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Participants rated different behaviors on how risky they think the behavior is, and then rated how likely they are to engage in the behavior. I want to know if their ratings of the behavior's riskiness predicts their willingness to engage in it. I calculated within-person correlations between their willingness ratings and risk ratings for each of the behaviors, and now have a total within-person correlation between willingness ratings and risk ratings for each participant. I will apply Fisher's R to Z transformation on these correlations.

My issue is that I want to see if the strength/ direction of these correlations are moderated by a personality trait (introversion/ extroversion), which is a continuous variable, and I am not sure how to do this without make the personality score dichotomous (into introverts and extroverts), which I would rather not do, because I don't know of any reasonable cut-off points between introverts and extroverts.

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  • $\begingroup$ Can you describe how willingness and riskiness are quantified (continuous or ordinal scale)? $\endgroup$
    – mkt
    Commented Jan 24, 2019 at 8:06
  • $\begingroup$ They are both continuous. For willingness they were asked, "How likely are you to engage in this behaviour?" and the rating was on a scale of 1 (completely unlikely) to 5 (completely likely). Risk was on a scale from 1 (not risky) to 5 (risky). $\endgroup$
    – mtass
    Commented Jan 25, 2019 at 11:43
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    $\begingroup$ These 2 types of judgments seem part and parcel of one another. I doubt they have good discriminant validity. It's dubious to treat them as distinct things such that one can meaningfully be said to cause the other. "We don't run away because we are afraid; we are afraid because we run away" (Skinner). I suggest running your plans by multiple people, analytical and lay. And I'd try to analyze this in multiple ways and not to rely too much on any one analysis. $\endgroup$
    – rolando2
    Commented Jan 25, 2019 at 22:08
  • $\begingroup$ An alternative, visual method is to use conditioning plots, see for example stats.stackexchange.com/questions/203494/… $\endgroup$
    – kjetil b halvorsen ♦
    Commented Nov 2, 2019 at 15:53

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A note of caution: it's not my area of expertise, but your scales seem ordinal to me.

But if it is reasonable to treat them as continuous, you can address your underlying question using a linear mixed-effects model. Your specific hypothesis would be evaluated by examining the interaction between introversion_score and riskiness.

In R, using the lme4 package, you would code the model this way:

lmer(willigness ~ riskiness * introversion_score + (1|individual))

Note that this includes just a random intercept for each individual; you might want to consider whether a random slope would be needed as well.

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