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I have a spatio-temporal data set with (n,m) spatial and k temporal dimensions.

My initial analysis consisted of spatially averaging the data and looking at the time dependent behavior. This resulted in a vector of length k for the mean and standard deviations.

Now I want to average the those means, to get an overall scalar value. How do I calculated the standard deviation of this new quantity? Should I be using the pooled variance to calculate it? Or is there another approach that is better suited?

Here is an example of the data after spatially averaging. The light regions represent 95% confidence intervals. What I would like to do, is average the last 10 seconds of data (50--60 s) and calculate the corresponding standard deviation so that I can get confidence estimates for the mean.

Blink
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  • Could you tell us what you intend to use this standard deviation for? – whuber Feb 26 '14 at 16:11
  • I am comparing the results from three different cases, and I want to see the deviation between each case. I would like to have the standard deviation to plot confidence intervals for each case to see if they have overlap. – Blink Feb 26 '14 at 16:15
  • Does the intention change the data analysis approach? – Blink Feb 26 '14 at 16:20
  • Absolutely: if you are using the SD to *describe* the summaries, you have a lot of latitude. If it's going into a subsequent analysis, then how it is computed (and what it actually measures) is critical. Your comment shows that the question is *really* about confidence intervals and not about a standard deviation *per se*. This, too, is important because spatio-temporal processes tend to exhibit rich and strong correlations, suggesting you will need more than just a standard deviation to compute an appropriate CI (you will need to use correlation estimates too). – whuber Feb 26 '14 at 16:24
  • @whuber: Thank for the information. I've updated my question with an example of my data. Should the question be phrased differently? Please feel free to edit it if so. My statistical background is weak, and my statistical lingo is even weaker. – Blink Feb 26 '14 at 16:45
  • good answers concerning this issue found here: [ARIMA model and other methods](https://stats.stackexchange.com/questions/274635/calculating-error-of-mean-of-time-series) – yipp123 Oct 02 '19 at 22:20

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