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Interactions Up to this point, when we’ve discussed the causal effect of one variable upon another we’ve assumed that the effect is additive and independent of other variables. There may be situations, however, where the influence of one variable upon another is contingent upon a third variable. For example, whether watching violent television leads to aggressive behavior might be dependent upon whether someone has been provoked or not.

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Interactions In such situations, we say that the two variables interact to influence the outcome variable. main effects vs. interactions The combination of main effects and interactions with just two variables can lead to a wide array of predictions.

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violent television viewing aggressive behavior provocation violent tv provocation In these situations, we say that the two variables interact to influence the dependent variable

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Aggressive TV viewing (X1) Provocations (X2) +1 555 +1555 55 This represents a situation in which the experimental manipulations have no effects on the dependent variable.

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Aggressive TV viewing (X1) Provocations (X2) +1 285 +1285 28

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Aggressive TV viewing (X1) Provocations (X2) +1 222 +1888 55

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Aggressive TV viewing (X1) Provocations (X2) +1 52 +15118 28

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Aggressive TV viewing (X1) Provocations (X2) +1 825 +1285 55

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Aggressive TV viewing (X1) Provocations (X2) +1 555 +1195 37

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Aggressive TV viewing (X1) Provocations (X2) +1 513 +1597 55

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Aggressive TV viewing (X1) Provocations (X2) +1 333 +13117 37

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violent television viewing aggressive behavior provocation violent tv provocation Interaction terms can be easily incorporated into the standard regression model that we’ve already developed The interaction is represented as a product term Doing so allows us to formally represent the notion that X 1, for example, is a function of X 2.

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If we go back through the previous slides, we can see that the means for each group are provided by this equation. coded –1 and + 1 (-1, -1) | 5 - 2 + 0 + 2 = 5 (-1, +1) | 5 - 2 + 0 - 2 = 1 (+1, -1) | 5 + 2 + 0 - 2 = 5 (+1, +1) | 5 + 2 + 0 + 2 = 9

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Interactions Interactions with continuous variables

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