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In this case the null density of ES, say, can be obtained by row randomization: sets of m rows of the data matrix X are drawn at random, giving randomized values.
We obtained the z-score value of the observed difference relative to the distribution of randomized values and tested for its significance.
For simplicity of calculation we consider randomized values for the pair in question).
2000 ANNs were trained, each with different randomized values for the initial weights.
To test for statistical significance, we used 9999 simulations to compare the K statistic generated from the real data to a distribution of randomized values.
The significance level is given by (n+1)/(N+1), were n is the number of randomized values that are equal to or more extreme than the observed correlation.
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The algorithm is based on a new notion of randomized value function exploration.
In our proposed method, the initial location of a node is calculated based on either randomized value (if node does not receive enough information from three anchors) or a value calculated using a trilateral method.
Spatial autocorrelation, validated with a Monte-Carlo analysis of randomized value assignments, was used to determine global trends of spatial organization (see Materials and Methods).
We used the λ model (Pagel, 1999) to test life-history variation simultaneously against randomized value (no effect of phylogeny) and against the diffusive or the Brownian motion (BM) model (neutral drift).
When this calculated R value was compared to the mean R value calculated from randomized models (X matrix rows randomized against Y matrix rows) we observed that this model was 6.36 standard deviations above the mean randomized value of 0.1847 corresponding to a P-value less than 0.0001.
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