Multiple Comparisons for Orthogonal Contrasts: Examples and Tables

Abstract

In many experimental situations the pertinent inferences are made on the basis of orthogonal contrasts among the treatment means (as in 2 ⁿ factorial experiments). In this setting a particularly useful form of inference is one involving multiple comparisons. The present article describes situations in which such inferences are meaningful, gives examples of their use, and provides a table of constants needed to implement such multiple comparison procedures. The procedures can also be used for statistically legitimate “data snooping” (in the sense ofScheffé 1959, p. 80) to help decide which contrasts within a specified set warrant further study.

KEY WORDS:

• Multiple comparisons
• Orthogonal contrasts
• Joint confidence intervals
• Experimentwise error rates
• Studentized maximum modulus
• Simultaneous inference