Hi,
I recently went through this paper in which they show a plot of a mean squared displacement analysis of some cell migration data.
http://www.nature.com/nature/journal/v503/n7475/fig_tab/nature12611_SF9.html
Here the authors say that
"[..In which brackets indicate averages over all starting times t0 and all cells N. For each time interval Δtime, mean and standard error of the mean are plotted. Error bars corresponding to s.e.m. are plotted, even if too small to be visible. ..]"
Now I am confused:
Two consecutive cell positions are non-independent variables. Indeed a successive position of the cell is correlated to the previous ones with a certain correlation time.
If they use averages over all starting times t0 for computing their mean squared displacement, then using the standard error of the mean is theoretically wrong, as the samples they are averaging for producing each point of the MSD curve are non-independent.
I think that to employ s.e.m, they should use non-overlapping time intervals for every interval Δtime.
Am I missing something?
Thanks in advance for any future input.
Best,
Jacopo
I will have to think more carefully about this question (just received an email from RG, asking me whether I had any idea about this question, and hence this response), but my initial view is that use of non-overlapping time intervals is not necessary. What is necessary in calculating the variance of the sample mean is taking into account the covariance of the samples. What I mean is explained here:
http://en.wikipedia.org/wiki/Variance#Sum_of_correlated_variables
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