Statistical Methods for Single-Case Studies in Neuropsychology: Comparing the Slope of a Patient's Regression Line with those of a Control Sample

Performance on some neuropsychological tests is best expressed as the slope of a regression line. Examples include the quantification of performance on tests designed to assess the accuracy of time estimation or distance estimation. The present paper presents methods for comparing a patient's performance with a control or normative sample when performance is expressed as slope. The methods test if there is a significant difference between a patient's slope and those obtained from controls, yield an estimate of the abnormality of the patient's slope, and provide confidence limits on the level of abnormality. The methods can be used with control samples of any size and will therefore be of particular relevance to single-case researchers. A method for comparing the difference between a patient's scores on two measures with the differences observed in controls is also described (one or both measures can be slopes). The methods require only summary statistics (rather than the raw data from the normative or control sample); it is hoped that this feature will encourage the development of norms for tasks that use slopes to quantify performance. Worked examples of the statistical methods are provided using neuropsychological data and a computer program (for PCs) that implements the methods is described and made available.

[1]  J. Grafman,et al.  Precision and accuracy of subjective time estimation in different memory disorders. , 1993, Brain research. Cognitive brain research.

[2]  Ira Sherwin,et al.  Temporal ordering deficits following anterior temporal lobectomy , 1980, Brain and Language.

[3]  T. R. Jordan,et al.  Perception and action in 'visual form agnosia'. , 1991, Brain : a journal of neurology.

[4]  A. Baddeley,et al.  Autobiographical memory and executive function in early dementia of Alzheimer type , 1995, Neuropsychologia.

[5]  L. Squire,et al.  Retrograde amnesia and memory consolidation: a neurobiological perspective , 1995, Current Opinion in Neurobiology.

[6]  Erminio Capitani,et al.  Normative Data and Neuropsychological Assessment. Common Problems in Clinical Practice and Research , 1997 .

[7]  Richard J. Brown.  Neuropsychology Mental Structure , 1989 .

[8]  Sergio Della Sala,et al.  Agnosia for Object Orientation: Naming and Mental Rotation Evidence , 2002, Neurocase.

[9]  A. Aspin.  Tables for use in comparisons whose accuracy involves two variances, separately estimated. , 1949, Biometrika.

[10]  F. E. Satterthwaite.  An approximate distribution of estimates of variance components. , 1946, Biometrics.

[11]  A. Milner,et al.  Perception and Action in Depth , 1998, Consciousness and Cognition.

[12]  M. Bartlett.  Properties of Sufficiency and Statistical Tests , 1992 .

[13]  Douglas G. Altman,et al.  Statistics with confidence: Confidence intervals and statistical guidelines . , 1990 .

[14]  A. Milner,et al.  Visuomotor sensitivity for shape and orientation in a patient with visual form agnosia , 1996, Neuropsychologia.

[15]  J. Hodges,et al.  A reversal of the temporal gradient for famous person knowledge in semantic dementia: implications for the neural organisation of long-term memory , 1998, Neuropsychologia.

[16]  J. Graham Beaumont,et al.  The Blackwell dictionary of neuropsychology , 1996 .

[17]  D. C. Howell,et al.  Comparing an Individual's Test Score Against Norms Derived from Small Samples , 1998 .

[18]  P. Nichelli,et al.  Impairment in dating and retrieving remote events in patients with early Parkinson's disease. , 1997, Journal of neurology, neurosurgery, and psychiatry.

[19]  K Willmes,et al.  An approach to analyzing a single subject's scores obtained in a standardized test with application to the Aachen Aphasia Test (AAT). , 1985, Journal of clinical and experimental neuropsychology.

[20]  P. Garthwaite,et al.  Intra-individual measures of association in neuropsychology: Inferential methods for comparing a single case with a control or normative sample , 2003, Journal of the International Neuropsychological Society.

[21]  Tim Shallice,et al.  Case study approach in neuropsychological research , 1979 .

[22]  W. Richards,et al.  Time reproductions by H.M. , 1973, Acta psychologica.

[23]  Paul H. Garthwaite,et al.  Wanted: Fully Operational Definitions of Dissociations in Single-Case Studies , 2003, Cortex.

[24]  C. A. Boneau,et al.  The effects of violations of assumptions underlying the test. , 1960, Psychological bulletin.

[25]  M. Jeannerod.  The timing of natural prehension movements. , 1984, Journal of motor behavior.

[26]  C. Code.  Classic cases in neuropsychology , 1996 .

[27]  D. C. Howell.  Statistical Methods for Psychology , 1987 .

[28]  A. Caramazza,et al.  The case for single-patient studies , 1988 .

[29]  R A McCarthy,et al.  The neuropsychology of object constancy , 1997, Journal of the International Neuropsychological Society.

[30]  S. Weisberg.  Applied Linear Regression , 1981 .

[31]  J R Crawford,et al.  Payne and Jones revisited: estimating the abnormality of test score differences using a modified paired samples t test. , 1998, Journal of clinical and experimental neuropsychology.

[32]  T. Hassard,et al.  Applied Linear Regression , 2005 .

[33]  David J. Hand,et al.  Elements of Statistics , 1996 .

[34]  G. Humphreys.  Case studies in the neuropsychology of vision , 1999 .

[35]  R. Glaser.  Bartlett's Test of Homogeneity of Variances , 2004 .

[36]  E. Warrington,et al.  Cognitive Neuropsychology: A Clinical Introduction , 1990 .

[37]  P. Garthwaite,et al.  Investigation of the single case in neuropsychology: confidence limits on the abnormality of test scores and test score differences , 2002, Neuropsychologia.

[38]  Satterthwaite Fe.  An approximate distribution of estimates of variance components. , 1946 .