A Note on Noncentrality Parameters for Contrast Tests in a One-Way Analysis of Variance

The noncentrality parameter for a contrast test in a one-way analysis of variance is based on the dot product of 2 vectors whose geometric meaning in a Euclidian space offers mnemonic hints about its constituents. Additionally, the noncentrality parameters for a set of orthogonal contrasts sum up to the noncentrality parameter for the omnibus F test. The author provides an example of Helmert contrasts to demonstrate the use of the noncentrality parameters in contrast tests.