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I am examining the moderating effect of IV1 in the relationship between IV2 and DV using hierarchical regression analysis. The study has 2 demographic variables: gender and age. To determine if it is necessary to control these demographic variables, can I conduct MANOVA tests with IV1, IV2, and DV as dependent variables?

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Your choice of control variables should be informed by the underlying causal model between the variables (as suggested in the comments). To specify such a causal model and read off what you need to adjust for, you can use tools such as the dagitty website/package.

For an introduction to causal models and how they can help in building the right sets of control variables, have a look at this introduction to directed acyclic graphs.

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There are a bunch of reasons to include control variables, and not all of them have anything to do with causation. These include:

  1. Where theory predicts them to be important.
  2. Where they are part of your hypotheses
  3. Where, even if they are not significant, they change the parameter estimates for your other independent variables.
  4. (Related to 1 and 2) Where a small effect would in interesting.
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