Regression tests for several samples

Psychometric Contributions: Focus on Test Scores

“…For example, some strategies center on assessing differences in the regression slopes of two groups and, if the slope differences are likely to be zero, assessing the intercept differences of the groups based on the groups' parallel regression lines using a common slope (Schultz and Wilks 1950). More expansive and general sequential tests involve likelihood ratio and F-ratio tests to sequentially test three hypotheses: first, whether the prediction error variances of the groups are equal; then, whether the regression slopes of the groups are equal (assuming equal error variances), and finally, whether the regression intercepts of the groups are equal (assuming equal error variances and regression slopes; Gulliksen and Wilks 1950). Significance procedures have also been described to consider how the correlation from the estimated regression model in Eq.…”

Pitfalls of Ability Research in Aviation Psychology

“…Further, they propose and demonstrate a general hierarchical linear models analysis to address the issue. The first step in the Ree et al approach is to test for equivalence of the variance errors of estimate (Gulliksen & Wilks, 1950;Jensen, 1980;Reynolds, 1982). If the errors of estimate are equal, a series of F tests of specified hierarchical linear models is appropriate.…”

Documentation of Muscularly Demanding Job Tasks and Validation of an Occupational Strength Test Battery (STB)

“…Unfairness is established if there is a difference in slopes, intercepts, or both; Barlett et al suggest checking intercepts before slopes. Gulliksen and Wilks (1950) suggest checking for a difference in slopes before intercepts, but the result would be the same--unfairness is established if a difference exists in either.…”