ON THE STANDARD LENGTH OF A TEST*

Abstract

ABSTRACT A new concept, that of the standard length of a test, seems useful in simplifying formulas for reliability and validity coefficients for tests of altered length. The usefulness of the concept is a consequence of the fact that it is possible to define a unit of test information, this being, in fact, the amount of information in a test of standard length. The amount of information in a test is its length L in terms of its standard length as a unit. From this one computes the reliability r of the test by the formula r = L/(L + 1). For small amounts of information, the reliability and the information are approximately equal. It is readily seen that the standard length of a test is that length which would make its reliability one half. The length of a test in terms of its standard length as a unit required to produce a given reliability is given by L = r/(1 ‐ r). Both formulas reduce to (1 + L) (1 ‐ r) = 1. The correlation between two tests of length L 1 and L 2 in terms of their standard lengths as units is r 12 = R 12 L 1 L 2 /(L 1 + 1)(L 2 + 1) 1/2 , where R 12 is the correlation corrected for attenuation. For the case of correlation with a criterion this becomes r 1c = R 1c L 1 /L 1 + 1 1/2 where R 1c is the validity coefficient corrected for attenuation.