Comparing an Individual's Test Score Against Norms Derived from Small Samples

Investigation of the single case in neuropsychology: confidence limits on the abnormality of test scores and test score differences

“…The control or normative sample for this test has an N of 15 and a mean and standard deviation of 50 and 10, respectively. Using Crawford and Howell's [10] method, the point estimate of the percentage of the population that would be expected to obtain a score lower than the patient (P 1 ) is 3.7%. To obtain 95% confidence limits on P 1 we proceed as follows:…”

“…Confidence limits on the equivalent positive values of c can be obtained by subtracting the percentages from 100 in which case the upper and lower limits are reversed. Table 1 also presents point estimates of the percentage falling below the score; these estimates were obtained using Crawford and Howell's [10] method. The 95% confidence interval of (0.02%, 13.6%) for the last example may be read from the middle of the third row of the table.…”

“…When the normative sample is reasonably large this is justifiable. However, Crawford and Howell [10] point out that there are a number of reasons why neuropsychologists may wish to compare the test scores of an individual with norms derived from a small sample. For example, although there has been a marked improvement in the quality of normative data in recent years, there are still many useful neuropsychological instruments that have modest normative data.…”

“…Crawford and Howell [10] have described and illustrated the use of a method that can be used to compare an individual with normative or control samples that have modest N. Their approach uses a formula given by Sokal and Rohlf [37] that treats the statistics of the normative or control sample as statistics rather than as population parameters and uses the t-distribution (with N − 1 degrees of freedom (d.f. )), rather than the standard normal distribution, to evaluate the abnormality of the individual's scores.…”

Progressive cortical visual failure associated with occipital calcification and coeliac disease with relative preservation of the dorsal ‘action’ pathway

“…Three practice trials were given before the start of each task. A modified independent samples t-test, which treated the normative scores as sample statistics rather than population parameters (see Crawford & Howell, 1998), indicated that in the perceptual task the patient produced a higher mean error (48 o ) than the controls (mean = 9 o , SD =5.6 o ), (t=6.4, p=0.003). In the reaching task, the iPod showed comparable mean rotational error in the patient (21 o ) and controls (mean = 13 o , SD = 8 o ) as it crossed the front edge of the box (t=.96, p=0.39).…”