In a study to determine whether a shift from Formula scoring to Rights scoring can be made without causing a discontinuity in the test scale, the analysis of special administrations of the Scholastic Aptitude Test and Chemistry Achievement Test and the variable section of an operational form of the Graduate Management Admission Test (GMAT) is discussed. Rights scoring counts correct test items, and Formula scoring involves a penalty for wrong responses. In the two study phases an Invariance Hypothesis was supported that Formula scores are invariant with respect to directions for guessing, indicating its usefulness in equating scores during the period when changed directions are instituted. The effects on examinee behavior of changes in scoring and guessing strategies for scoring consistency are discussed. In the experimental phase the Invariant Hypothesis and a Differential Effects Hypothesis which implies a disadvantage with Formula directions are compared. The effects of the operational phase's realistic conditions to ensure a typical examinee sample and investigation of different item types are discussed. There is an appendix of 18 statistical tables. (CM)