There are many fold-change calculation formulars. Since I read the paper A comparison of fold-change and the t-statistic for microarray data analysis, I think I need to summaries each mathods and make sure I understand them.

Because fold-change is widely used in RNA research. The background of the fold-change calculation in this post is based on how find the differentially-expressed genes in a experiment.

### The original method

The standard definition of the fold-change is

$foldchange = \frac{control}{treatment}$

Note: control and treatment are the raw expression levels.

### An simple method

$foldchange = control - treatment$

In some papers, I found they use deviation of control and treatment as the fold-change result.

If the difference of control and treatment data are not to large, I think we should use the simple method.

Some differentially expressed genes have large differences (B-A) but small ratios (A/B), this is another point why using simple methold instead of the original method.

### log fold-changes

If the difference or ratios of control and treatment is dynamic between genes, we need to scale the range of fold-change result.

Here we need the log fold-changes.

$foldchange = log_2(\frac{control}{treatment})= log_2(control)-log_2(treatment)$

### delta-delta-Ct method

$foldchange = \frac{2^{treatment}}{2^{control}} = 2^{treatment - control}$

This method is used in qPCR experiment.

DCt: Target Ct - Housekeeping Ct

DDCt: Sample DCt - Calibrator DCt (Calibrator is your group of comparison)

Fold calculus: 2^-DDCt

$foldchange = SIGN(treatment - control)*2^{\left|treatment - control\right|}$