Summary and Conclusion
The basic questions involved in this investigation were the effect of initial standing and item difficulty on the gain established on final over initial measures in achievement testing. The hypotheses were advanced that the use of gain discriminated against bright students on two counts; first, by limiting possibility for gain and second, that equal gains might really represent different levels of performance. It has been shown that the use of a measure of achievement, the effectiveness index, which is independent of initial standing, shows a higher positive correlation with intelligence than the correlation obtained between gain and intelligence. The use of partial correlation to hold the factor of initial standing constant raised the relation found between gain and intelligence in 11 out of 12 cases, indicating that the higher initial standing of brighter students tended to limit their performance. Further, it has been shown that the gain of bright students tends to be established on more difficult items. In addition, the film apparently facilitated the success of students with above average intelligence on difficult items since the relationship found between intelligence and gain or nongain on test items was markedly higher in experimental than in control sections.
To the extent that the gains made on the tests employed in this investigation are representative of gains made on achievement tests in general, in pretest and posttest situations, it may be concluded that bright students are discriminated against when gain is the measure of performance. The bright students must overcome the twin difficulties of establishing their gain on more difficult items in competition with students who havemore items on which improvement, i.e., gain, may be established. It is obvious that groups and individuals differing widely in their initial performance on tests should not be compared using gain as a criterion unless there is some compensation for these factors.