# Correlation for a sample with constant dependent variable

Generally, I am trying to calculate correlation coefficients (best case even Pearson r) of several independent variables on one single dependent variable. I am looking at several studies, where some use Likert scales for the measurement of the independent variables, others use agreement statements.

Several motivational factors are the independent variables; [the likelihood of] participation is the dependent. The problem is, that for some studies, the data was collected on a basis of people who were participating anyway. i.e. the binary dependent variable is 1(=did participate) for all subjects. Those are all individual observations (i.e. a cross section of individuals) by the way.

Going the normal way, the correlation equals zero, as no matter what they answered to the questions (e.g. "I participate because I want to earn money"), the subjects all participated anyway.

I was thinking that maybe I can assume, that for the certain study, all 4 independent variables are responsible for x% of the total variance of the dependent variable. From there, I could maybe allocate fractions of x to the respective independent variables by considering the agreement level of the regarded independent variable as a fraction of the total agreement.

A short example might clarify what I am looking at:

651 participants were asked why they participated in a crowd-sourcing application. They could either agree with a statement("I participated because I...") or not agree. The results (% of participants agreeing) are the following:

• 71,9% Fun
• 79,1% Improving skills
• 89,8% Payment
• 49,8% Recognition

If I would assume that those 4 variables explain x% of the variance for the dependent variable, (estimation based on other studies concerned with the same correlations, that explicitly state that R^2) is there any way I could calculate correlation coefficients?

I would really appreciate if somebody would take the time to help me or point me towards the right direction!

• If your data stems from studies where everybody participated in activity xyz (i.e. dependent variable =1), this data can not tell you anything about how the independent variables affect participation. They can however tell you something about how the indep. variables correlate with each other (within the set of people that participated). – sheß Sep 1 '15 at 11:59
• What exactly is the research question your after? Is it; "How does each of the considered factors contribute to the probability of participation?" – sheß Sep 1 '15 at 12:00
• @ sheß Thanks for your reply! The research question is basicly the one you stated. I want to know which factor influences the likelyhood of participation the most. I am looking at many studies though and I want to transform the data into a comparable and aggregatable format. – user87346 Sep 1 '15 at 12:12
• Your problem is quite interesting I think. Obviously what you can infer about how your independent variables affect participation has to be based on data where you have variation in the independent variable. Yet the partition of the data without that variation should be somehow able to contribute to improving precision of your estimation. The simplest case would certainly be to just pool all the available data. But since this is a meta-study combining different sources, you'd certainly want to include study fixed-effects, which would not work then. – sheß Sep 1 '15 at 12:49