The hypothesis that some students, when tested under formula directions, omit items about which they have useful partial knowledge implies that such directions are not as fair as rights directions, especially to those students who are less inclined to guess. This hypothesis may be called the differential effects hypothesis. An alternative hypothesis states that examinees would perform no better than chance expectation on items that they would omit under formula directions but would answer under rights directions. This may be called the invariance hypothesis. Experimental data on this question were obtained by conducting special test administrations of College Board SAT‐verbal and Chemistry tests and by including experimental tests in a Graduate Management Admission Test administration. The data provide a basis for evaluating the two hypotheses and for assessing the effects of directions on the reliability and parallelism of scores for sophisticated examinees taking professionally developed tests. Results support the invariance hypothesis rather than the differential effects hypothesis.

Educational Testing ServiceDuring the past 60 years, correlation and regression have come to occupy a central position in measurement and research.Results obtained by these methods are particularly important in the evaluation of tests and in the use of test scores.Psychologists and educational researchers use these methods with confidence based on familiarity.Many persons concerned with research and testing, however, find results expressed in these terms difficult or impossible to interpret, and prefer to have results expressed in a more concrete form. This is particularly true if they are to make decisions on the basis of the results.In response to this need, expectancy tables have been developed.Walter V. Bin~ham was a particularly forceful advocate of their use for th~s purp~" This paper will offer a tentative classification of expectancy tables, together with some comments on the characteristics of various approaches.The somewhat form~ consideration of the possibilities may serve to clarify issues and may suggest suitable ways of dealing with specific problems.