  In this paper we discuss testing for an interaction in the two-way ANOVA with
just one observation per cell. The known results are reviewed and a simulation
study is performed to evaluate type I and type II risks of the tests. It is
shown that the Tukey and Mandel additivity tests have very low power in case of
more general interaction scheme. A modification of Tukey's test is developed to
resolve this issue. All tests mentioned in the paper have been implemented in R
package AdditivityTests.
