APPLYING THE STANDARD ERROR OF MEASUREMENT CONCEPT TO A SPECIAL SCHOLARSHIP SELECTION PROCESS
The problem involved in this situation is one in which an applicant for a special scholarship program received a lower score on an entry-assessment test than the minimum score required for admission to the special scholarship program. The assessment test score for the applicant was 65, while the minimum required score is 70.
The question at this point in the process is the extent to which the single assessment test score can be considered to be within a score-band that includes the minimum required score for admission at a confidence level that would justify a degrading of the established standards for admission to the special scholarship program. The approach to making such a determination is to apply the standard error of measurement concept to the available data to (a) identify the relevant score-band and (b) determine the relevant confidence level. The standard error of measurement provides a basis for developing the probable limits of an individual's band of scores had the test instrument been administered to the individual multiple times, as opposed to a single administration (Embretson & Hershberger, 1999; Linacre, 1999).
As indicated above, the applicant's assessment test score was 65 and the minimum score for admission into the special scholarship program is 70. Additionally, it is known that the standard deviation [SD] of all scores on the entry-assessment test is 7.6 and that the reliability [r] coefficient of the entry-assessment test is 0.65. The first step in applying the standard error of measurement concept to this case is the calculation of the standard error of measurement [SEM]. The equation for this calculation is as follows:
A reliability coefficient of 0.65 is quite low, and that low level of instrument reliability
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