Five statistical indices are developed and described which may be used for determining (1) when linear equating of two approximately parallel tests is adequate, and (2) whan a more complex method such as equipercentile equating must be used. The indices were based on: (1) similarity of cumulative score distributions; (2) shape of the raw-score to scaled-score transformation; (3) consistency of linear and equipercentile equating results; (4) similarity of item difficulty distributions; and (5) similarity of item discrimination distributions. Data used in the study were collected from between 5000 and 6000 examinees participating in a national aptitude testing program used for college admission selection purposes. Eight forms of the test were used in five separate equatings over three years. Four of five indices of the adequacy of linear equating distinguish markedly between two equatings for which the linear equating method was demonstrably inadequate, and three equatings for which it appeared to be satisfactory. The index based on similarity of item difficulty distributions appeared to be the most useful and discriminated very clearly between problematic and satisfactory linear equatings. (Author/RL)