How to sum up the results of multiple variables using the same experiment for correlation analysis?

#1
Hello everyone,

I need some help with the analysis part of my bachelor thesis.
To sum it up, I used the Ellsberg-Experiment (two urns, a certain amount of balls in both of them, one has the color distribution 50/50, the distribution of the other is unknown). I then asked people to fill out a Big 5 personality inventory. What I'm trying to determine is whether Big Five personality traits have an influence on whether people choose the urn with the unknown distribution of colors more frequently.

The context behind is Ellsbergs Experiment from 1961 where it was speculated that people have a natural tendency to avoid ambiguity aka the urn with the unknown color distribution.

Now, I made four experiments inspired by this, each one with different amounts of balls in them to make sure the amount of balls wouldn't influence the answers (as in - trying to avoid that people would prefer for example the urn with known color distribution in more simple designs where the amount would only be 10 balls, while maybe avoiding it when the amount of balls would be 1000 and imagining the outcome possibilities would be a more complex process). So each of these four experiments are essentially the same with different amounts of balls. They either choose one urn or the other. And they are all presented in one survey, so I don't have multiple subject groups, just one.
Now, my professor advised me to merge all of these four results into one variable for my Pearsons R analysis. I was very unsure of how to do this, but I read somewhere that in this case it would make sense to multiply all four of these with each other, like you do with an interaction variable. So I did exactly that. Before that I coded the results of each experiment into four dummy variables (0 for urn 1, 1 for urn 2), one variable for each experiment respectively.

I have to mention I'm really not good at statistics and was pretty insecure about this. So naturally, I asked my prof again - was this the right way? I explained in detail what I did and he basically signed off on it and said it surely would work out that way.
Now I've given him my first draft of the thesis in which I also explained that I multiplied these four variables in the Method section.
His feedback regarding this was that I would have to explain more clearly how I summed up the results of those four experiments, because you'd need at least two variables to compute an interaction variable and that these urns are not able to interact with each other.

And now, I'm just really confused. Was multiplying them even the right way? He's very much the type to say 'I'm sure you'll figure this out' when asked specific questions, so I have a feeling pressing him further about this won't result to anything, if he would even reply to my messages.

I hope I was able to explain this well enough, as this isn't my first language and I sincerely hope someone can help me, because I have searched in various places and just can't seem to find a definitive answer.
 
#2
How to sum up the results of multiple variables using the same experiment for correlation analysis?

The maximum degree of linear association that may be produced between two or more independent variables and a single dependent variable is determined by the multiple correlation coefficient (R). (R is never written with a Plus or a minus sign.) The proportion of the total variance in the dependent variable that can be explained by the independent variables is known as R2.) Each of the independent variables is properly weighted to ensure that their composite has the greatest potential correlation with the dependent variable. Because, like any statistic, the derivation of these weights (beta coefficients) is always influenced by sampling error (the R is always inflated), the multiple R is properly “shrunken” to account for the bias caused by sampling error.