Normally we design experiment with 3 replicates, each replicate has like 10 samples/treatment (so total number of samples n = 30/treatment). Then we average the results of these 10 samples to get 1 number/replicate and use these 3 numbers/treatment to performing statistical analysis. However, I have seen some people design experiment with 30 replications, each replication is one sample, so they perform statistical analysis with 30 numbers/treatment. Is this better or bias in any way? I have tried to perform statistical analysis with my data using this setup, and it seems to be much easier to get significant difference among treatments than the usual way with 3 replicates, so I am kind of skeptical. If the total number of samples (n = 30) does not change, what are the good and bad things among designs like 10 samples x 3 replicates, 5 samples x 6 replicates or 1 samples x 30 replicates?
Usually, in repeated measures (ie. replications) we observe same subject. I mean observe 10 subjects 3 three times. So we measure the effect between subjects and within subject differently at each case. Additionally you can not measure between and within subject variations in 30X1 model but you can obtain some descriptives.
Sabri's answer is, of course, correct for a basic repeated measures design but the situation is more complicated in a general experimental design. See p. 17 of the following linked book:
https://www.amazon.com/Analysis-Experiments-Chapman-Statistical-Science/dp/1439868131/ref=sr_1_1?ie=UTF8&qid=1520979711&sr=8-1&keywords=john+lawson+r
Best, David
PS The classic treatment is due to R. A. Fisher and can be found in his books that are still available.
You should never "average" the replicate values - use the in the raw values in the DOE. The variation within the replicates will help to determine the stability and reliability of the model.
It is about your experiment design. Your observations are your sample, a part of population and main objective is to get an idea about the population. For a robust statistical anaylsis, you need to have enough observations in each experiment (for example people use bootstrapping in many cases with few number of observations). You need replications to see how the measures change in different situations and understand the behavior of your observations. Also, it is not possible to average everything.
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