Tukey's test of additivity

In statistics, Tukey's test of additivity, named for John Tukey, is an approach used in two-way ANOVA (regression analysis involving two qualitative factors) to assess whether the factor variables are additively related to the expected value of the response variable. It can be applied when there are no replicated values in the data set, a situation in which it is impossible to directly estimate a fully general non-additive regression structure and still have information left to estimate the error variance. The test statistic proposed by Tukey has one degree of freedom under the null hypothesis, hence this is often called "Tukey's one-degree-of-freedom test."