Kappa statistics are widely-used to assess performance in quality assurance schemes. Low values, however, are difficult to interpret, especially when confidence intervals have not been calculated. A model of a dichotomous decision in pathology (benignancy or malignancy in fine needle aspirates of the breast) was used to calculate kappa statistics (with confidence limits) for increasing false positive rates. It was found that the level at which the upper 95% confidence interval for the kappa statistic fell below 1 was an insensitive method of detecting unsatisfactory performance as at that level the false positive rate was unacceptably high (> 1%) for all populations of specimens less than 800 in number. Either large populations of samples are required in quality assurance schemes which use kappa statistics (which may well be impractical) or other methods of assessing performance, possibly with weighted outcomes, are required.