# Correct/complete representation of RTPCR statistics

In papers reporting a relative quantification of gene expression by RTPCR, I often see a bar chart with mean ± standard error or deviation, with the deviation belonging to biological replicates. This ignores all the previous layers of technical replicates. In the regular $2^{\Delta(\Delta Ct)}$ estimation with 3 reactions per primer/template, we have the standard deviation (SD) from each technical replicate, then the SD from normalization, end finally the SD from quantification. If the end results are fold changes, add one more layer to this. I'm not even including normalization with the geometric mean of 3 housekeeping genes (the better method) How can I correctly calculate / depict the statistical variations in this case?

• Maybe these articles show relative expression changes between time points? In my institute we do these as well and the SD comes from the biological replicates in these cases. Also it might only be a data representation issue. – Nandor Poka Apr 17 '15 at 0:56

## 1 Answer

I think you can follow this method:

1. Test the statistical significance of a single experiment by comparing technical replicates (lets say Tests: T1, T2, T3 and Controls: C1, C2, C3). This will tell you if the instrument can reliably detect difference or not. Note that you should compare the relative expression (i.e. wrt your reference gene) and not the CT values. The ΔΔCt method is fine but you should note that it is not necessarily a power of 2; 2 denotes perfect PCR efficiency. See these posts:
2. If the difference is found significant in all technical replicates then test the difference between biological replicates by using the means of the technical replicates in each experiment; for example mean of T1, T2 and T3 in biological replicate-a ($\bar{T_a}$) used as the sample value for that replicate. You can proceed with t-test for computing statistical significance which will tell you if the difference in expression is because of a random cellular behaviour or not. You can also do an ANOVA to compare the variance between technical replicates (within an experiment) and biological replicates (mean of the technical replicates between experiments). ANOVA lets you know some aspects of reproducibility of a measurement technique.
3. Fold changes (FC) are a problematic issue because many biologists seem to mess up with the interpretation of the data. First of all a t-test cannot be applied to FC directly (especially if FC is calculated pairwise for each replicate). Now all you have is a single random variable i.e fold change that you cannot statistically compare with anything. Fold changes are not really bad but I would recommend that a t-test be done between the control and the test samples and if the difference is found statistically relevant then report the FC. I personally know many people who do the other way round and set variance of the control sample as zero (because pairwise FC would be = 1 in all cases): This is a blunder.