Noooooooooooooo…………………….

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From the Polmeth mailing list:

Someone writes:

If I find that an interaction term is statistically significant (t-test) but the single terms are not, do I need to conduct an F-test for joint significance of the interaction term and the two single terms? When is this necessary? I’ve seen it done in papers but it seems redundant to me insofar as the interaction itself is getting at the joint “effect” of these variables, why the need for an F test?

My quick answer, in all seriousness: You never have to do an F test. Just forget about that stuff!

11 thoughts on “Noooooooooooooo…………………….”

  1. So then just leave the model as-is? With all three independent variables in it (the two single terms, and the interaction term)?

  2. Gabe: It depends what you want to do with the model. All I can say for sure is that an F test has nothing to do with it. Also, I prefer the term "predictors" rather than "independent variables," a phrase which is particularly nonsensical when used to refer to main effects and interactions at the same time. (An interaction can't, except in degenerate circumstances, be statistically independent of the variables that were multiplied to create it.)

    P.S. Please don't take "nonsensical" as a personal criticism. I know that the term "independent variable" has been used in this way by lots of respected researchers. I just don't think it makes sense.

  3. Fair enough. When I was in Hogan's and Paninski's classes, they basically used the two terms interchangeably.

    But yes, I agree with you regarding the notion of independence and the interaction.

  4. about the correlation between interaction and main effect:
    I kind of remember in balanced studies with 2 factors,the contrast to estimate the interaction effect is 'orthogonal' to the contrasts to estimate the main effects; and I think this orthogonality can be related (translated) to zero linear correlation.

  5. For some multiplicative modeling is difficult for social scientists to grasp. I wonder why this is? Also, I was wondering if you could comment briefly on the best way to calculate the standard error of an interaction term. I have seen a few different approaches.

  7. I'm basically opposed to the notion of "preliminary" hypothesis tests, as, in this case, the test of the interaction. Suppose it is not significant? Shouldn't we think about its power before we draw any conclusions?

    If you can think logically and meaningfully about the power of interaction tests, what the alternatives hypotheses are, etc., without getting a severe migraine, then you are a better man than I am, Charlie Brown.

  9. Are you talking to me, Matt? I guess I disagree with Shapiro. If the action you want to take depends on whether there is interaction, then doesn't it make sense, if the interaction test is not significant, to be able to judge whether interaction might have gone undetected because of low power of detecting it? If the preliminary test of interaction is that important, maybe we should design for it, that is, choose a sample size that gives us confidence we can detect the interaction if it exists.

    But what is the "effect size" of interaction? How do you define it? etc.

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