Figure - available from: PLOS One
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The EDI is not strictly symmetrically distributed under H0 EDI is the difference between the average diagonal entries (blue) and the average off-diagonal entries (red). The distributions of these averages can be skewed or non-skewed and have the same or different shapes. Note that under H0, the two distributions have the same expected value (gray vertical line). When the two distributions are both symmetric (right panels) or when they are both of the same shape (lower panels), their difference will be symmetrically distributed about 0. To see this, consider the fact that for any two points (one from each distribution, e.g. blue X and red X), another equally probable two points exist (blue O and red O) such that their difference has the same absolute value and the opposite sign. However, the distribution can be asymmetric (and thus non-Gaussian) when the two distributions are both skewed and have different shapes (upper left panel).
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[This corrects the article DOI: 10.1371/journal.pone.0232551.].
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