Open AccessAN EXAMINATION OF THE ASSUMPTION THAT THE EQUATING OF PARALLEL FORMS IS POPULATION‐INDEPENDENT
Author(s) -
Angoff William H.,
Cowell William R.
Publication year - 1985
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/j.2330-8516.1985.tb00107.x
Subject(s) - equating , statistics , mathematics , raw score , population , standard error , variance (accounting) , test (biology) , homogeneous , econometrics , raw data , demography , combinatorics , paleontology , business , accounting , sociology , rasch model , biology
Linear and equipercentile conversions were developed relating Forms 3DGR1 and 3DGR3 of the homogeneous GRE quantitative test and the specially constituted heterogeneous GRE verbal‐plus‐quantitative test, using randomly equivalent populations of about 13,500 cases taking each form, drawn from the entire candidate group tested in the regular October 1981 administration of the Graduate Record Examinations. For purposes of this study these samples of 13,500 cases were taken as representing their respective total populations, and the conversions based on them were taken as “population conversions.” Empirical standard errors of equating were then developed for samples of 1,000 by drawing 100 samples of that size from each of the two base populations and calculating the variance error of equated scores on Form D1 (i.e., 3DGR1) for each successive raw score on Form D3 (i.e., 3DGR3) and fitting a second‐degree equation to those variance errors. Samples of 1,000 cases taking each form were then selected at random from specially defined subpopulations homogeneous with respect to sex, race, field of study, and level of performance (the last of these defined by scores on the GRE analytical test) and used as the basis of additional conversions between the two test forms. Departures of the conversions based on each of these specially selected samples from the population conversion were calculated and evaluated in terms of the standard error of equating at five selected raw score points on Form D3, adjusted for the disparity between the means, as well as the three higher moments–variance, skewness, and kurtosis–for these subpopulations and the corresponding moments of the total populations. The results of this phase of the study showed that the conversions for the samples drawn from the Physical Science subpopulation differed significantly from that of the total population. When, in the second phase of the study, the appropriate adjustments for the moments were made, it was found that the Physical Sciences conversions fell clearly in line for the homogeneous GRE quantitative test, but not quite so clearly for the heterogeneous GRE verbal‐plus‐quantitative test. The conversions for all other subpopulation samples were acceptably within range of the population conversion. It was concluded that the assumption of population‐independence for equating is supportable for homogeneous tests but, because of evidence of nonparallelism between the two forms, the assumption is not as clearly established by the data of this study for heterogeneous tests.