THE PRECISION OF MEASUREMENTS

Measurements are said to be precise to the extent that they are free o f random error, or equivalently, to the extent that they are consisten t 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 diffi cult 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 variabili ty. 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 to lerance for error in a particular context. The tolerance for error spe cifies how large errors can be before they interfere with the intended use of the measurement procedure and is based on an analysis of the r equirements for precision in that context. Because the tolerance for e rror is a function of the intended interpretations and uses of the mea surement procedure, precision is an integral part of validity.