Table 1.

The dimensionalities of lesion-deficit inference. The inferential consequences of neglecting the dimensionality of lesion-deficit data vary depending on the source. Where the anatomy is complex, mass univariate methods are inefficient but not necessarily biased. By contrast, where the lesion anatomy is complex, mass univariate methods become unquantifiably biased. High-dimensional multivariate inference solves both problems, but is conditional on the availability of large datasets. Note what constitutes sufficient data is difficult to prescribe, for conventional power analyses are not applicable here: the only guide is behavioural predictive performance of the anatomical model, tested on independent, “out-of-sample” data.

	Dimensionality of functional anatomy	Dimensionality of lesion anatomy
Mass-univariate inference	Insensitive but spatially mostly unbiased, given sufficient data	Spatially biased, regardless of data size.
High-dimensional multivariate inference	Sensitive and spatially unbiased, given sufficient data	Sensitive and spatially unbiased, given sufficient data