I have a question regarding variance and sample error in paired sampling.
If I want to see how a parameter changes over time i take sample "A", then re-sample "A2" at a later time. In my case, the sampling is destructive, so sample A cannot be re-taken at a later time. I will therefore have to take sample B2. When sample B2 is taken at a later time, I cannot be sure whether the difference i see (A minus B2) is because the samples were different in the first place, or whether the difference is caused by an increase or decrease in the parameter with time. To investigate this issue further i have therefore taken sample B at the same time and in as close proximity to A as possible. This means that any difference i find between A and B, can be described as a sample error (or "location error", and not an increase or decrease in time).
I have taken many A-B sample pairs. Sample populations and the differences (A minus B) between the paired samples are normally distributed.
If i run a paired t-test on A and B, i cannot reject the H0, meaning that i cannot say there is a significant difference between the two sample populations.
I would like to estimate the minimum detectable difference of sample population A. For this estimation i need a variance. I assume that the future sampling will be paired.
How would you proceed from here? Would it be correct of me to use the variance of population A and add the variance of the differences between the sample pairs? Or is it enough to use the variance of sample population A (since the populations are not significantly different)?
Hope somebody can help clarify,
Thanks a lot,
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