Hello!
I'm currently analysing some RT-qPCR data by Pfaffl method.
My experiment consisted in:
-the expression of 5 genes in two embryo stages (T4B and T7).
I also used:
- two biological replicates(BR) of each embryo stage.
- 3 technical replicates(TR) for each mesurement
- 3 reference genes.
- calibrator is the pool of the embryo stages.
I know that there are many significance tests: parametric (for normal distribution of the results) and non-parametric, paired-test (for dependent samples) and non-paired. And I know that the most commum tests are t-test, mann-whitney u-test, and one-way and two-way ANOVA.
My doubts are:
1. how to realize if my results follow a normal distribution and what is the suitable test?
2. which significance test should I apply to my data, and in relation to what?
a. significance of the difference between each stage (T4B and T7) and the pool?
b. significance of the difference between each biological replicate?
c. significance of the difference between all the analysed genes?
d. other?
Thank you for your time!
There is not much fun doing some testing for only two biological replicates...
The log normalized expression values [LNE] or the dCt values will be approximately normal distributed, so in principal a t-test would fit.The technical replicates should be averaged before (average the LNE / dCt values), so that you will have two values per gene and emryo state.
It might go beyond your request, but I would like to recommend using a procedure that makes use of *all* you data to estimate the standard errors. A conventional t-test uses the information from one gene only (what is only one fifth of your total information!), ignoring that the other genes also do provide some information about the variance of the measurements. An ANOVA is not an option here because each gene is a different response (ANOVA can analyze the same response in +2 groups). An MANOVA would be possible, but I bet that you are not interested in testing the hypothesis of the MANOVA (I guess you will want to know which of your genes is differentially expressed between T4B and T7 - this is not answered by MANOVA).
A nice solution is provided by limma. This is an R-package that has originally been developed to analyze expression data from microarrays that typically suffer very small sample sizes, too, but measure the expression of many different genes per sample in parallel. If you can find a bioinformatician who is experienced in the analysis of microarray data with R, then you can ask for help (should not be a lot of effort for such a person). This would make the optimum use of your data.
https://www.r-project.org/
http://bioconductor.org/packages/release/bioc/html/limma.html
There is not much fun doing some testing for only two biological replicates...
The log normalized expression values [LNE] or the dCt values will be approximately normal distributed, so in principal a t-test would fit.The technical replicates should be averaged before (average the LNE / dCt values), so that you will have two values per gene and emryo state.
It might go beyond your request, but I would like to recommend using a procedure that makes use of *all* you data to estimate the standard errors. A conventional t-test uses the information from one gene only (what is only one fifth of your total information!), ignoring that the other genes also do provide some information about the variance of the measurements. An ANOVA is not an option here because each gene is a different response (ANOVA can analyze the same response in +2 groups). An MANOVA would be possible, but I bet that you are not interested in testing the hypothesis of the MANOVA (I guess you will want to know which of your genes is differentially expressed between T4B and T7 - this is not answered by MANOVA).
A nice solution is provided by limma. This is an R-package that has originally been developed to analyze expression data from microarrays that typically suffer very small sample sizes, too, but measure the expression of many different genes per sample in parallel. If you can find a bioinformatician who is experienced in the analysis of microarray data with R, then you can ask for help (should not be a lot of effort for such a person). This would make the optimum use of your data.
https://www.r-project.org/
http://bioconductor.org/packages/release/bioc/html/limma.html
Thank you very much Jochen Wilhelm!
Yes, I have so few replicates that I am concerned if I could assume a normal distribution or if is better to consider it as non-normal.
Meantime I also read that I could use this scheme:
1. Significance difference between my technical replicates (using deltaCT data);
2. Significance difference between my biological replicates (using relative expression/fold exchange data, after average technical replicates);
3. Significance difference between tested embryo stages and POOL-calibrator (using relative expression/fold exchange data, after average biological replicates);
4. And Yes, I would like to compare also between the two embryo stages T4B and T7.
I always like to read your answers to RT-PCR questions :)
I will study that statistical program!
Thank you again!
Sónia,
I don't really understand your points 1-3. To my understanding, only 4 makes sense.
And: yes, dCt values, and, therefore, LNE values and ddCt values and log fold-changes can be assumed normal distributed.
Reformulating 2 for exemple:
My results are an average between the two biological replicates (BR). Before I calculate this average, shouldn't I do a significant test to show that my BR are significant different, and not by random. Or is not necessary?
I think most people calculate the significance of the mean difference between the groups. This can be obtained from a t-test using the dCt values or LNE values. This is also what limma does give you, but with the advantage that limma calculates a moderated t-statistic based on a pooled (from the different target genes) estimate of the standard error.
Note: The significance (i..e., the "p-value") does not tell you whether the difference is "real" or "random". These concepts do not go with statistics. Statistics is about quantifying an expectation (or uncertainty) of "events" (an event is, so to say, some unobserved observation - we know that such an observation is possible, but we don't know if this observation happens to be the case in an actual experiment/study). The p-value quantifies the expectation for "more extreme data" (than the actually observed data) in a particular model with a particular restriction (the "null hypothesis"). If this event (getting more extreme data) is very unexpected and if the model would generally allow such events, then we may conclude that the restriction ("null hypothesis") is detrimental to account for the observations we already have. There is no statement about the "truth" or "falsehood" of an effect (like a mean difference). The only statement is about the data in relation to some statistical model, and it may lead to the rejection of the selected restriction of this model.
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