Development of a Revised Formula for Correcting the Direct Range Restriction

Abstract

The purposes of this research were to develop a revised formula for correcting the direct range restriction and to compare the average bias value of correlation coefficient that was corrected by a revised or new formula and the one corrected by the formula of Thorndike’s case II under the 4 ituations with 135 conditions, by using Monte Carlo method through Simulación 4.0 program to generate 10,000 data in each condition. The research results were as follows:

1. The revised formula for correcting the direct range restriction was

RXY = (Uxyrxy )/ (Ux2y − 1)rx2y + 1 ;Uxy SDX sdxsdy = / When RXY was correlation coefficient value of prediction variable and criterion variable that was range unrestriction. rXY was correlation coefficien value of prediction variable and criterion variable that was range restriction. Uxy was selectioื proportion between standard deviation value of prediction variable score (SDx ) and square root of multiplication between standard deviation value of prediction variable score that was range estriction (sdx ) and standard deviation value of criterion variable score that was range restriction (sdy ). 2. The revised formula for correcting the direct range restriction could be used to adjust the bias value of estimation better than the formula of Thorndike’s case II significantly at the level of .01 in these situations when (1) Level of range restriction correlation coefficient was lower than .70, (2) Dispersion value of criterion variable score was 1.5, 2, 2.5, and 3 times less than that of prediction variable, and ( 3) Levels of selection proportion was between 1.50 and 4.00. 3. The revised formula for correcting the direct range restriction was general case of Thorndike’s case II which was specific case.