Interaction (statistics)

Interaction (statistics)

In this example, there is no interaction between the two treatments — their effects are additive. The reason for this is that the difference in mean response between those subjects receiving treatment A and those not receiving treatment A is −2 regardless of whether treatment B is administered (−2 = 4 − 6) or not (−2 = 5 − 7). Note that it automatically follows that the difference in mean response between those subjects receiving treatment B and those not receiving treatment B is the same regardless of whether treatment A is administered (7 − 6 = 5 − 4).

In contrast, if the following average responses are observed

then there is an interaction between the treatments — their effects are not additive. Supposing that greater numbers correspond to a better response, in this situation treatment B is helpful on average if the subject is not also receiving treatment A, but is more helpful on average if given in combination with treatment A. Treatment A is helpful on average regardless of whether treatment B is also administered, but it is more helpful in both absolute and relative terms if given alone, rather than in combination with treatment B.