Consider situations where the treatment may cause an initial effect and may also cause a long-range effect. We want to evaluate the treatment, or to compare two treatments, when the effect of treatment may result from the two distinct mechanisms, M1 and M2. We may wish to evaluate M1 and M2 separately, but we may also want to evaluate their combined effect M3. Examples are given and the general results are applied to the special case arising in weather modification studies and elsewhere: the possible effects are multiplicative and the distribution of non-zero variables is gamma with at most the scale parameter affected by treatment. An example demonstrates that the two components may be too weak to be judged significant while their sum is large and significant. The locally optimum C(α) test is used.

There is a brief discussion of the power function of the tests. The asymptotic power agrees well, in general, by the results of the Monte Carlo simulation for the test Z3 of the combined effect. If the zero values are discarded and then Z2 employed, there is large bias in the power. The bias is more pronounced if the Wilcoxon, Mann–Whitney test is employed. Notice that the two effects under study may be acting in the same direction or they may be in opposition.