Author(s): Hamed Nili, Alexander Walther, Arjen Alink, Nikolaus Kriegeskorte
The captions for Figs 1-10 are missing. Please see all complete, correct figure captions here.
Fig 1. Definition of the exemplar discriminability index (EDI). (A) The exemplar discriminability index (EDI) is defined as the difference of the average between-exemplar and average within-exemplar distance. Split-data RDMs (sdRDMs) are shown for two scenarios. In the scenario on the left, the face exemplars are not discriminable and the EDI is insignificant (H0 simulation). In the scenario on the right, the EDI is large and exemplars are discriminable (H1 simulation). (B) Applying multi-dimensional scaling (MDS; Kruskal and Wish, 1978; Torgerson, 1958) allows simultaneous visualisation of the representational geometries from both data sets (H0 on the left, H1 on the right). Exemplars are colour-coded and there are two pattern estimates for each exemplar. MDS gives a low dimensional (2D here) arrangement, wherein the distances between projections approximate the original distances in the high-dimensional pattern space. Here, to obtain MDS plots, we consider a distance matrix composed of comparisons between any two patterns (aggregated from both datasets A and B). When the EDI is significantly positive (right), repetitions of the same exemplar yield patterns that are more similar to each other than presentations of two different exemplars. [see PDF for image]
Fig 2. 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). [see PDF for image]
Fig 3. t test and Wilcoxon signed-rank tests examine different null hypotheses about the data distribution. The graph depicts four different sets of simulated EDIs (A to D) sampled from Gaussian distributions with different means and variances. Gray points indicate the sample data. The superimposed black point depicts the mean of each sample. The sample variance around its mean is depicted by black lines emanating from the mean (i .e ., the black dot). Each set consists of 12 values, representing 12 subjects, which are submitted to both a t test and a Wilcoxon signed-ranked test. Both tests are right-tailed (meaning the tail extending into the positive direction) and test the null hypothesis that the data come from a distribution with...