Interaction Effect

Interaction in statistics refers to the interplay among two or more INDEPENDENT VARIABLES as they influence a DEPENDENT VARIABLE. Interactions can be conceptualized in two ways. First is that the effect of each independent variable on an outcome is a conditional effect (i.e., depends on or is conditional on the value of another variable or variables). Second is that the combined effect of two or more independent variables is different from the sum of their individual effects; the effects are NONADDITIVE. Interactions between variables are termed HIGHER ORDER effects in contrast with the FIRST-ORDER effect of each variable taken separately.

As an example, consider people's intention to protect themselves against the exposure to the sun as a function of the distinct region of the country in which they reside (rainy northwest, desert southwest) and their high versus low objective risk for skin cancer (see Table 1).

In Table 1, risk and region do not interact. In the northwest, those at low risk have a mean intention of 6; those at high risk have a mean intention of 7, or a 1-point difference in intention produced by risk. In the southwest, high risk again raises intention by 1 point, from 8 to 9. Looked at another way, people residing in the southwest have 2-point higher intention than in the northwest whether they are at low risk (8 vs. 6, respectively) or at high risk (9 vs. 7, respectively). The impact of risk is not conditional on region and vice versa. Finally, risk (low to high) raises intention by 1 point and region (northwest to southwest) raises intention by 2 points; we expect a 1 + 2 = 3-point increase in intention from low-risk individuals residing in the northwest to high-risk individuals residing in the southwest, and this is what we observe (from 6 to 9, respectively), an additive effect of risk and region.

In Table 2, risk and region interact. Lowversus high-risk individuals in the northwest differ by 1 point in intention, as in Table 1 (termed the simple effect of risk at one value of region, here northwest). However, in the southwest, the difference due to risk is quadrupled (8 vs. 12 points). Looked at another way, among low-risk individuals, there is only a 2-point difference in intention (6 to 8) as a function of region; for high-risk individuals, there is a 5-point difference (7 to 12). The impact of region is conditional on risk and vice versa. Instead of the additive 3-point effect of high risk and southwest region from Table 1, in Table 2, high-risk individuals in the southwest have a 6-point higher intention to sun protect than low-risk individuals in the northwest (12 vs. 6, respectively). The combined effects of region and risk are nonadditive, following the second definition of interaction.

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