The precision of measurements

Measurements are said to be precise to the extent that they are free of random error, or equivalently, to the extent that they are consistent across different observations for an object of measurement. Standard errors of measurement provide convenient indexes of consistency, but their magnitude depends on the score scale and, therefore, it is difficult to make evaluative judgments about standard errors without having some benchmark for comparison. Reliability coefficients address this need by comparing the standard error with the observed score variability. The ratios defining reliability coefficients and generalizability coefficients are independent of the scale but are strongly linked to a norm-referenced interpretation of test scores. A more fundamental way to evaluate precision is to compare errors of measurement with the tolerance for error in a particular context. The tolerance for error specifies how large errors can be before they interfere with the intended use of the measurement procedure and is based on an analysis of the requirements for precision in that context. Because the tolerance for error is a function of the intended interpretations and uses of the measurement procedure, precision is an integral part of validity.