The aim of singcar is to provide and encourage usage of appropriate statistical methods for comparing a case against a control sample. For instance, they may commonly be done in a neuropsychological context, in which an individual has incurred a specific brain injury and we wish to test whether this damage has led to an impairment of some cognitive function and whether two different functions are dissociable. For many cognitive functions there is normed data available which the patient can be compared against directly. However, when this is not possible a control sample estimating the population, against which we wish to compare the patient, must be used. Both frequentist and Bayesian methods have been developed to do this, first and foremost by John Crawford and Paul Garthwaite (Crawford et al., 2011; Crawford & Garthwaite, 2002, 2007, 2005; Crawford & Howell, 1998). It is these methods that singcar implements. Power calculators for each respective test are also provided. Although the canonical applications for these tests are in Cognitive Neuropsychology or Clinical Neuropsychology, they are potentially applicable to any circumstance in which a measure taken from a single individual is to be compared against data from a normative sample (i.e. a control group). It should be noted that these statistical methods could also be applied as a general method of outlier detection in small samples.
Crawford, J., & Garthwaite, P. (2002). Investigation of the single case in neuropsychology: Confidence limits on the abnormality of test scores and test score differences. Neuropsychologia, 40(8), 1196-1208. https://doi.org/10.1016/S0028-3932(01)00224-X
Crawford, J., & Garthwaite, P. (2007). Comparison of a single case to a control or normative sample in neuropsychology: Development of a Bayesian approach. Cognitive Neuropsychology, 24(4), 343-372. https://doi.org/10.1080/02643290701290146
Crawford, J., & Garthwaite, P. (2005). Testing for Suspected Impairments and Dissociations in Single-Case Studies in Neuropsychology: Evaluation of Alternatives Using Monte Carlo Simulations and Revised Tests for Dissociations. Neuropsychology, 19(3), 318-331. https://doi.org/10.1037/0894-4184.108.40.2068
Crawford, J., Garthwaite, P., & Ryan, K. (2011). Comparing a single case to a control sample: Testing for neuropsychological deficits and dissociations in the presence of covariates. Cortex, 47(10), 1166-1178. https://doi.org/10.1016/j.cortex.2011.02.017
Crawford, J., & Howell, D. (1998). Comparing an Individual's Test Score Against Norms Derived from Small Samples. The Clinical Neuropsychologist, 12(4), 482-486. https://doi.org/10.1076/clin.12.4.482.7241
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