# Correct measure of error for experimental data

I am recording data in real time, my signal has a stability period and then a relatively stable period (with noise, red) outlined in the image. I am require to repeat this type of measurement N times (lets say 10 times) and between each measurement the signal must be switched off and turn back on again, hence 10 stability periods.

My question is, how should the average value and associated error be reported?

I believe I should be evaluating the mean value (between the red lines) for each of the 10 repeats. Here the standard deviation would reflect the noise.

To then consider the 10 repeat measurements I take the average of these mean values, but i don't understand how the errors propagate, this obviously isn't the SD on these mean values.

If anyone can provide any insight, it would be much appreciated.

• If you're confident the different "stability periods" should represent the same state, you can take the average over the $N$ repetitions of your signal. As a general rule, save all the raw data so that you re-analyze it later on. – stafusa Sep 26 '17 at 22:58

The average value could be calculated either as the average of all N averages, or the average of all n data points when the N runs are pooled $(n \gg N)$. These options will give the same answer.
The appropriate measurement of the error is the standard error in the mean (SEM). This should be the SEM of all data points, not the SEM of the N averages. SEM can be calculated from the standard deviation of the pooled data set divided by $\sqrt{n}$.