Inferring exemplar discriminability in brain representations.

Representational distinctions within categories are important in all perceptual modalities and also in cognitive and motor representations. Recent pattern-information studies of brain activity have used condition-rich designs to sample the stimulus space more densely. To test whether brain response patterns discriminate among a set of stimuli (e.g. exemplars within a category) with good sensitivity, we can pool statistical evidence over all pairwise comparisons. Here we describe a wide range of statistical tests of exemplar discriminability and assess the validity (specificity) and power (sensitivity) of each test. The tests include previously used and novel, parametric and nonparametric tests, which treat subject as a random or fixed effect, and are based on different dissimilarity measures, different test statistics, and different inference procedures. We use simulated and real data to determine which tests are valid and which are most sensitive. A popular test statistic reflecting exemplar information is the exemplar discriminability index (EDI), which is defined as the average of the pattern dissimilarity estimates between different exemplars minus the average of the pattern dissimilarity estimates between repetitions of identical exemplars. The popular across-subject t test of the EDI (typically using correlation distance as the pattern dissimilarity measure) requires the assumption that the EDI is 0-mean normal under H0. Although this assumption is not strictly true, our simulations suggest that the test controls the false-positives rate at the nominal level, and is thus valid, in practice. However, test statistics based on average Mahalanobis distances or average linear-discriminant t values (both accounting for the multivariate error covariance among responses) are substantially more powerful for both random- and fixed-effects inference. Unlike average cross-validated distances, the EDI is sensitive to differences between the distributions associated with different exemplars (e.g. greater variability for some exemplars than for others), which complicates its interpretation. We suggest preferred procedures for safely and sensitively detecting subtle pattern differences between exemplars.