Do you really expect that another sample of size 2 would give you the same answer, or even a qualitatively similar answer? Realizing that these are pseudoreplicates and that the sample size is 1, does that change your answer?

With a sample size of 1, the calculation for the standard deviation is the square root of the sum of the squared differences between the mean and each observation and that quantity divided by n-1. In the math that I am used to, division by zero is not allowed. The standard deviation is undefined. It is not zero (as I have seen published). It can be blank, or NA, or missing, or "." or any other equivalent.

So I have one observation from each treatment. For the sake of argument, I will pretend that there is no treatment effect. What is the probability that my lone observation from Treatment 1 is on the opposite side of the true mean from the observation in treatment 2? This is kind of like flipping a coin and declaring a significant difference if the second flip lands on the opposite side of the coin from the first.

If this is an important study involving high risk and great expense then treat it as a case study. If this is a class exercise where the goal is to run numbers through a statistics program and interpret the result, then doing so is entirely appropriate. I would preface the term paper with "assuming that these two technical replicates provide a mean and variance that are good estimates of the underlying distribution" with full knowledge that this is highly unlikely. For publication or as preliminary data in a grant proposal I would suggest leaving these data out. They will do you no good.

Trying to hide the poor sample size with error bars would be dishonest. As a reviewer, if I get a paper with error bars but no indication of sample size I move the paper one step closer to rejection. More often these days the journal asks if I would review the paper again, and if the sample size is 1 or is still missing in the revision then I would simply reject the manuscript.

You have an experiment with a treatment at two levels (A and B). You have ten plots for treatment A, and ten plots for treatment B. Within each plot you took two samples. In this case, you have done well. Simply average the two subsamples and proceed with the analysis.

You have an experiment with a treatment at two levels (A and B) You have one plot of each, and each plot was sampled twice. It does not matter what you do with these data. This is a learning exercise, or it might be presented as a case study if circumstances are appropriate. Either way, you will not get any meaningful outcome using statistics. What you have is n=1 with pseudoreplication, and that is not publishable.

Dear Prashank Mishra ,

You are allowed to plot error bars reflecting the standard deviation, the standard error of the mean, the confidence interval (or any other metric revealing the spread of results) estimated from any number of observations (including your case of n=2). I am not aware of any rule that precludes this.

Both options (all observations or mean+error bars) are valid but, in this case, I rather prefer a chart with all the observations, that is, the duplicates and no error bars. However, this is a personal opinion and may be called a "flavour based choice".

Regards, Luis

Considering that there were only 2 measurements, I think it would be reasonable to show them both without error bars. If you do a statistical test, you can show the result on the plot in any of various ways.