Statistics on microcomputers: a non-algebraic guide to the appropriate use of statistical packages in biomedical research and pathology laboratory practice. 6. Statistical methods for diagnostic tests.

Reference ranges Most tests used in clinical medicine give a numerical result on a continuous measurement scale. Pathologists or clinicians attempt to interpret the result by comparing it with a "reference range" previously calculated from a study of people who do not have the disease in question. By current convention, the reference range includes all but the top and bottom 2 5% of the results expected from a population of healthy people, so that 5% of the "normal" healthy population will have test values falling outside the reference range. Consequently, the fact that the test result for an individual subject is outside the reference range does not necessarily imply that the individual is abnormal-this is one reason why the older term "normal range" is becoming obsolete. A reference range may be determined from test values obtained from a sample of healthy subjects provided: (i) the subjects constitute a random sample from the healthy portion ofthe population; and (ii) the sample size is sufficiently large for it to be representative of the population and for the sample mean and standard deviation to be precise estimates of the population mean and standard deviation. If the population distribution of the test results is normal, then 95% of all values will lie within the range population mean ± 1 96 (population standard deviation) (Article 2). The sample mean and standard deviation are estimates of the unknown population mean and standard deviation and by convention the reference range is taken to be: sample mean ± 1-96 (sample standard deviation) The sample mean and standard deviation, however, are subject to sampling variation-that is, each random sample gives rise to different sample statistics-and so the limits of the reference range will be imprecise. Confidence intervals can be calculated for the upper and lower reference limits to indicate the imprecision of the reference range. If the sample size is large a 95% confidence interval for each end of the reference range is: reference limit ± 1-96 1/3 (SE mean).