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A Method of Adjusting for Lack of Equivalence in Groups

Schultz, Douglas G.; Wilks, Samuel S.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Equated Scores, Error of Measurement, Regression (Statistics)


A method is presented for lack of equivalence in groups. The method involves several steps. The first is that the regression coefficient of the dependent variable (y) on the control variable (x) is computed independently for each group. The second is that the reliability of the difference of the regression coefficients is determined. If the difference is not significant, it can be assumed that the regression lines are parallel. Then, a weighted, combined value of the regression coefficient is calculated. Using the best estimate of the slope of the parallel regression lines, a line with this slope is placed through the center of each sample. Then, the difference and the reliability of the difference between the y intercepts of these two lines is computed. This procedure does not investigate the standard measurement errors of estimate for the two samples. Since the present method is formulated in terms of critical ratios, only two groups can be compared at a time. (SGK).

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