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I have to start by saying that stats is a foreign language for me. Thus being said, back to my problem.

I am doing experiments with 3 technical replicates and 3 biological replicates. So basically I have 3 wells per experiment and in total 3 experiments from which I want to get a mean and a deviation.

I started by averaging the technical replicates and calculating the SD. Then, I normalized my control to 1 and expressed all other samples (mean and SD) to the initial value of the sample that I set as 1 (so let's say my control is 39=1. Its SD is 3. Then I divided 3/39 and I got the normalized SD of 0.07 and so on for all samples and their SDs that I always divided by 39).

Now, I have 3 independent experiments that I want to average. I have 3 values of 1 for my control and various values for the SD. Same for my samples. I made the average of the individual experiments but I don't know how to calculate the SD. Theoretically, I would calculate the SD of the 3 independent values, but this means that my control will have no SD since all 3 values were set as 1. How should I proceed in this case? Should I average the normalized SDs from each independent experiment?

Thanks! Eveline

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  • $\begingroup$ Perhaps it would be better if you told us what the point of your experiment is. What is the scientific question you want your analysis to answer? $\endgroup$ – mdewey Aug 23 '17 at 17:08
  • $\begingroup$ I am testing different treatments to see if they can impact the size of the cell. $\endgroup$ – Eveline Aug 24 '17 at 8:27
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It's probably time to start learning the "foreign language" of statistics, or at least to get a reliable local interpreter.

The way that you are approaching this situation is potentially throwing away a lot of useful information. For example, it doesn't allow you to test for systematic differences among your three biological replicates (either in terms of baseline results or in terms of responses to any experimental treatments). Also, you are not taking full advantage of your well-designed experiment. It's much better to pool information among the technical and biological replicates to get estimates of underlying technical errors, rather than to base calculations on the SD values for each individual set of 3 technical replicates.

With a nicely balanced experimental design like yours, a classic analysis of variance (ANOVA) should work well. Don't start by normalizing; work with the actual values instead. ANOVA will give you an estimate of technical error that is pooled across all of your work, taking into account differences among biologic replicates and differences among treatments. That pooled technical error estimate then is used to evaluate the significance of any differences among biological replicates and treatments. Using the pooled error estimate from ANOVA is a much more powerful way to proceed than what you are now trying.

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  • $\begingroup$ Well, it's always a long way from planning to actual start learning statistics...by yourself :) I thought that normalizing is more informative (I am not interested in the absolute numbers but in the degree of decrease in cell size due to my treatment). Also, I did it like this because I have high variability in cell size between the experiments and I thought normalizing would "correct" for that. So, if i understood correctly, I should use the actual numbers and put in a table all the values (from the technical replicates and the biological ones) and then perform an ANOVA? $\endgroup$ – Eveline Aug 24 '17 at 8:47

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