The development of a statistical procedure to correct the effects of restriction of range on validity coefficients

Abstract

In the validation of tests used for selection purposes, the obtained validity coefficients are invariably underestimates of the true validities, due to explicit and implicit selection in respect of the relevant variables. Both explicit and implicit selection leads to restriction of range of the relevant variables, and this in turn reduces the obtained validites. A formal proof for this is given. A number of researchers have developed formulae for correcting sample validities in order to get better estimates of the true validities (Pearson/ 1903; Thorndike, 1949; Gulliksen, 1950; Rydberg, 1962 and Lord & Novick, 1968). It is, however, virtually impossible to obtain a complete view of the problem of restriction of range in this way. In the present paper a different approach has been followed: Population correlations have been computed for various degrees of truncation of the explicit selection variable. This has been done for population correlations ranging from 0,10 to 0,99. A graphical display, indicating the shrinkage of the population correlations for various truncation ratios, has been prepared.

Opsomming
In die geldigheidsbepaling van toetse wat vir keuringsdoeleindes gebruik word, is die verkree geldigheidskoeffisiente sender uitsondering onderskattings van die ware geldighede as gevolg van eksplisiete en implisiete keuring ten opsigte van die tersaaklike veranderlikes. Sowel eksplisiete as implisiete keuring lei tot inperking van die variasiewydte van die relevante veranderiikes, en dit reduseer om die beurt weer die verkree geldighede. 'n Formele bewys hiervoor word in die referaat gegee. 'n Aantal navorsers het formules ontwikkel om steekproefgeldighede te korrigeer ten einde beter beramings van die ware geldighede te verkry (Pearson/ 1903; horndike, 1949: Gulliksen, 1950; Rygberg, 1962 en Lord & Novick, 1968). Dit is egter bykans onmoontlik om op hierdie wyse 'n geheelbeeld van die probleem van inperking van variasiewydte te vorm. In die huidige referaat is 'n ander benadering gevolg: Populasiekorrelasies is bereken vir verskillende grade van afknotnng van die eksplisiete keuringsveranderlike. Dit is gedoen vir populasiekorrelasies wat wissel van 0/10 tot 0/99. Voorts is 'n grafiese voorstelling voorberei, wat die krimpring van die populasiekorrelasies vir verskillende afknottingsverhoudings, uitbeeld.