Effect size+power calculations for spotlight analyses

EDIT: I mistakenly typed "spotlight" when I really meant "floodlight". Corrected for that.

I have a question about calculating effects sizes and power when dealing with a floodlight analysis. As an example, let's say we are dealing with the following variables:

1. Continuous variable--measured expertise (1-7 scale)
2. Categorical variable--presence vs. absence of info
3. Their interaction
4. DV=likelihood of purchase (1-7 scale)

Using a floodlight analysis, we are finding that at 1.15 SD below the mean of expertise there is a positive effect of information such that purchase intentions are higher when info is present vs. absent (beta =1.34, se = 1.2--just example numbers). Additionally, this is the only window of significance (i.e., no effect for those high in expertise).

In my paper, I have studies where both IVs are manipulated, and studies like this example where one of the variables is measured. For the manipulated studies, it is easy to calculate effect sizes and do power analyses (i.e., cohen's d, etc.), and reviewers have a number that they can grasp (e.g., cohen's d=.5...that's a medium sized effect). However, the reviewers are also asking for a cohen's d for the floodlight analysis as well--even though it is not possible given that there are no "means".

So, any thoughts as to how to satisfy the reviewers in this situation? I know that the R^2 gives us the effect size for the whole model, but it doesn't speak to the size of the effect we are seeing for those low in expertise. Is there a number I can give them so that they can easily categorize the size of the effect? I know that the regression coefficient is an indicator of effect size, but they don't seem satisfied with that. Even standardized coefficients wouldn't help in this regard because there is no "rule of thumb" in terms of effect sizes and standardized coefficients. Also, in this situation (i.e., floodlight analysis with one categorical and one continuous IV), how would you do power calculations?

Thanks in advance!

Last edited by carlsonturner; 06-28-2016 at 11:00 AM.

Re: Effect size+power calculations for spotlight analyses

Hello there!

Though I am not really familiar with "floodlight" analysis (but will surely look into that in the future), I'd say that the best way to explore the magnitude of the interactions' effects would be to plot them. In other words, you can plot a regression line of x on y for the given values of z (your binary moderator).

Re: Effect size+power calculations for spotlight analyses

Also, a cursory examination suggests that spotlights and floodlights are similar in spirit to Stata's -margins- command. That being said, if you are familiar with Stata, you can simulate you analysis using -margins- and then plot them using -marginsplot-