# E-learning in analysis of genomic and proteomic data 2. Data analysis 2.1. General analysis workflow 2.1.2. Class comparison (searching for differences between classes) 2.1.2.1. Calculation of effect sizes

We will explain the calculation of effect sizes on the example of gene expression analysis, but it can be generalized to any type of data.

The easiest way how to measure differencesbetween two groups is to answer the question: *“How many times is the expression of the gene higher in group A in comparison to group B?”* . The answer is to calculate the mean gene expression in group A, than the mean gene expression in group B and divide the group B mean by group A mean. This is called the *fold change* (FCH).

Fold change is a measure that belongs to the group of measures called the *effect size measures*. The effect size is a measure of the strength of the relationship between two variables and fold change certainly is such a measure, between gene expression and group. For instance, if the mean expression of a gene is 4 in group A and 8 in group 2, the fold change is equal to 2 and we can say that the gene expression in group B is twice as high as in group A.

A most common consensus is to use the **2-fold change **as a threshold for biologically relevant difference in the expression. In this case a 2-fold change cutoff is applied to select differentially expressed genes between groups. Please note that 2-fold change applies on both directions (When comparing group A to B, either FCH >= 2 or FCH<= ½ are significant).

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However, assessing the biological relevancy or non-relevancy is not straightforward** for the following reasons:

- Some genes with relatively weak effects can in coordination with other genes have a considerably high impact.
- Then, the fold change can be systematically biased down to zero based on the quality of the sample used for the mRNA extraction. The quality of the sample reflects the heterogeneity of the cells in the inspected sample and a method of sample preparation/conservation. A tumor sample, for instance, is almost always a mix of tumor and normal cells. Further, there is also heterogeneity between the tumor cells because different parts of tumor reveal different stages of tumor progression. The fold changes can be biased due to this source of variation. Another issue is the sample conservation/preparation. Fresh frozen samples are certainly of higher quality than formalin fixed, paraffin embedded samples. In the latter, the RNA is more degraded what can result in less specific hybridization and consequently in worse signal intensities and smaller fold changes.
- Last, simple filtering by change in expression is missing the information about the reliability of the result. How do we know that the effect size is real and not just due to the experimental error or a random selection imposing higher gene expression values in one group by chance? The answer is to determine the statistical significance, which can only be assessed, if replicate measures of the same gene (in terms of multiple samples) were performed during the experiment. Statistical hypothesis testing or regression techniques can be applied to determine the significance of gene expression changes between one or more groups.