the Group 2 panel (renamed Normal) 
• The Add Contrast button can now be selected (Figure 2)
  
  

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SubtitleText Adding a contrast of Down Syndrome and Normal samples AnchorName Configuring ANOVA Contrasts

Because the data is log₂ transformed, PGS will automatically detect this and will automatically select Yes in the Data is already log transformed? at the top right-hand corner. PGS will use the geometric mean of the samples in each group to calculate the fold change and mean ratio for the contrast between the Down syndrome and Normal samples.

• Select Add Contrast to add the Down Syndrome vs. Normal contrast 
• Select OK to apply the configuration
• If successfully added, the Contrasts… button will now read Contrasts Included (Figure 3)
  
  

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SubtitleText ANOVA configuration with contrasts included AnchorName ANOVA Configuration with Contrasts

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The result will be displayed in a child spreadsheet, ANOVA-3way (ANOVAResults). In the child result spreadsheet, each row represents a gene, and the columns represent the computation results for that gene (Figure 4). By default, the genes are sorted in ascending order by the p-value of the first categorical factor. In this tutorial,Type is the first categorical factor, which means the most highly significant differently expressed gene between Down syndrome and normal samples is at the top of the spreadsheet in row 1.

 

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SubtitleText ANOVA spreadsheet AnchorName ANOVA Spreadsheet

For additional information about ANOVA in PGS, see Chapter 11 Inferential Statistics in the User’s Manual (Help > User’s Manual).

Viewing the Sources of Variation

Deciding which factors to include in the ANOVA may be an iterative process while you decide which factors and interactions are relevant as not all factors have to be included in the model. For example, in this tutorial, Gender and Scan date were not included.  The Sources of Variation plot is a way to quantify the relative contribution of each factor in the model towards explaining the variability of the data.

• View the sources of variation for each of the factors across the whole genome by clicking Plot Sources of Variation from the Analysis section of the Gene Expression workflow with the ANOVA result spreadsheet active
• A Sources of Variation tab will appear (Figure 5) with a bar chart showing the signal to noise ratio for each factor. Sources of variation can also be viewed as a pie chart showing sum or squares by selecting the Pie Chart (Sum of Squares) tab in the upper left-hand side of the Sources of Variation tab
  
  

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• Right-click on a row header in the ANOVA spreadsheet (Figure 6)
• Select ANOVA Interaction Plot from the options to generate an Interaction Plot tab for that individual gene
  
  

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SubtitleText Calling an ANOVA Interaction Plot for a gene AnchorName Calling ANOVA Interaction Plot

Generate these plots for rows 3 (DSCR3) and 8 (CSTB). If the lines in this plot are not parallel, then there is a chance there is an interaction between Tissue and Type. DSCR3 is a good example of this (Figure 7). We can look at the p-values in column 9, p-value(Type * Tissue) to check if this apparent interaction is statistically significant. 

 

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SubtitleText Interaction Plot for DSCR3 AnchorName Interaction Plot

Create Gene List

Now that you have obtained statistical results from the microarray experiment, you can now take the result of 22,283 genes and create a new spreadsheet of just those genes that pass certain criteria. This will streamline data management by focusing on just those genes with the most significant differential expression or substantial fold change. In PGS, the List Manager can be used to specify numerous conditions to use in the generation of our list of genes of interest. In this tutorial, we are going to create a gene list with a fold change between -1.3 to 1.3 with an unadjusted p-value of < 0.0005. 

• Invoke the List Manager dialog by selecting Create Gene List in the Analysis section of the Gene Expression workflow
• Ensure that the 1/ANOVA-3way (ANOVAResults) spreadsheet is selected as this is the spreadsheet we will be using to create our new gene list as shown (Figure 8)
• Select the ANOVA Streamlined tab. In the Contrast: find genes that change between two categories panel, choose Down Syndrome vs. Normal and select Have Any Change from the Setting dropdown menu list. This will find genes that have a fold change different between the types of samples
• In the Configuration for “Down Syndrome vs Normal” panel, check that Include size of the change is selected and enter 1.3 into Fold change >  and -1.3 in OR Fold change <
• Select Include significance of the change, choose unadjusted p-value from the dropdown menu, and < 0.0005 for the cutoff. The number of genes that pass your cutoff criteria will be shown next to the # Pass field. In this example, 23 genes pass the criteria. 
• Set Save the list as A, select Create, and then select Close to view the new gene list spreadsheet
  
  

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You should take some time creating new gene list criteria of your own to become familiar with the List Manager tool in PGS. For more information, you can always click on the () buttons.

Generating Gene Lists from a Volcano Plot

Next, we will generate a list of genes that passed a p-value threshold of 0.05 and fold-changes greater than 1.3 using a volcano plot.

• Select the 1/ANOVA-3way (ANOVAResults) spreadsheet in the Analysis tab. Thisis the spreadsheet we will be using to create the gene list
• Select View > Volcano Plot from the PGS main menu (Figure 9)
  
  

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SubtitleText Generating a Volcano Plot from ANOVA results AnchorName Generating Volcano Plot

• Set X Axis (Fold-Change) to 12. Fold-Change(Down Syndrome vs. Normal), and the Y axis (p-value) to be 110. p-value(Down Syndrome vs. Normal)
• Select OK to generate a Volcano Plot tab and for genes in the ANOVA spreadsheet (Figure 10)
  
  

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SubtitleText Volcano plot generated from ANOVA spreadsheet AnchorName Volcano Plot

In the plot, each dot represents a gene. The X-axis represents the fold change of the contrast, and the Y-axis represents the range of p-values. The genes with increased expression in Down syndrome samples on the right side; genes with reduced expression in Down syndrome samples are on the left of the N/C line. The genes become more statistically significant with increasing Y-axis position. The genes that have larger and more significant changes between the Down syndrome and normal groups are on the upper right and upper left corner. 

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• Select Rendering Properties ()
• Choose the Axes tab
• Check Select all points in a section to allow PGS to automatically select all the points in any given section
• Select the Set Cutoff Lines button and configure the Set Cutoff Lines dialog as shown (Figure 11)
  
  

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SubtitleText Setting cutoff lines for -1.3 to 1.3 fold changes and a p-value of 0.05 AnchorName Set Cutoff Lines

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• Right-click on the selected region in the plot and choose Create List to create a list including the genes from the section selected (Figure 12). Note that these p-values are uncorrected
  
  

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• Specify a name for the gene list (example: volcano plot list) and write a brief description about the list. The description is shown when you right-click on the spreadsheet > Info > Comments. Here, I have named the list "volcano plot list" and described it as "Genes with >1.3 fold change and p-value <0.05" (Figure 13). 

 The list can be saved as a text file (File > Save As Text File) for use in reports or by downstream analysis software.

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