singcar: Comparing single cases to small samples in R

Case-control comparisons are a class of statistical tests allowing researchers to compare single cases to populations estimated from a sample. Such tests have wide potential utility, but historically have been applied mostly in the fields of cognitive and clinical neuropsychology, to infer whether individuals have suffered significant cognitive changes as the consequence of a brain lesion. One may wish to estimate whether that individual has abnormally low performance on some cognitive ability, or if one cognitive ability is abnormally discrepant with respect to another cognitive ability. John Crawford, Paul Garthwaite and colleagues have developed several related methods to statistically test for abnormality on a single variate and abnormality of the difference between two variates when a single case is compared to a small sample, while controlling the Type I error rate (Crawford et al., 2011; Crawford & Garthwaite, 2002, 2007, 2005; e.g., Crawford & Howell, 1998). This paper presents the R package singcar in which they are implemented. Due to recent discussion on the fundamental power limits of these tests (McIntosh & Rittmo, 2020) the package also includes associated power calculators.