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For your reference:
  length of error bar
  ~ standard error
  = \sqrt{\sum_i (x_i - <x>^2 / N} / \sqrt{N}
  = \sigma / \sqrt(N),
where x_i are the N independent measured values ,
<x> is their mean (average) value, and \sigma is the
standard deviation. Also note that in matlab, the function
std() corresponds to \sigma rather than the standard error.
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A practical result: Decreasing the uncertainty in a mean value estimate by a factor of two requires acquiring four times as many observations in the sample. Or decreasing standard error by a factor of ten requires a hundred times as many observations.
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