A comparison of procedures for general contrasts -unequal sample size case

Abstract

Three procedures for general contrasts among the means in the unbalanced models are compared. These include the Tukey (T), Scheffe (S) and transformed-Tukey (T-T') procedures. The comparison is based on the lengths of the confidence Intervals. It is shown that the Tukey procedure gives the shortest confidence intervals for pairwise contrasts. A numerical study is carried out for the general contrasts. It is found that the T and T-T' procedures perform similarly. In general, the S'procedure is recommended for contrasts involving many μ_i's. Recommendations for the choice of the procedures are given.

Keywords:

• multiple comparisons
• contrasts
• Tukey method
• Scheffe method
• Studentized augmented range