De fout bij het gebruik van een tweetal benaderingsformules

Summary For the sake of efficiency, the use of simplified formulae in item analysis is recommended. For adequate use of such formulae the systematic error must be known. For two important formulae this error is estimated: the KUDER‐RICHARD‐SON‐21 (instead of 20) and a formula for the correction of the spurious part‐whole correlation. As for the KR, if itemscores are 1 andO, the KR20 is given in (I) and the KR21 in (2). The difference dr between them, given in (5), is directly proportional to the variance of the itemdifficulties. This variance turns out to be rarely greater than 0,05. If the distribution of itemdifficulties is unimodal, a value greater than 0,05 is indeed improbable in four‐choice tests. The KR21, which does not need an item analysis, can be used as a substitute of the KR20. The KR21 coefficient itself is an lower limit, the KR21 plus dr ‐ estimated by (6) ‐ a probable upper limit of the KR20 coefficient. The part‐whole correlation of tests is spurious. If one wants to correct for this spuriousness it is theoretically preferable to estimate the part‐parallel test correlation instead ofthe part rest correlation. This is done here with the assumptions of classical test theory. The part‐parallel test correlation is given in (12), the easily computed first approximation, called A, in (13) and the second approximation in (75), in which last formula the corrected correlation is expressed as a function of A, the standard deviations of part and whole, and the reliability of the test. One can compute with this formula a maximum A, below which the first approximation is sufficiently precise.