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I need some help with the statistical analysis of an experiment. It would be great if you could cite on what literature you base your answer if possible.

For simplicity let us assume I have 3 repetitions of the same experiment $exp_1$, $exp_2$ and $exp_3$, where $x^i$, $x^j$ and $x^k$ are the same specific measurements across the repeats:

  • $exp_1$: $\ x_1^i, \ x_1^j, \ x_1^k$
  • $exp_2$: $\ x_2^i, \ x_2^j, \ x_2^k$
  • $exp_3$: $\ x_3^i, \ x_3^j, \ x_3^k$

I want to compute the standard deviation for the means across measurements and repeats. My naive approach right now is to compute the means: $m_1 = \text{mean}(x_1^i, x_1^j, x_1^k), \ m_2.., m_3..$. Next I compute the mean of means $m_{all} = \text{mean}(m_1, m_2, m_3)$ and the standard deviation of means $s_{all} = \text{std}(m_1, m_2, m_3)$ but I think this is not the right way to do it and I should compute $s_{all}$ based on the individual $s_1, \ s_2, \ s_3$?

Thanks in advance!

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1 Answer 1

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If you want to know the standard deviation for all nine observations, throw the nine values into the standard deviation formula.

If you want to know the standard deviation for the three means, throw those three values into the standard deviation formula. It sounds like this is the standard deviation you want to know.

That you’re skeptical about the calculation, however, makes me wonder what you’re trying to do. Please don’t hesitate to post a comment with your goal.

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  • $\begingroup$ I think your first comment is correct considering that what I called "mean of means" is the mean across measurements and repetitions. Thinking about it know it seems obvious to just compute the standard deviation based on all nine values. Thank you! $\endgroup$
    – AuSch
    Jul 15, 2020 at 11:23

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