Nested ANOVA
(This feature is only available in GenEx Pro/Enterprise)
Theory
A nested experimental design is when the levels of one of the studied factors are similar, but not identical for different levels of another factor. An example of a nested design is a typical qPCR analyses. When performing qPCR analysis, the samples are typically prepared in a number of steps before it is analyzed with qPCR, e.g. sample extraction from several animals (subjects) followed by reverse transcription (RT). Each preparation step introduces variance to the final qPCR data which can be reduced by performing replicates in each step. One could have 3 subjects and take 3 samples for each subject. Each sample is used in 3 RT reactions, and finally each RT tube is split into 3 qPCR tubes. This makes up a 3x3x3x3 nested design with all and all 81 qPCR reactions (see figure). The variance contribution of each factor can be estimated with Nested ANOVA.
How to
Enter the data in the Data editor. It can have 2-3 classification columns specifying the 2-3 factors nested into each other, and include one or several different genes. The classification number must be unique for each set of replicates in each column, which means that you cannot have several "nr 1" sets of replicates in a column. Also, the data must be balanced, which means that there must be the same number of replicates for each level of each factor. In the example given above, this would mean the same number of samples taken from each subject, the same number of RT replicates for each sample, and the same number of qPCR replicates for each RT tube. To estimate the variance contribution in a step, there must be at least two replicates in that level.
To analyze the data, press the Nested ANOVA button in the Statistics tab in to top of the main window.
This will open the analysis in the Control panel where you choose the genes that you want to analyze and which of the classification columns that represent the different factors. If you have only two factors in your design, select None in the Upper level drop-down list. There are check boxes that let you customize the output of the analysis. To see the results, press the Run button down at the right and the selected output is displayed one table/plot type per selected gene.
If the ANOVA table check box is ticked, a table is displayed with sums of squares (SS), degrees of freedom (df), mean sums of squares (MS), F-statistics (F), and p-values. A low p-value indicates that there is a significant difference between the units on the given level nested within their respective upper level units.
There are also two types of variance contribution plots. One that shows the absolute values of the variance contributions, and one that shows them as percent of total variation.
The variance contribution plots can be used to see how the variance changes when the data is normalized with reference gene. Perform the analysis for unnormalized data without the reference genes first, and then for the normalized data and compare the plots to see if the total variance is decreased.
Warning: Do not use 0 (zero) in the classification columns that defines the groups.