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Tukey's test of non-additivity

Tukey's test of non-additivity provides a test for a particular form of interaction between factors even when there is no replication. It can therefore be used to test for interaction between the treatment and block factors in a randomized complete block design. The test is best at detecting interactions which involve different magnitudes of treatment effects for each block but not different directions of treatment effects (in other words where lines cross). Some authorities (for example Kirk (1995) suggest using a liberal significance level (say 0.10 or 0.25) to reduce the risk of not detecting an interaction.